Category Archives: Quantum Physics
Quantum simulator sheds light on quantum theory of gravity – Interesting Engineering
Quantum mechanics and the theory of relativity are pillars of modern physics. Quantum mechanics explains all the phenomena and behavior of particles at the smallest of scales, whereas relativity is on the other end of the spectrum and explains cosmic structures at the largest of scales.
However, combining the two theories for aquantum theory of gravityhas eluded physicists for decades.
Now, a group of scientists from TU Wien in Vienna have used a quantum simulator to study the effects of curved spacetime. The simulator allows scientists to create a model system resembling quantum particles in curved spacetime, combining aspects of both theories.
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Quantum simulator sheds light on quantum theory of gravity - Interesting Engineering
EDITORIAL ANALYSIS : The promise in India’s National Quantum Mission – INSIGHTSIAS – Insights IAS
Source: Indian Express, Indian Express
Prelims: Current events of national importance, quantum, National Quantum Mission, quantum computing, Nano Mission, National Supercomputing Mission etc
Mains GS Paper II and III: Development process and the development industry-the role of NGOs,SHGs etc
ARTICLE HIGHLIGHTS
INSIGHTS ON THE ISSUE
Context
Quantum technology:
National Quantum Mission (NQM):
Advantages:
Quantum materials:
Quantum devices:
Need for a Quantum Mission:
How to achieve the targets?
Challenges:
Way Forward
QUESTION FOR PRACTICE
How is the S-400 air defense system technically superior to any other system presently available in the world ?(UPSC 2021) (200 WORDS, 10 MARKS)
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EDITORIAL ANALYSIS : The promise in India's National Quantum Mission - INSIGHTSIAS - Insights IAS
Heisenberg’s Uncertainty Principle: Everything You Need to Know – Popular Mechanics
Stop me if youve heard this one.
Werner Heisenberg is driving down the road when he gets pulled over by a traffic cop.
Excuse me, sir, the cop says. Do you know how fast you were going?No, Heisenberg replies. But, I know exactly where I am.
Whether youre laughing right nowor staring at your screen in confusionhinges on how much you know about one of the foundational ideas in quantum physics: Heisenbergs uncertainty principle.
In its most basic and commonly known form, the uncertainty principle says that the more precisely you know the position of a particle in a quantum system, the less well you know its momentum (and vice-versa). The principle also applies to other pairs of characteristics in quantum systems, like energy and time. But every physics graduate first starts to unpack this concept through the lens of position and momentum, so we will, too.
If this was all Heisenbergs uncertainty principle said, it probably wouldnt have been profound enough to weave its way into pop culture in the form of mugs, T-shirts, and cartoonslet alone place its pioneer as an alias for an infamous meth-cooking chemistry teacher.
German theoretical physicist Werner Heisenberg first introduced his uncertainty principle in a 1925 paper. Its special because it remains intact no matter how good our experimental methods get; this isnt a lack of precision in measurement. It doesnt matter how smart you are, or how sophisticated your equipment, is you cant think your way past it. Its a fact of nature.
Legendary physicist and master bongo player Richard Feynman put it like this: The uncertainty principle protects quantum mechanics. Heisenberg recognized that if it were possible to measure both the momentum and the position simultaneously with greater accuracy, quantum mechanics would collapse. So he proposed that must be impossible.
Reality is telling us that we can have our quantum cake, but we cant eat it, too.
Getty Images
Chad Orzel is an associate professor in the Department of Physics and Astronomy at Union College in Schenectady, New York, who is also the author of several books that explain often complicated and esoteric ideas to a layman audience. In his book, How to Teach Quantum Physics to Your Dog, he covers Heisenbergs uncertainty principle.
The origin of the uncertainty principle is found in the duality of particles in quantum physics; depending on what theyre doing, they can be described as either a particle or a wave, Orzel tells Popular Mechanics.
At the turn of the 20th century, physicists were engaged in a heated debate regarding the nature of light, and whether it exists as a particle or a wave. Thanks to a pioneering test known as Youngs Double-Slit experiment, physicists discovered the answer was Door No. 3 as Orzel puts it. That is, light isnt a particle or a waveit has properties of both. And, shockingly, particles of matter like electrons also demonstrate this particle-wave duality.
Werner Karl Heisenberg, a Nobel Laureate who later became a key figure in Hitlers atomic project.
So every particle in the universeor every kind of object that we know of in the universe has this combination of properties we associate with waves, and properties we associate with particles; theyre a third kind of object that isnt really one or the other, Orzel says. And its because of that you cant get rid of the Heisenberg uncertainty principle with a better experimental technique, because its really fundamental to that dual nature.
He continues by explaining the fact that you need to have both wave-like properties and particle-like properties, meaning you cant measure either of them perfectly.
Being able to have both requires that each be imperfect, in a way, and theres just no way around that, Orzel explains. We know from experiments that things that we think of as particles, like an electron, would have a well-defined position, but they also have a wavelength associated with them, and that wavelength is related to the momentum.
When the particle is moving, its doing wavy stuff that has a characteristic wavelength associated with itand that length, it turns out, is inversely proportional to the momentum. This means the faster the particle is going, the shorter the wavelength, and the slower the particle is going, the longer the wavelength.
You need to have both of these things if you want to have the position well defined and momentum well defined, Orzel says. It has to have both a position in space that you can point to and say it is right here. And it has to have a wavelength with some characteristic length associated with it. And those things are incompatible.
Think of the momentum of a traveling particle as a wave; the peaks of the wave represent the probability of the particles position. One infinitely long wavelength represents a very precise momentum. Problem is, with that single infinite wavelength, there is an infinity of peaks, thus the momentum is precisely known, but the position is completely unknown. The particle could be anywhere. That means in that situation, youve got an exact momentum, but no clue about location.
To get a read on the particle, what we could start doing is stacking different wavelengths, each representing different momentums for the particle. Where a peak meets a trough, you get destructive interference, and the wavelength is flattened. Where the peaks meet, you get an increased peak, and thus an increased probability of finding the particle.
Add enough wavelengths and birth enough constructive and destructive interference, and youve got a single peak and close to a definite position for the particle. In the process of creating this peak, youve also destroyed the wavelength, meaning you now know zilch about the momentumyouve sacrificed it for certainty about the position.
The best you can do is create a wave packet, which is flat, and then you have some waves that get bigger and bigger and they come to a peak and then they get smaller on the other side, sort of tapering off on either side, Orzel says. You can look at that region of space and say, here are the peaks, and Ive got so many here. We also have a wavelength giving the momentum, but the region in which thats happening is relatively confined and can be quite small.
That means momentum and a position can be given for a system using this wave packet, but crucially theres an uncertainty to both measurements. Were all clued in on the joke now, but theres still the question of what makes it ludicrous.
Getty Images
Obviously, a carwhether its driven by one of the founders of quantum mechanics or notisnt a quantum object. It doesnt travel like a wave, meaning your car cant diffract around corners, and thus it isnt governed by the rules of the subatomic or the uncertainty principle; nor are tennis balls, or comic books, or squirrels. The reason you cant find your keys every morning isnt that you know their momentum precisely and thus cant possibly know their positionso no more using that as an excuse for being late for work.
The big question is: why doesnt the Heisenberg uncertainty principle affect everyday or macroscopic objects?
The answer lies in the equation that describes the phenomena.
The generalized form of the Heisenberg uncertainty principle says that if you measure the momentum of a particle with uncertainty p, then this affects the uncertainty of the position x, which cant be any less than /2p.
The whole equation looks like this: x /2p. Its the (pronounced H-bar) element were interested in here.
This is known as the reduced Plancks constant, and the thing about it is . . . its small, very small, and it constrains the values of the uncertainties of our two properties and makes them small, too.
Institute of Physics
The uncertainties are so small for macroscopic objects that if you have an object thats one kilogram, moving at one meter per second, its wavelength would be 10-34 meters, [thats zero, a decimal point followed by another 33 zeroes], which is a distance thats so small, it doesnt really make sense to talk about, Orzel explains. Then the uncertainty in the position is going to be some smallish multiple of that, which is just so tiny its ridiculous. So, you cant see the uncertainty principle with ordinary macroscopic objects.
You can see that uncertainty with subatomic objects like electrons, however, when the wave properties become apparent; thats because their wavelengths are long enough. As Orzel points out, thats also when you can measure that uncertainty.
Exactly where the line between quantum and non-quantum behaviors lies is currently a hot research topic in physics, with scientists discovering quantum effects in particles as large (and even larger) than Carbon-60 atoms, also known as Buckyballs, because of their resemblance to the hexagonal egg carton-like architecture of Buckminster Fuller.
As for why the uncertainty principle is so captivating, Orzel explains:
Its telling us something fascinating about the universe, which is that at a very deep fundamental level, the nature of reality is such that there will always be some uncertainty and that it is impossible, even in principle, to know certain things about the world or certain combinations of things about the world.
Oh, and it makes for great jokes, too.
Robert Lea is a freelance science journalist focusing on space, astronomy, and physics. Robs articles have been published in Newsweek, Space, Live Science, Astronomy magazine and New Scientist. He lives in the North West of England with too many cats and comic books.
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Heisenberg's Uncertainty Principle: Everything You Need to Know - Popular Mechanics
Quantum Physics Could Explain Nearly All the Mysteries of How Life Works – Inverse
Imagine using your cell phone to control the activity of your own cells to treat injuries and diseases. It sounds like something from the imagination of an overly optimistic science fiction writer. But this may one day be a possibility through the emerging field of quantum biology.
Over the past few decades, scientists have made incredible progress in understanding and manipulating biological systems at increasingly small scales, from protein folding to genetic engineering. And yet, the extent to which quantum effects influence living systems remains barely understood.
Quantum effects are phenomena that occur between atoms and molecules that cant be explained by classical physics. It has been known for more than a century that the rules of classical mechanics, like Newtons laws of motion, break down at atomic scales. Instead, tiny objects behave according to a different set of laws known as quantum mechanics.
For humans, who can only perceive the macroscopic world, or whats visible to the naked eye, quantum mechanics can seem counterintuitive and somewhat magical. Things you might not expect happen in the quantum world, like electrons tunneling through tiny energy barriers and appearing on the other side unscathed or being in two different places at the same time in a phenomenon called superposition.
I am trained as a quantum engineer. Research in quantum mechanics is usually geared toward technology. However, and somewhat surprisingly, there is increasing evidence that nature an engineer with billions of years of practice has learned how to use quantum mechanics to function optimally. If this is indeed true, it means that our understanding of biology is radically incomplete. It also means that we could possibly control physiological processes by using the quantum properties of biological matter.
Researchers can manipulate quantum phenomena to build better technology. In fact, you already live in a quantum-powered world: from laser pointers to GPS, magnetic resonance imaging, and the transistors in your computer all these technologies rely on quantum effects.
In general, quantum effects only manifest at very small length and mass scales or when temperatures approach absolute zero. This is because quantum objects like atoms and molecules lose their quantumness when they uncontrollably interact with each other and their environment. In other words, a macroscopic collection of quantum objects is better described by the laws of classical mechanics. Everything that starts quantum dies classical. For example, an electron can be manipulated to be in two places at the same time, but it will end up in only one place after a short while exactly what would be expected classically.
In a complicated, noisy biological system, it is thus expected that most quantum effects will rapidly disappear, washed out in what the physicist Erwin Schrdinger called the warm, wet environment of the cell. To most physicists, the fact that the living world operates at elevated temperatures and in complex environments implies that biology can be adequately and fully described by classical physics: no funky barrier crossing, no being in multiple locations simultaneously.
Chemists, however, have for a long time begged to differ. Research on basic chemical reactions at room temperature unambiguously shows that processes occurring within biomolecules like proteins and genetic material are the result of quantum effects. Importantly, such nanoscopic, short-lived quantum effects are consistent with driving some macroscopic physiological processes that biologists have measured in living cells and organisms. Research suggests that quantum effects influence biological functions, including regulating enzyme activity, sensing magnetic fields, cell metabolism, and electron transport in biomolecules.
The tantalizing possibility that subtle quantum effects can tweak biological processes presents both an exciting frontier and a challenge to scientists. Studying quantum mechanical effects in biology requires tools that can measure the short time scales, small length scales, and subtle differences in quantum states that give rise to physiological changes all integrated within a traditional wet lab environment.
In my work, I build instruments to study and control the quantum properties of small things like electrons. In the same way that electrons have mass and charge, they also have a quantum property called spin. Spin defines how the electrons interact with a magnetic field in the same way that charge defines how electrons interact with an electric field. The quantum experiments I have been building since graduate school and now in my own lab aim to apply tailored magnetic fields to change the spins of particular electrons.
Research has demonstrated that many physiological processes are influenced by weak magnetic fields. These processes include stem cell development and maturation, cell proliferation rates, genetic material repair, and countless others. These physiological responses to magnetic fields are consistent with chemical reactions that depend on the spin of particular electrons within molecules. Applying a weak magnetic field to change electron spins can thus effectively control a chemical reactions final products, with important physiological consequences.
Currently, a lack of understanding of how such processes work at the nanoscale level prevents researchers from determining exactly what strength and frequency of magnetic fields cause specific chemical reactions in cells. Current cellphone, wearable, and miniaturization technologies are already sufficient to produce tailored, weak magnetic fields that change physiology, both for good and for bad. The missing piece of the puzzle is; hence, a deterministic codebook of how to map quantum causes to physiological outcomes.
In the future, fine-tuning natures quantum properties could enable researchers to develop therapeutic devices that are noninvasive, remotely controlled, and accessible with a mobile phone. Electromagnetic treatments could potentially be used to prevent and treat diseases, such as brain tumors, as well as in biomanufacturing, such as increasing lab-grown meat production.
Quantum biology is one of the most interdisciplinary fields to ever emerge. How do you build community and train scientists to work in this area?
Since the pandemic, my lab at the University of California, Los Angeles, and the University of Surreys Quantum Biology Doctoral Training Centre have organized Big Quantum Biology meetings to provide an informal weekly forum for researchers to meet and share their expertise in fields like mainstream quantum physics, biophysics, medicine, chemistry and biology.
Research with potentially transformative implications for biology, medicine, and the physical sciences will require working within an equally transformative model of collaboration. Working in one unified lab would allow scientists from disciplines that take very different approaches to research to conduct experiments that meet the breadth of quantum biology from the quantum to the molecular, the cellular, and the organismal.
The existence of quantum biology as a discipline implies that the traditional understanding of life processes is incomplete. Further research will lead to new insights into the age-old question of what life is, how it can be controlled, and how to learn with nature to build better quantum technologies.
This article was originally published on The Conversation by Clarice D. Aiello Nab at University of California, Los Angeles. Read the original article here.
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Quantum Physics Could Explain Nearly All the Mysteries of How Life Works - Inverse
Large predators push coyotes and bobcats near people and to their demise – Science News Magazine
When wild animals take refuge from predators by straying near people, the illusion of safety can be deadly.
In the wilderness, mid-sized predators like coyotes have learned to fear larger carnivores like wolves and cougars, which will violently attack and kill those smaller carnivores. A new study finds that when those larger predators are around, the smaller ones will try to evade attack by moving into spaces shaped by people. But that ends up putting them at a much higher risk of getting killed by people, scientists report in the May 19 Science.
The study is among the first to show that large cats and wolves shape the behavior of other predators outside of wilderness areas, says Laura Prugh, a wildlife ecologist at the University of Washington in Seattle.
When large carnivore populations plummeted from being hunted in vast stretches of North America, predators less threatening to humans flourished. Then, as large predators were reintroduced into the wild including wolves in Yellowstone National Park scientists started to notice deadly (and mostly-one sided) violence erupting between old and new meat-eating residents (SN: 7/21/20).
What the aftermath of this violence looks like is something that Prugh has witnessed firsthand. During a field season in Alaska, the wildlife ecologist came across the remains of coyotes massacred by wolves.
The wolves had buried [the coyotes] heads in the snow, recalls Prugh. It was a little macabre.
Understandably, smaller predators will try to stay clear of their murderous kin. Yet how this works outside of wilderness areas is unclear. Some animals will hide from danger in spaces shaped by people be it farms or suburbs in a phenomenon called the human shield effect. But other research indicates that mid-sized predators keep away from people when given the chance.
Animals are really, really scared of humans, explains Taal Levi, a wildlife ecologist at Oregon State University in Corvallis, who was not involved in the study. In experiments where scientists played recordings of either growling or human voices, smaller meat-eaters like coyotes were more likely to avoid areas where you play recordings of Rush Limbaugh or people talking in general, he says.
To see how smaller predators behave near human territory, Prugh and her colleagues attached radio collars to 37 bobcats and 35 coyotes, as well as to 22 wolves and 60 cougars, in two rural areas of Washington State. These collars tracked the location of the animals every four hours for up to two years one of the most impressive datasets on predator movement outside of a wilderness area to date, Levi says.
Tracking these animals revealed that coyotes and bobcats, the mid-sized predators, were twice as likely to spend time near ranches, roads, fields and towns when large carnivores were around. But the animals traded one threat for another: People shot, trapped or otherwise killed 25 bobcats and coyotes during the study period. Wolves and cougars killed just eight, meaning people killed three times as many coyotes and bobcats than the large predators.
This may be because animals arent good at reading danger signs from people in a modern world, Prugh says. A coyote is unlikely to make the connection that a person is behind a gun. But the smell and sound of wolves which evolved alongside coyotes for millennia are hard to forget if youve been attacked.
The study shows that large carnivores shape the behavior of smaller predators even outside wilderness areas, something not all scientist agreed would be the case, Levi says.
As wolves recover outside of national parks, there was this major question about whether they could recover enough to actually fulfill their ecological role of controlling the numbers of smaller carnivores, he says. This study shows that large carnivores can and will shape how smaller meat-eaters live and die near people.
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Large predators push coyotes and bobcats near people and to their demise - Science News Magazine
Can you spot the quantum physics around your house? – The Hindu
Sir, what is this Fermi energy? I cant find a reasonable explanation. Which electrons have this energy and why?
A visibly annoyed Hardik, one of my students, asked this as I started my class the other day. Hardik is one of a few undergraduate students taking a physics department elective course in IIT Kanpur, where I teach.
That copper, a garden-variety material that runs through the network of wires in our homes and lines the bottom of a few cooking utensils, has electrons at effectively at least 50,000 C was as surprising as it was worrisome for the students. And my insistent logic to prove this by assertion was not helping.
Forty-five degree celsius is already hot enough for the humans of Kanpur to curse at passersby. To imagine we are carrying 50,000-degree electrons in our pockets should be difficult to contemplate. Water boils at 100 C; aluminium melts at 600 C, and 5,000 C is around the surface temperature of the sun. How then can we make sense of 50,000 C, that too inside everyday objects?
I could see why my students were upset.
Quantum physics is often understood to be the physics of things that can both be located and absent at a place, things that tunnel through walls, and things that can act across very large distances in an instant. But this is also a romantic conception that takes for granted, and thus overlooks, quantum physicss role in shaping the fascinating properties of the objects in our daily lives. Indeed, it offers a host of counterintuitive principles to grapple with, but it also makes some of the most quantitatively accurate predictions that we can actually test.
Take the Fermi energy of electrons in copper, for example. Quantum physics tells us that electrons are not particles like the little marbles that we play with. Instead, they are treated as waves, like the ones you see on a surface of water or that you create when you pluck a guitar string.
A wave is typically drawn like a curvy line (shaped like an S but rotated 90). Like all waves, an electron has a wavelength the distance after which the wavy pattern repeats. The shorter an electrons wavelength, the more energy it holds. So a wave that changes smoothly has less energy than a wave that is more corrugated.
Consider this loose, and probably rather bad, analogy: you are driving a car over a series of speed bumps. If the bumps are smooth and vary slowly, you will have a lower energy. But if the bumps are sharp and modulate fast, you and your car will also oscillate faster and have more energy.
Ripples on water. | Photo Credit: Jackson Hendry/Unsplash
One of the fundamental principles of this universe is that nature is lazy. More appropriately, everything tries to minimise the amount of energy it contains. A bunch of electrons in a metal would like to do the same thing as well, to lower their energy by being waves of larger and larger wavelengths. The largest wavelength they can take is however fixed just about the size of the metal piece.
Now, it so happens that electrons are fermions, types of particles that are bound by Paulis exclusion principle. The principle states that not all electrons in a system can have the same wavelength.
So now the electrons have a problem.
While they want to lower their energy, they cant all have the same longest possible wavelength. They need to have different wavelengths. As we increase the number of electrons in a material, every new electron we add has to have a shorter wavelength, and thus more energy. So the more electrons there are, the more energy every additional electron will have.
How many electrons does a simple block of metal, like a cupboard key, contain? In a metal such as copper, the copper atoms are about 10 -10 m apart thats ten-billionth of a metre, or one angstrom. The total human population is about 8 billion. Even if each copper atom has one electron, a cube of copper that is 1 cm to a side will have about a million billion billion electrons!
This in turn is a humongous number of electrons, which are all also behaving like waves that need to choose different wavelengths. And it turns out that the shortest wavelength they can reach is about one angstrom, about the distance between the copper atoms.
In this picture, we can estimate the energy of these highest-energy electrons: a couple of electron-volts (eV). eV is a unit of energy, just like temperature. If an object is at 27 C, we can also say that its temperature is about one-hundredth of an eV.
When electrons have such small wavelengths that they have high energies a few eV it translates to an effective temperature of tens of thousands of degrees celsius. This highest energy that the electrons are at is called the Fermi energy.
Representative illustration. | Photo Credit: Jr Korpa/Unsplash
All metals around us have exorbitant Fermi energies. Copper has a Fermi energy of 80,000 C; aluminium, 130,000 C; and silver the beautiful chaandi used in auspicious objects and jewellery about 60,000 C. Note that this is an effective temperature, not the actual temperature. A metal is of course not this hot inside.
In fact, even if you take a block of metal to -273 C the lowest temperature possible in the universe the Fermi energy of its electrons will remain high.
The Fermi energy and the fermionic behaviour of electrons (i.e. due to the exclusion principle) follows from a basic quantum mechanical principle and is at the heart of all the properties of metals we see around us and take for granted. Its crucial to understand why metals reflect light (so we can see ourselves in a mirror), why they conduct electricity (so we have lights and fans), why they heat up easily (so they are good cooking utensils), and so on.
The next time you wonder whether youve encountered quantum physics, just like Hardik who was worried about the dizzying electrons, pick up a piece of metal around you a key, a spoon, or a pen with a metal tip and youll be holding a beautiful quantum material in your hand.
Adhip Agarwala is an assistant professor of physics at IIT Kanpur.
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Can you spot the quantum physics around your house? - The Hindu
Quantum physics proposes a new way to study biology and the results could revolutionize our understanding of how life works – KRQE News 13
(THE CONVERSATION) Imagine using your cellphone to control the activity of your own cells to treat injuries and disease. It sounds like something from the imagination of an overly optimistic science fiction writer. But this may one day be a possibility through the emerging field of quantum biology.
Over the past few decades, scientists have made incredible progress in understanding and manipulating biological systems at increasingly small scales, fromprotein foldingtogenetic engineering. And yet, the extent to which quantum effects influence living systems remains barely understood.
Quantum effects are phenomena that occur between atoms and molecules that cant be explained by classical physics. It has been known for more than a century that the rules of classical mechanics, like Newtons laws of motion,break down at atomic scales. Instead, tiny objects behave according to a different set of laws known asquantum mechanics.
For humans, who can only perceive the macroscopic world, or whats visible to the naked eye, quantum mechanics can seem counterintuitive and somewhat magical. Things you might not expect happen in the quantum world, likeelectrons tunneling throughtiny energy barriers and appearing on the other side unscathed, or being in two different places at the same time in aphenomenon called superposition.
I am trained as aquantum engineer. Research in quantum mechanics is usually geared toward technology. However, and somewhat surprisingly, there is increasing evidence that nature an engineer with billions of years of practice has learned how touse quantum mechanics to function optimally. If this is indeed true, it means that our understanding of biology is radically incomplete. It also means that we could possibly control physiological processes by using the quantum properties of biological matter.
Quantumness in biology is probably real
Researchers can manipulate quantum phenomena to build better technology. In fact, you already live in aquantum-powered world: from laser pointers to GPS, magnetic resonance imaging and the transistors in your computer all these technologies rely on quantum effects.
In general, quantum effects only manifest at very small length and mass scales, or when temperatures approach absolute zero. This is because quantum objects like atoms and moleculeslose their quantumnesswhen they uncontrollably interact with each other and their environment. In other words, a macroscopic collection of quantum objects is better described by the laws of classical mechanics. Everything that starts quantum dies classical. For example, an electron can be manipulated to be in two places at the same time, but it will end up in only one place after a short while exactly what would be expected classically.
In a complicated, noisy biological system, it is thus expected that most quantum effects will rapidly disappear, washed out in what the physicist Erwin Schrdinger called the warm, wet environment of the cell. To most physicists, the fact that the living world operates at elevated temperatures and in complex environments implies that biology can be adequately and fully described by classical physics: no funky barrier crossing, no being in multiple locations simultaneously.
Chemists, however, have for a long time begged to differ. Research on basic chemical reactions at room temperature unambiguously shows thatprocesses occurring within biomoleculeslike proteins and genetic material are the result of quantum effects. Importantly, such nanoscopic, short-lived quantum effects are consistent with driving some macroscopic physiological processes that biologists have measured in living cells and organisms. Research suggests that quantum effects influence biological functions, includingregulating enzyme activity,sensing magnetic fields,cell metabolismandelectron transport in biomolecules.
How to study quantum biology
The tantalizing possibility that subtle quantum effects can tweak biological processes presents both an exciting frontier and a challenge to scientists. Studying quantum mechanical effects in biology requires tools that can measure the short time scales, small length scales and subtle differences in quantum states that give rise to physiological changes all integrated within a traditional wet lab environment.
In my work, I build instruments to study and control the quantum properties of small things like electrons. In the same way that electrons have mass and charge, they also have aquantum property called spin. Spin defines how the electrons interact with a magnetic field, in the same way that charge defines how electrons interact with an electric field. The quantum experiments I have been buildingsince graduate school, and now in my own lab, aim to apply tailored magnetic fields to change the spins of particular electrons.
Research has demonstrated that many physiological processes are influenced by weak magnetic fields. These processes includestem cell developmentandmaturation,cell proliferation rates,genetic material repairandcountless others. These physiological responses to magnetic fields are consistent with chemical reactions that depend on the spin of particular electrons within molecules. Applying a weak magnetic field to change electron spins can thus effectively control a chemical reactions final products, with important physiological consequences.
Currently, a lack of understanding of how such processes work at the nanoscale level prevents researchers from determining exactly what strength and frequency of magnetic fields cause specific chemical reactions in cells. Current cellphone, wearable and miniaturization technologies are already sufficient to producetailored, weak magnetic fields that change physiology, both for good and for bad. The missing piece of the puzzle is, hence, a deterministic codebook of how to map quantum causes to physiological outcomes.
In the future, fine-tuning natures quantum properties could enable researchers to develop therapeutic devices that are noninvasive, remotely controlled and accessible with a mobile phone. Electromagnetic treatments could potentially be used to prevent and treat disease, such asbrain tumors, as well as in biomanufacturing, such asincreasing lab-grown meat production.
A whole new way of doing science
Quantum biology is one of the most interdisciplinary fields to ever emerge. How do you build community and train scientists to work in this area?
Since the pandemic, my lab at the University of California, Los Angeles and the University of Surreys Quantum Biology Doctoral Training Centre have organizedBig Quantum Biology meetingsto provide an informal weekly forum for researchers to meet and share their expertise in fields like mainstream quantum physics, biophysics, medicine, chemistry and biology.
Research with potentially transformative implications for biology, medicine and the physical sciences will require working within an equally transformative model of collaboration. Working in one unified lab would allow scientists from disciplines that take very different approaches to research to conduct experiments that meet the breadth of quantum biology from the quantum to the molecular, the cellular and the organismal.
The existence of quantum biology as a discipline implies that traditional understanding of life processes is incomplete. Further research will lead to new insights into the age-old question of what life is, how it can be controlled and how to learn with nature to build better quantum technologies.
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Physicists Make Matter out of Light to Find Quantum Singularities – Scientific American
Many seemingly mundane materials, such as the stainless steel on refrigerators or the quartz in a countertop, harbor fascinating physics inside them. These materials are crystals, which in physics means they are made of highly ordered repeating patterns of regularly spaced atoms called atomic lattices. How electrons move through a lattice, hopping from atom to atom, determines many of a solid's properties, such as its color, transparency, and ability to conduct heat and electricity. For example, metals are shiny because they contain lots of free electrons that can absorb light and then reemit most of it, making their surfaces gleam.
In certain crystals the behavior of electrons can create properties that are much more exotic. The way electrons move inside graphenea crystal made of carbon atoms arranged in a hexagonal latticeproduces an extreme version of a quantum effect called tunneling, whereby particles can plow through energy barriers that classical physics says should block them. Graphene also exhibits a phenomenon called the quantum Hall effect: the amount of electricity it conducts increases in specific steps whose size depends on two fundamental constants of the universe. These kinds of properties make graphene intrinsically interesting as well as potentially useful in applications ranging from better electronics and energy storage to improved biomedical devices.
I and other physicists would like to understand what's going on inside graphene on an atomic level, but it's difficult to observe action at this scale with current technology. Electrons move too fast for us to capture the details we want to see. We've found a clever way to get around this limitation, however, by making matter out of light. In place of the atomic lattice, we use light waves to create what we call an optical lattice. Our optical lattice has the exact same geometry as the atomic lattice. In a recent experiment, for instance, my team and I made an optical version of graphene with the same honeycomb lattice structure as the standard carbon one. In our system, we make cold atoms hop around a lattice of bright and dim light just as electrons hop around the carbon atoms in graphene.
With cold atoms in an optical lattice, we can magnify the system and slow down the hopping process enough to actually see the particles jumping around and make measurements of the process. Our system is not a perfect emulation of graphene, but for understanding the phenomena we're interested in, it's just as good. We can even study lattice physics in ways that are impossible in solid-state crystals. Our experiments revealed special properties of our synthetic material that are directly related to the bizarre physics manifesting in graphene.
The crystal phenomena we investigate result from the way quantum mechanics limits the motion of wavelike particles. After all, although electrons in a crystal have mass, they are both particles and waves (the same is true for our ultracold atoms). In a solid crystal these limits restrict a single electron on a single atom to only one value of energy for each possible movement pattern (called a quantum state). All other amounts of energy are forbidden. Different states have separate and distinctdiscreteenergy values. But a chunk of solid crystal the size of a grape typically contains more atoms (around 1023) than there are grains of sand on Earth. The interactions between these atoms and electrons cause the allowed discrete energy values to spread out and smear into allowed ranges of energy called bands. Visualizing a material's energy band structure can immediately reveal something about that material's properties.
For instance, a plot of the band structure of silicon crystal, a common material used to make rooftop solar cells, shows a forbidden energy rangealso known as a band gapthat is 1.1 electron volts wide. If electrons can jump from states with energies below this gap to states with energies above the gap, they can flow through the crystal. Fortunately for humanity, the band gap of this abundant material overlaps well with the wavelengths present in sunlight. As silicon crystal absorbs sunlight, electrons begin to flow through itallowing solar panels to convert light into usable electricity.
The band structure of certain crystals defines a class of materials known as topological. In mathematics, topology describes how shapes can be transformed without being fundamentally altered. Transformation in this context means to deform a shapeto bend or stretch itwithout creating or destroying any kind of hole. Topology thus distinguishes baseballs, sesame bagels and shirt buttons based purely on the number of holes in each object.
Topological materials have topological properties hidden in their band structure that similarly allow some kind of transformation while preserving something essential. These topological properties can lead to measurable effects. For instance, some topological materials allow electrons to flow only around their edges and not through their interior. No matter how you deform the material, the current will still flow only along its surface.
I have become particularly interested in certain kinds of topological material: those that are two-dimensional. It may sound odd that 2-D materials exist in our 3-D world. Even a single sheet of standard printer paper, roughly 0.004 inch thick, isn't truly 2-Dits thinnest dimension is still nearly one million atoms thick. Now imagine shaving off most of those atoms until only a single layer of them remains; this layer is a 2-D material. In a 2-D crystal, the atoms and electrons are confined to this plane because moving off it would mean exiting the material entirely.
Graphene is an example of a 2-D topological material. To me, the most intriguing thing about graphene is that its band structure contains special spots known as Dirac points. These are positions where two energy bands take on the same value, meaning that at these points electrons can easily jump from one energy band to another. One way to understand Dirac points is to study a plot of the energy of different bands versus an electron's momentum a property associated with the particle's kinetic energy. Such plots show how an electron's energy changes with its movement, giving us a direct probe into the physics we're interested in. In these plots, a Dirac point looks like a place where two energy bands touch; at this point they're equal, but away from this point the gap between the bands grows linearly. Graphene's Dirac points and the associated topology are connected to this material's ability to display a form of the quantum Hall effect that's unique even among 2-D materialsthe half-integer quantum Hall effectand the special kind of tunneling possible within it.
To understand what's happening to electrons at Dirac points, we need to observe them up close. Our optical lattice experiments are the perfect way to do this. They offer a highly controllable replica of the material that we can uniquely manipulate in a laboratory. As substitutes for the electrons, we use ultracold rubidium atoms chilled to temperatures roughly 10 million times colder than outer space. And to simulate the graphene lattice, we turn to light.
Light is both a particle and a wave, which means light waves can interfere with one another, either amplifying or canceling other waves depending on how they are aligned. We use the interference of laser light to make patterns of bright and dark spots, which become the lattice. Just as electrons in real graphene are attracted to certain positively charged areas of a carbon hexagon, we can arrange our optical lattices so ultracold atoms are attracted to or repelled from analogous spots in them, depending on the wavelength of the laser light that we use. Light with just the right energy (resonant light) landing on an atom can change the state and energy of an electron within it, imparting forces on the atom. We typically use red-detuned optical lattices, which means the laser light in the lattice has a wavelength that's longer than the wavelength of the resonant light. The result is that the rubidium atoms feel an attraction to the bright spots arranged in a hexagonal pattern.
We now have the basic ingredients for an artificial crystal. Scientists first imagined these ultracold atoms in optical lattices in the late 1990s and constructed them in the early 2000s. The spacing between the lattice points of these artificial crystals is hundreds of nanometers rather than the fractions of a nanometer that separate atoms in a solid crystal. This larger distance means that artificial crystals are effectively magnified versions of real ones, and the hopping process of atoms within them is much slower, allowing us to directly image the movements of the ultracold atoms. In addition, we can manipulate these atoms in ways that aren't possible with electrons.
I was a postdoctoral researcher in the Ultracold Atomic Physics group at the University of California, Berkeley, from 2019 to 2022. The lab there has two special tables (roughly one meter wide by two and a half meters long by 0.3 meter high), each weighing roughly one metric ton and floating on pneumatic legs that dampen vibrations. Atop each table lie hundreds of optical components: mirrors, lenses, light detectors, and more. One table is responsible for producing laser light for trapping, cooling and imaging rubidium atoms. The other table holds an ultrahigh vacuum chamber made of steel with a vacuum pressure less than that of low-Earth orbit, along with hundreds more optical components.
The vacuum chamber has multiple, sequential compartments with different jobs. In the first compartment, we heat a five-gram chunk of rubidium metal to more than 100 degrees Celsius, which causes it to emit a vapor of rubidium atoms. The vapor gets blasted into the next compartment like water spraying from a hose. In the second compartment, we use magnetic fields and laser light to slow the vapor down. The sluggish vapor then flows into another compartment: a magneto-optical trap, where it is captured by an arrangement of magnetic fields and laser light. Infrared cameras monitor the trapped atoms, which appear on our viewing screen as a bright glowing ball. At this point the atoms are colder than liquid helium.
We then move the cold cloud of rubidium atoms into the final chamber, made entirely of quartz. There we shine both laser light and microwaves on the cloud, which makes the warmest atoms evaporate away. This step causes the rubidium to transition from a normal gas to an exotic phase of matter called a Bose-Einstein condensate (BEC). In a BEC, quantum mechanics allows atoms to delocalizeto spread out and overlap with one another so that all the atoms in the condensate act in unison. The temperature of the atoms in the BEC is less than 100 nanokelvins, one billion times colder than liquid nitrogen.
At this point we shine three laser beams separated by 120 degrees into the quartz cell (their shape roughly forms the letter Y). At the intersection of the three beams, the lasers interfere with one another and produce a 2-D optical lattice that looks like a honeycomb pattern of bright and dark spots. We then move the optical lattice so it overlaps with the BEC. The lattice has plenty of space for atoms to hop around, even though it extends over a region only as wide as a human hair. Finally, we collect and analyze pictures of the atoms after the BEC has spent some time in the optical lattice. As complex as it is, we go through this entire process once every 40 seconds or so. Even after years of working on this experiment, when I see it play out, I think to myself, Wow, this is incredible!
Like real graphene, our artificial crystal has Dirac points in its band structure. To understand why these points are significant topologically, let's go back to our graph of energy versus momentum, but this time let's view it from above so we see momentum plotted in two directionsright and left, and up and down. Imagine that the quantum state of the BEC in the optical lattice is represented by an upward arrow at position one (P1) and that a short, straight path separates P1 from a Dirac point at position two (P2).
To move our BEC on this graph toward the Dirac point, we need to change its momentumin other words, we must actually move it in physical space. To put the BEC at the Dirac point, we need to give it the precise momentum values corresponding to that point on the plot. It turns out that it's easier, experimentally, to shift the optical latticeto change its momentumand leave the BEC as is; this movement gives us the same end result. From an atom's point of view, a stationary BEC in a moving lattice is the same as a moving BEC in a stationary lattice. So we adjust the position of the lattice, effectively giving our BEC a new momentum and moving it over on our plot.
If we adjust the BEC's momentum so that the arrow representing it moves slowly on a straight path from P1 toward P2 but just misses P2 (meaning the BEC has slightly different momentum than it needs to reach P2), nothing happensits quantum state is unchanged. If we start over and move the arrow even more slowly from P1 toward P2 on a path whose end is even closer tobut still does not touchP2, the state again is unchanged.
Now imagine that we move the arrow from P1 directly through P2that is, we change the BEC's momentum so that it's exactly equal to the value at the Dirac point: we will see the arrow flip completely upside down. This change means the BEC's quantum state has jumped from its ground state to its first excited state.
What if instead we move the arrow from P1 to P2, but when it reaches P2, we force it to make a sharp left or right turnmeaning that when the BEC reaches the Dirac point, we stop giving it momentum in its initial direction and start giving it momentum in a direction perpendicular to the first one? In this case, something special happens. Instead of jumping to an excited state as if it had passed straight through the Dirac point and instead of going back down to the ground state as it would if we had turned it fully around, the BEC ends up in a superposition when it exits the Dirac point at a right angle. This is a purely quantum phenomenon in which the BEC enters a state that is both excited and not. To show the superposition, our arrow in the plot rotates 90 degrees.
Our experiment was the first to move a BEC through a Dirac point and then turn it at different angles. These fascinating outcomes show that these points, which had already seemed special based on graphene's band structure, are truly exceptional. And the fact that the outcome for the BEC depends not just on whether it passes through a Dirac point but on the direction of that movement shows that at the point itself, the BEC's quantum state can't be defined. This shows that the Dirac point is a singularitya place where physics is uncertain.
We also measured another interesting pattern. If we moved the BEC faster as it traveled near, but not through, the Dirac point, the point would cause a rotation of the BEC's quantum state that made the point seem larger. In other words, it encompassed a broader range of possible momentum values than just the one precise value at the point. The more slowly we moved the BEC, the smaller the Dirac point seemed. This behavior is uniquely quantum mechanical in nature. Quantum physics is a trip!
Although I just described our experiment in a few paragraphs, it took six months of work to get results. We spent lots of time developing new experimental capabilities that had never been used before. We were often unsure whether our experiment would work. We faced broken lasers, an accidental 10-degree-C temperature spike in the lab that misaligned all the optical components (there went three weeks), and disaster when the air in our building caused the lab's temperature to fluctuate, preventing us from creating a BEC. A great deal of persistent effort carried us through and eventually led to our measuring a phenomenon even more exciting than a Dirac point: another kind of singularity.
Before we embarked on our experiment, a related project with artificial crystals in Germany showed what happens when a BEC moves in a circular path around a Dirac point. This team manipulated the BEC's momentum so that it took on values that would plot a circle in the chart of left-momentum versus up-down momentum. While going through these transformations, the BEC never touched the Dirac point. Nevertheless, moving around the point in this pattern caused the BEC to acquire something called a geometric phasea term in the mathematical description of its quantum phase that determines how it evolves. Although there is no physical interpretation of a geometric phase, it's a very unusual property that appears in quantum mechanics. Not every quantum state has a geometric phase, so the fact that the BEC had one here is special. What's even more special is that the phase was exactly .
My team decided to try a different technique to confirm the German group's measurement. By measuring the rotation of the BEC's quantum state as we turned it away from the Dirac point at different angles, we reproduced the earlier findings. We discovered that the BEC's quantum state wraps around the Dirac point exactly once. Another way to say this is that as you move a BEC through momentum space all the way around a Dirac point, it goes from having all its particles in the ground state to having all its particles in the first excited state, and then they all return to the ground state. This measurement agreed with the German study's results.
This wrapping, independent of a particular path or the speed the path is traveled, is a topological property associated with a Dirac point and shows us directly that this point is a singularity with a so-called topological winding number of 1. In other words, the winding number tells us that after a BEC's momentum makes a full circle, it comes back to the state it started in. This winding number also reveals that every time it goes around the Dirac point, its geometric phase increases by .
Furthermore, we discovered that our artificial crystal has another kind of singularity called a quadratic band touching point (QBTP). This is another point where two energy bands touch, making it easy for electrons to jump from one to another, but in this case it's a connection between the second excited state and the third (rather than the ground state and the first excited state as in a Dirac point). And whereas the gap between energy bands near a Dirac point grows linearly, in a QBTP it grows quadratically.
In real graphene, the interactions between electrons make QBTPs difficult to study. In our system, however, QBTPs became accessible with just one weird trick.
Well, it's not really so weird, nor is it technically a trick, but we did figure out a specific technique to investigate a QBTP. It turns out that if we give the BEC a kick and get it moving before we load it into the optical lattice, we can access a QBTP and study it with the same method we used to investigate the Dirac point. Here, in the plot of momentum space, we can imagine new points P3 and P4, where P3 is an arbitrary starting point in the second excited band and a QBTP lies at P4. Our measurements showed that if we move the BEC from P3 directly through P4 and turn it at various angles, just as we did with the Dirac point, the BEC's quantum state wraps exactly twice around the QBTP. This result means the BEC's quantum state picked up a geometric phase of exactly 2. Correspondingly, instead of a topological winding number of 1, like a Dirac point has, we found that a QBTP has a topological winding number of 2, meaning that the state must rotate in momentum space around the point exactly twice before it returns to the quantum state it started in.
This measurement was hard-won. We tried nearly daily for an entire month before it eventually workedwe kept finding fluctuations in our experiment whose sources were hard to pinpoint. After much effort and clever thinking, we finally saw the first measurement in which a BEC's quantum state exhibited wrapping around a QBTP. At that moment I thought, Oh, my goodness, I might actually land a job as a professor. More seriously, I was excited that our measurement technique showed itself to be uniquely suited to reveal this property of a QBTP singularity.
These singularities, with their strange geometric phases and winding numbers, may sound esoteric. But they are directly related to the tangible properties of the materials we studyin this case the special abilities of graphene and its promising future applications. All these changes that occur in the material's quantum state when it moves through or around these points manifest in cool and unusual phenomena in the real world.
Scientists have predicted, for instance, that QBTPs in solid materials are associated with a type of exotic high-temperature superconductivity, as well as anomalous properties that alter the quantum Hall effect and even electric currents in materials whose flow is typically protected, via topology, from disruption. Before attempting to further investigate this exciting physics, we want to learn more about how interactions between atoms in our artificial crystal change what we observe in our lab measurements.
In real crystals, the electrons interact with one another, and this interaction is usually quite important for the most striking physical effects. Because our experiment was the first of its kind, we took care to ensure that our atoms interacted only minimally to keep things simple. An exciting question we can now pose is: Could interactions cause a QBTP singularity to break apart into multiple Dirac points? Theory suggests this outcome may be possible. We look forward to cranking up the interatomic interaction strength in the lab and seeing what happens.
See the article here:
Physicists Make Matter out of Light to Find Quantum Singularities - Scientific American
Thermomagnetic properties and its effects on Fisher entropy with … – Nature.com
The Nikiforov-Uvarov Functional Analysis (NUFA) method recently developed by Ikot et al.52 has been very helpful in providing solutions for exponential type potentials both in relativistic and nonrelativistic wave equations When using this method to solve either the Schrdinger or KleinGordon equation, the energy eigen equation is directly presented in a factorized, closed and compact form. This gives the method an edge over other methods. Meanwhile, the NUFA theory involves solving second order Schrdinger-like differential equation through the analytical combination of Nikiforov-Uvarov (NU) method and functional analysis approach53,54,55. NU is applied to solve a second-order differential equation of the form
$$frac{{d^{2} {uppsi }left( {text{s}} right)}}{{ds^{2} }} + frac{{tilde{tau }left( s right)}}{sigma left( s right)}frac{{d{uppsi }left( {text{s}} right)}}{ds} + frac{{tilde{sigma }left( s right)}}{{sigma^{2} left( s right)}}psi left( s right) = 0$$
(4)
where (sigma (s)) and (widetilde{sigma }left(sright)) are polynomials at most degree two and (widetilde{tau }(s)) is a first-degree polynomial. Tezean and Sever56 latter introduced the parametric form of NU method in the form
$$frac{{d^{2} psi (s)}}{{ds^{2} }} + frac{{alpha_{1} - alpha_{2} s}}{{s(1 - alpha_{3} s)}}frac{{d^{2} psi (s)}}{{ds^{2} }} + frac{1}{{s^{2} (1 - alpha_{3} s)^{2} }}left[ { - U_{1} s^{2} + U_{2} s - U_{3} } right]psi (s) = 0,$$
(5)
where (alpha_{i}) and (xi_{i} (i = 1,2,3)) are all parameters. The differential Eq. (3) has two singularities which is at (s to 0) and (s to frac{1}{{alpha_{3} }}) thus, the wave function can be expressed in the form.
$$Psi_{n} (s) = s^{lambda } (1 - alpha_{3} s)^{v} f(s)$$
(6)
Substituting Eq.(6) into Eq.(5) and simplifying culminate to the following equation,
$$begin{aligned} s(1 - alpha_{3} s)frac{{d^{2} f(s)}}{{ds^{2} }} & + left[ {alpha_{1} + 2lambda - (2lambda alpha_{3} + 2valpha_{3} + alpha_{2} )s} right]frac{df(s)}{{ds}} \ & - alpha_{3} left( {lambda + v + frac{1}{2}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right) + sqrt {frac{1}{4}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right)^{2} + frac{{U_{1} }}{{alpha_{3}^{2} }}} } right)\&quad left( {lambda + v + frac{1}{2}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right) - sqrt {frac{1}{4}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right)^{2} + frac{{U_{1} }}{{alpha_{3}^{2} }}} } right)fleft( s right) \ & + left[ {frac{{lambda (lambda - 1) + alpha_{1} lambda - U_{3} }}{s} + frac{{v(v - 1)alpha_{3} + alpha_{2} v - alpha_{1} alpha_{3} v - frac{{U_{1} }}{{alpha_{3} }} + U_{2} - U_{3} alpha_{3} }}{{left( {1 - alpha_{3} s} right)}}} right]fleft( s right) = 0 \ end{aligned}$$
(7)
Equation(7) can be reduced to a Guassian- hypergeometric equation if and only if the following functions vanished
$$lambda left( {lambda - 1} right) + alpha_{1} lambda - U_{3} = 0$$
(8)
$$upsilon left( {upsilon - 1} right)alpha_{3} + alpha_{2} upsilon - alpha_{1} alpha_{3} upsilon - frac{{U_{1} }}{{alpha_{3} }} + U_{2} - U_{3} alpha_{3} = 0.$$
(9)
Applying the condition of Eq.(8) and Eq.(9) into Eq.(7) results into Eq.(10)
$$begin{aligned} s(1 - alpha_{3} s) & frac{{d^{2} f(s)}}{{ds^{2} }}left[ {alpha_{1} + 2lambda - (2lambda alpha_{3} + 2valpha_{3} + alpha_{2} )s} right]frac{df(s)}{{ds}} \ & ;; - alpha_{3} left( {lambda + v + frac{1}{2}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right) + sqrt {frac{1}{4}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right)^{2} + frac{{U_{1} }}{{alpha_{3}^{2} }}} } right)\ & quadleft( {lambda + v + frac{1}{2}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right) - sqrt {frac{1}{4}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right)^{2} + frac{{U_{1} }}{{alpha_{3}^{2} }}} } right)fleft( s right) = 0 \ end{aligned}$$
(10)
The solutions of Eqs. (8) and (9) are given as
$$lambda = frac{1}{2}left( {left( {1 - alpha_{1} } right) pm sqrt {left( {1 - alpha_{1} } right)^{2} + 4U_{3} } } right)$$
(11)
$$upsilon = frac{1}{{2alpha_{3} }}left( {left( {alpha_{3} + alpha_{1} alpha_{3} - alpha_{2} } right) pm sqrt {left( {alpha_{3} + alpha_{1} alpha_{3} - alpha_{2} } right)^{2} + 4left( {frac{{U_{1} }}{{alpha_{3} }} + alpha_{3} U_{3} - U_{2} } right)} } right)$$
(12)
Equation(10) is the hypergeometric equation type of the form
$$xleft( {1 - x} right)frac{{d^{2} f(s)}}{{ds^{2} }} + left[ {c - left( {a + b + 1} right)x} right]frac{df(x)}{{dx}} - left[ {ab} right]f(x) = 0$$
(13)
where a, b and c are given as follows:
$$a = sqrt {alpha_{3} } left( {lambda + v + frac{1}{2}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right) + sqrt {frac{1}{4}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right)^{2} + frac{{U_{1} }}{{U_{3}^{2} }}} } right)$$
(14)
$$b = sqrt {alpha_{3} } left( {lambda + v + frac{1}{2}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right) - sqrt {frac{1}{4}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right)^{2} + frac{{U_{1} }}{{alpha_{3}^{2} }}} } right)$$
(15)
$$c = alpha_{1} + 2lambda$$
(16)
Setting either a or b equal to a negative integer n, the hypergeometric function f(s) turns to a polynomial of degree n. Hence, the hypergeometric function f(s) approaches finite in the following quantum condition, i.e.,(a = - n) where (n = 0,1,2,3 ldots n_{max }) or (b = - n).
Using the above quantum condition,
$$sqrt {alpha_{3} } left( {lambda + upsilon + frac{1}{2}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right) + sqrt {frac{1}{4}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right)^{2} + frac{{U_{1} }}{{alpha_{3}^{2} }}} } right) = - n$$
(17)
$$lambda + upsilon + frac{1}{2}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right) + frac{n}{{sqrt {alpha_{3} } }} = - sqrt {frac{1}{4}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right)^{2} + frac{{U_{1} }}{{alpha_{3}^{2} }}}$$
(18)
By simplifying Eq.(18), the energy eigen equation using NUFA method is given as
$$lambda^{2} + 2lambda left( {upsilon + frac{1}{2}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right) + frac{n}{{sqrt {alpha_{3} } }}} right) + left( {upsilon + frac{1}{2}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right) + frac{n}{{sqrt {alpha_{3} } }}} right)^{2} - frac{1}{4}left( {frac{{alpha_{2} }}{{alpha_{3} }} - 1} right)^{2} - frac{{U_{1} }}{{alpha_{3}^{2} }} = 0$$
(19)
By substituting Eqs. (9) and (10) into Eq.(6), the corresponding wave equation for the NUFA method as
$$Psi_{n} (s) = N_{n} S^{{frac{{left( {1 - alpha_{1} } right) + sqrt {left( {alpha_{1} - 1} right)^{2} + 4U_{3} } }}{2}}} left( {1 - alpha_{3} } right)^{{frac{{left( {alpha_{3} + alpha_{1} alpha_{3} - alpha_{2} } right) + sqrt {left( {alpha_{3} + alpha_{1} alpha_{3} - alpha_{2} } right)^{2} + 4left( {frac{{U_{1} }}{{alpha_{3}^{2} }} + alpha_{3} U_{3} - U_{2} } right)} }}{{2alpha_{2} }}}} {}_{2}F_{1} (a,b,c;s)$$
(20)
The thermomagnetic energy spectra of 2-Dimensional Schrdinger equation under the influenced of AB and Magnetic field with SPMR potential can be obtained from charged particle Hamiltonian operator of the form
$$left{ {frac{1}{2mu }left( {ihbar nabla - frac{e}{c}vec{A}} right)^{2} + Dleft[ {1 - sigma_{0} left( {frac{{1 + e^{ - alpha r} }}{{1 - e^{ - alpha r} }}} right)} right]^{2} - left( {frac{{c_{1} e^{ - 2alpha r} + c_{2} e^{ - alpha r} }}{{left( {1 - e^{ - alpha r} } right)^{2} }}} right)} right}Rleft( {r, varphi } right) = E_{nm} Rleft( {r, varphi } right)$$
(21)
(E_{nm}) is the thermomagnetic energy spectra, (e) and (mu) represent the charge of the particle and the reduced mass respectively. (c) is the speed of light. Meanwhile, The vector potential (overrightarrow{A}=left({A}_{r},{A}_{phi }, {A}_{z}right)) can be written as the superposition of two terms such that (overrightarrow{A}=overrightarrow{{A}_{1}}+overrightarrow{{A}_{2}}) is the vector potential with azimuthal components such that (overrightarrow{{A}_{1}}=) and (overrightarrow{{A}_{2}}=), corresponding to the extra magnetic flux (Phi_{AB}) generated by a solenoid with (overrightarrow{nabla }.overrightarrow{{A}_{2}}=0) and (overrightarrow{B}) is the magnetic vector field accompanied by (overrightarrow{nabla }times overrightarrow{{A}_{1}}=overrightarrow{B}) ,(overrightarrow{nabla }times overrightarrow{{A}_{2}}=0). The vector potential (overrightarrow{A}) can then be expressed as
$$vec{A} = left( {0,frac{{Be^{ - alpha r} hat{varphi }}}{{1 - e^{ - alpha r} }} + frac{{Phi_{AB} }}{2pi r}hat{varphi },0} right) = left( {frac{{Be^{ - alpha r} hat{varphi }}}{{1 - e^{ - alpha r} }} + frac{{Phi_{AB} }}{2pi r}hat{varphi }} right)$$
(22)
The Laplacian operator and the wave function in cylindrical coordinate is given as
$$begin{aligned} nabla^{2} & = frac{{partial^{2} }}{{partial r^{2} }} + frac{1}{r}frac{partial }{partial r} + frac{1}{{r^{2} }}frac{{partial^{2} }}{{partial varphi^{2} }} + frac{{partial^{2} }}{{partial z^{2} }} \ Psi left( {r,varphi } right) & = frac{1}{{sqrt {2pi r} }}R_{nm} (r)e^{imvarphi } \ end{aligned}$$
(23)
where (m) represents the magnetic quantum number. Substituting Eqs. (23) and (22) into Eq.(21) and with much algebraic simplification gives rise to the Schrdinger -like equation of the form
$$frac{{d^{2} R_{nm} (r)}}{{dr^{2} }} + frac{2mu }{{h^{2} }}left[ begin{gathered} E_{nm} - Dleft[ {1 - sigma_{0} left( {frac{{1 + e^{ - alpha r} }}{{1 - e^{ - alpha r} }}} right)} right]^{2} + left( {frac{{c_{1} e^{ - 2alpha r} + c_{2} e^{ - alpha r} }}{{left( {1 - e^{ - alpha r} } right)^{2} }}} right) - hbar omega_{c} left( {m + xi } right)frac{{e^{ - alpha r} }}{{left( {1 - e^{ - alpha r} } right)r}} hfill \ - left( {frac{{mu omega_{c}^{2} }}{2}} right)frac{{e^{ - 2alpha r} }}{{left( {1 - e^{ - alpha r} } right)^{2} }} - frac{{hbar^{2} }}{2mu }left( {frac{{left( {m + xi } right)^{2} - frac{1}{4}}}{{r^{2} }}} right) hfill \ end{gathered} right]R_{nm} (r) = 0.$$
(24)
where (xi = frac{{Phi_{AB} }}{{phi_{0} }}) is an absolute value containing the flux quantum (phi_{0} = frac{hc}{e}). The cyclotron frequency is represented by (omega_{c} = frac{{evec{B}}}{mu c}). Equation(24) is not exactly solvable due to the presence of centrifugal barrier (frac{1}{{r^{2} }}). In order to provide an analytical approximate solution to Eq.(24), we substitute the modified Greene-Aldrich approximation of the form (frac{1}{{r^{2} }} = frac{{alpha^{2} }}{{left( {1 - e^{ - alpha r} } right)^{2} }}) into Eq.(24) to deal with the centrifugal barrier. Also, using the coordinate transformation (s = e^{ - alpha r}) together with the approximation term, Eq.(24) reduced to the hyper-geometric equation of the form
$$frac{{d^{2} R_{nm} (s)}}{{ds^{2} }} + frac{{left( {1 - s} right)}}{{sleft( {1 - s} right)}}frac{{dR_{nm} (s)}}{ds} + frac{1}{{s^{2} left( {1 - s} right)^{2} }}left{ begin{gathered} - left( {varepsilon^{2} + chi_{1} + 2chi_{1} sigma_{0} + chi_{1} sigma_{0}^{2} - chi_{2} + chi_{5} } right)s^{2} hfill \ + left( {2varepsilon^{2} + 2chi_{1} - 2chi_{1} sigma_{0}^{2} + chi_{3} - chi_{4} } right)s hfill \ - left( {varepsilon^{2} + chi_{1} - 2chi_{1} sigma_{0} + chi_{1} sigma_{0}^{2} + chi_{6} } right) hfill \ end{gathered} right}R_{nm} (s) = 0.$$
(25)
where
$$begin{aligned} varepsilon^{2} & = - frac{{2mu E_{nm} }}{{hbar^{2} alpha^{2} }}begin{array}{*{20}c} , & {chi_{1} = frac{2mu D}{{hbar^{2} alpha^{2} }}} \ end{array} begin{array}{*{20}c} , & {chi_{2} = frac{{2mu c_{1} }}{{hbar^{2} alpha^{2} }}} \ end{array} begin{array}{*{20}c} , & {chi_{3} = frac{{2mu c_{2} }}{{hbar^{2} alpha^{2} }}} \ end{array} \ chi_{4} & = frac{{2mu omega_{c} left( {m + xi } right)}}{hbar alpha }begin{array}{*{20}c} , & {chi_{5} = frac{{mu^{2} omega_{c}^{2} }}{{hbar^{2} alpha^{2} }}} \ end{array} begin{array}{*{20}c} , & {chi_{6} = left( {m + xi } right)^{2} - frac{1}{4}} \ end{array} . \ end{aligned}$$
(26)
Comparing Eq.(25) with NUFA differential equation in Eq.(5), the following polynomial equations can be obtained.
$$begin{gathered} U_{1} = left( {varepsilon^{2} + chi_{1} + 2chi_{1} sigma_{0} + chi_{1} sigma_{0}^{2} - chi_{2} + chi_{5} } right)begin{array}{*{20}c} , & {U_{2} = left( {2varepsilon^{2} + 2chi_{1} - 2chi_{1} sigma_{0}^{2} + chi_{3} - chi_{4} } right)} \ end{array} hfill \ U_{3} = left( {varepsilon^{2} + chi_{1} - 2chi_{1} sigma_{0} + chi_{1} sigma_{0}^{2} + chi_{6} } right),alpha_{1} = alpha_{2} = alpha_{3} = 1. hfill \ end{gathered}$$
(27)
Using equation NUFA in Eqs. (11), (12), (14), (15) and (16) the following polynomial equations can be obtained
$$lambda = sqrt {varepsilon^{2} + chi_{1} - 2chi_{1} sigma_{0} + chi_{1} sigma_{0}^{2} + chi_{6} } ,$$
(28)
$$upsilon = frac{1}{2} + frac{1}{2}sqrt {16chi_{1} sigma_{0}^{2} - 4chi_{2} + 4chi_{5} + 4chi_{6} - 4chi_{3} + 4chi_{4} + 1} ,$$
(29)
$$a = left( begin{gathered} sqrt {varepsilon^{2} + chi_{1} - 2chi_{1} sigma_{0} + chi_{1} sigma_{0}^{2} + chi_{6} } + frac{1}{2} + frac{1}{2}sqrt {16chi_{1} sigma_{0}^{2} - 4chi_{2} + 4chi_{5} + 4chi_{6} - 4chi_{3} + 4chi_{4} + 1} hfill \ + sqrt {varepsilon^{2} + chi_{1} + 2chi_{1} sigma_{0} + chi_{1} sigma_{0}^{2} - chi_{2} + chi_{5} } hfill \ end{gathered} right),$$
(30)
$$b = left( begin{gathered} sqrt {varepsilon^{2} + chi_{1} - 2chi_{1} sigma_{0} + chi_{1} sigma_{0}^{2} + chi_{6} } + frac{1}{2} + frac{1}{2}sqrt {16chi_{1} sigma_{0}^{2} - 4chi_{2} + 4chi_{5} + 4chi_{6} - 4chi_{3} + 4chi_{4} + 1} hfill \ - sqrt {varepsilon^{2} + chi_{1} + 2chi_{1} sigma_{0} + chi_{1} sigma_{0}^{2} - chi_{2} + chi_{5} } hfill \ end{gathered} right),$$
(31)
$$c = left( {1 + 2sqrt {varepsilon^{2} + chi_{1} - 2chi_{1} sigma_{0} + chi_{1} sigma_{0}^{2} + chi_{6} } } right).$$
(32)
using Eq.(19), the thermo-magnetic energy eigen equation
$$begin{aligned} varepsilon^{2} & = frac{1}{4}left{ {frac{{left( {n + frac{1}{2} + frac{1}{2}sqrt {16chi_{1} sigma_{0}^{2} - 4chi_{2} + 4chi_{5} + 4chi_{6} - 4chi_{3} + 4chi_{4} + 1} } right)^{2} + chi_{2} - chi_{5} + chi_{6} - 4chi_{1} sigma_{0} }}{{left( {n + frac{1}{2} + frac{1}{2}sqrt {16chi_{1} sigma_{0}^{2} - 4chi_{2} + 4chi_{5} + 4chi_{6} - 4chi_{3} + 4chi_{4} + 1} } right)}}} right}^{2} \ & ;;; + 2chi_{1} sigma_{0} - chi_{1} - chi_{1} sigma_{0}^{2} - chi_{6} \ end{aligned}$$
(33)
Substituting the parameters of Eq.(26) into Eq.(33), the thermomagnetic energy equation become
$$begin{aligned} E_{nm} & = frac{{h^{2} alpha^{2} }}{2mu }left( {left( {m + xi } right)^{2} - frac{1}{4}} right) + Dleft( {sigma_{0} - 1} right)^{2} \ & ;;; - frac{{h^{2} alpha^{2} }}{8mu }left{ {frac{begin{gathered} left[ {n + frac{1}{2} + frac{1}{2}sqrt {frac{{32mu Dsigma_{0}^{2} }}{{h^{2} alpha^{2} }} - frac{{8mu c_{1} }}{{h^{2} alpha^{2} }} - frac{{8mu c_{2} }}{{h^{2} alpha^{2} }} + frac{{4mu^{2} omega_{c}^{2} }}{{h^{2} alpha^{2} }} + 4left( {m + xi } right)^{2} + frac{{8mu omega_{c} }}{halpha }left( {m + xi } right)} } right]^{2} hfill \ + frac{{2mu c_{1} }}{{h^{2} alpha^{2} }} - frac{{mu^{2} omega_{c}^{2} }}{{h^{2} alpha^{2} }} - frac{{8mu Dsigma_{0} }}{{h^{2} alpha^{2} }} + left( {m + xi } right)^{2} - frac{1}{4} hfill \ end{gathered} }{{left[ {n + frac{1}{2} + frac{1}{2}sqrt {frac{{32mu Dsigma_{0}^{2} }}{{h^{2} alpha^{2} }} - frac{{8mu c_{1} }}{{h^{2} alpha^{2} }} - frac{{8mu c_{2} }}{{h^{2} alpha^{2} }} + frac{{4mu^{2} omega_{c}^{2} }}{{h^{2} alpha^{2} }} + 4left( {m + xi } right)^{2} + frac{{8mu omega_{c} }}{halpha }left( {m + xi } right)} } right]}}} right}^{2} \ end{aligned}$$
(34)
The 2D nonrelativistic energy eigen equation can be obtained with the condition that (omega_{c} = xi = 0), (m = l + frac{1}{2}).
Then Eq.(34) become
$$begin{aligned} E_{nm} & = frac{{h^{2} alpha^{2} lleft( {l + 1} right)}}{2mu } + Dleft( {sigma_{0} - 1} right)^{2} \ & ;;; - frac{{h^{2} alpha^{2} }}{8mu }left{ {frac{{left[ {n + frac{1}{2} + frac{1}{2}sqrt {1 + frac{{32mu Dsigma_{0}^{2} }}{{h^{2} alpha^{2} }} - frac{{8mu c_{1} }}{{h^{2} alpha^{2} }} - frac{{8mu c_{2} }}{{h^{2} alpha^{2} }} + 4lleft( {l + 1} right)} } right]^{2} + frac{{2mu c_{1} }}{{h^{2} alpha^{2} }} - frac{{8mu Dsigma_{0} }}{{h^{2} alpha^{2} }} + lleft( {l + 1} right)}}{{left[ {n + frac{1}{2} + frac{1}{2}sqrt {1 + frac{{32mu Dsigma_{0}^{2} }}{{h^{2} alpha^{2} }} - frac{{8mu c_{1} }}{{h^{2} alpha^{2} }} - frac{{8mu c_{2} }}{{h^{2} alpha^{2} }} + 4lleft( {l + 1} right)} } right]}}} right}^{2} \ end{aligned}$$
(34a)
Substituting (c_{1} = c_{2} = 0).into Eq.(3), then, the potential reduces to Schioberg potential given as
$$Vleft( r right) = Dleft[ {1 - sigma_{0} left( {frac{{1 + e^{ - alpha r} }}{{1 - e^{ - alpha r} }}} right)} right]^{2} .$$
(34b)
Substituting the same condition to Eq.(34) gives the energy-eigen equation for Schioberg potential under the influence of magnetic and AB field as
$$begin{aligned} E_{nm} & = frac{{h^{2} alpha^{2} }}{2mu }left( {left( {m + xi } right)^{2} - frac{1}{4}} right) + Dleft( {sigma_{0} - 1} right)^{2} \ & ;;; - frac{{h^{2} alpha^{2} }}{8mu }left{ {frac{{left[ {n + frac{1}{2} + frac{1}{2}sqrt {frac{{32mu Dsigma_{0}^{2} }}{{h^{2} alpha^{2} }} + frac{{4mu^{2} omega_{c}^{2} }}{{h^{2} alpha^{2} }} + 4left( {m + xi } right)^{2} + frac{{8mu omega_{c} }}{halpha }left( {m + xi } right)} } right]^{2} - frac{{mu^{2} omega_{c}^{2} }}{{h^{2} alpha^{2} }} - frac{{8mu Dsigma_{0} }}{{h^{2} alpha^{2} }} + left( {m + xi } right)^{2} - frac{1}{4}}}{{left[ {n + frac{1}{2} + frac{1}{2}sqrt {frac{{32mu Dsigma_{0}^{2} }}{{h^{2} alpha^{2} }} + frac{{4mu^{2} omega_{c}^{2} }}{{h^{2} alpha^{2} }} + 4left( {m + xi } right)^{2} + frac{{8mu omega_{c} }}{halpha }left( {m + xi } right)} } right]}}} right}^{2} \ end{aligned}$$
(34c)
Substituting (D = 0) into Eq.(3), then the potential reduces to Manning-Rosen potential of the form
$$Vleft( r right) = - left( {frac{{c_{1} e^{ - 2alpha r} + c_{2} e^{ - alpha r} }}{{left( {1 - e^{ - alpha r} } right)^{2} }}} right)$$
(34d)
Substituting the same condition to Eq.(34) gives the energy eigen equation of Manning-Rosen potential under the influence of magnetic and AB fields as
$$begin{aligned} E_{nm} & = frac{{h^{2} alpha^{2} }}{2mu }left( {left( {m + xi } right)^{2} - frac{1}{4}} right) \ & ;;; - frac{{h^{2} alpha^{2} }}{8mu }left{ {frac{{left[ {n + frac{1}{2} + frac{1}{2}sqrt { - frac{{8mu c_{1} }}{{h^{2} alpha^{2} }} - frac{{8mu c_{2} }}{{h^{2} alpha^{2} }} + frac{{4mu^{2} omega_{c}^{2} }}{{h^{2} alpha^{2} }} + 4left( {m + xi } right)^{2} + frac{{8mu omega_{c} }}{halpha }left( {m + xi } right)} } right]^{2} + frac{{2mu c_{1} }}{{h^{2} alpha^{2} }} - frac{{mu^{2} omega_{c}^{2} }}{{h^{2} alpha^{2} }} + left( {m + xi } right)^{2} - frac{1}{4}}}{{left[ {n + frac{1}{2} + frac{1}{2}sqrt { - frac{{8mu c_{1} }}{{h^{2} alpha^{2} }} - frac{{8mu c_{2} }}{{h^{2} alpha^{2} }} + frac{{4mu^{2} omega_{c}^{2} }}{{h^{2} alpha^{2} }} + 4left( {m + xi } right)^{2} + frac{{8mu omega_{c} }}{halpha }left( {m + xi } right)} } right]}}} right}^{2} \ end{aligned}$$
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Thermomagnetic properties and its effects on Fisher entropy with ... - Nature.com
That flawed diamond could be a quantum physicist’s best friend – Princeton University
Shoppers like flawless diamonds, but for quantum physicists, the flaws are the best part.
Senior Elisabeth Rlke has spent the past year using lasers and flawed diamonds tiny wafers of diamond with flaws the size of a single atom to develop a quantum sensor.
The clear wafer at the center of the equipment is a diamond plate, precisely manufactured to be 2 mm on a side and .3 mm thick, with atomic-sized flaws at which Rlke and her adviser Nathalie de Leon shine green and orange lasers.
Photo by
David Kelly Crow for the Office of Engineering Communications
Unlike quantum computers, which are still more theoretical than practical, quantum sensors are already in use. Rlke and her adviser, quantum physicist Nathalie de Leon, are working on a new approach to quantum sensing that depends on using two of these single-atom defects simultaneously.
Because they are so, so small, you could begin to map and sense things on a scale that has never been feasible before, said Rlke, a physics concentrator pursuing a certificate in applied and computational mathematics. It would be revolutionary to chemistry, biology and especially medical devices.
Working with very bright students like Elisabeth is always just a privilege, said de Leon, an associate professor of electrical and computer engineering who is associated faculty in the physics department. She brings a fresh perspective and a different take on things, and that brought a little more creativity on the project than I think would have happened otherwise. Im lucky to be at Princeton and get these really great students knocking on my door.
Rlke knew before she came to Princeton that she wanted to study physics and astronomy, but she also knew that she wanted to take full advantage of the liberal arts. I have taken courses in history, philosophy, religion, entrepreneurship, film, art and others, and I believe it has been a cornerstone of my Princeton experience. The wonderful part about Princetons liberal arts education is that it allows you to take classes in a range of subjects, meaning that what you choose to major in isnt the only focus of your education, as is the case with most British universities and a strong reason why I wanted to study in the U.S., said Rlke, who was born and raised in London.
I do think that there is overlap in the critical and creative thinking used in both higher-level physics and mathematics courses and the humanities subjects, she added.
When Princeton closed its campus to in-person instruction in March of Rlkes first year, she went home to London for Zoom classes. That summer, when travel restrictions eased, she and a Princeton classmate moved into an apartment in Rome. I took an art history class that fall, and it was amazing, Rlke said. I remember one assignment asked us to go find art wherever you are. Most of my classmates looked at, like, a teapot from their house, and I chose a Bernini sculpture.
After she returned to campus, she decided to focus her first junior paper on a truly enormous question: the nature of dark energy in the universe.
She hadnt had a course in general relativity, she hadnt had a course in cosmology, and she wasnt daunted at all, said Paul Steinhardt, Princetons Albert Einstein Professor in Science and a professor of physics who was her adviser on that paper. It was clearly a stretch for her, but she was just full of energy and enthusiasm. I really enjoy seeing a student stretching and learning, and that certainly characterized Elisabeth. She broke her leg that semester, but she still always came to our weekly meetings with enthusiasm and cheer and lots of great research questions.
After they worked together on that paper, Steinhardt served as the second reader on Rlkes second junior paper, then reprised that role for her senior thesis. Ill have read all her theses by the time were through, he said.
Rlke came to Princeton knowing she wanted to immerse herself in STEM science, technology, engineering and mathematics and specifically in physics and astronomy.
The Princeton astrophysics and physics departments are absolutely amazing, she said. I feel so lucky. When I visited Princeton after I got in, I went to go see Einsteins old classroom and walked to his house, which is near campus.
In the lab, Rlkeperforms a confocal scan to locate NV centers in a diamond lattice.
Photo by
Denise Applewhite, Office of Communications
After tackling theoretical cosmology for her first independent research project, she wanted to try something more hands-on, so she did her second junior paper on plasma propulsion. Both were very, very interesting. The first one was very theoretical, and the second was almost too experimental, she said. I was actually climbing into a thrust tank with tools and tinkering with stuff in there. So for my thesis, I wanted something in the middle.
Her broad perspective has served Rlke well as she tackles quantum sensing, a problem that has brought together professors from physics, chemistry and engineering with the goal of tackling a large range of problems, from biophysics and biomedical applications to condensed matter physics and designing new navigational sensors.
The general ethos of my research group is to try to see problems without any borders as much as possible, said de Leon. Our approach to problems tends to start with, What does it take to solve this? We have all of physics and all of chemistry and all of materials engineering all the tools of humanity so lets see if we can MacGyver our way to a solution. Elisabeth definitely fit in like a fish in water.
Diamonds are made of pure carbon, as are charcoal and the graphite in pencils. But you can write with pencils (and charcoal) because those carbon atoms are organized in sheets that slide apart with the barest pressure, leaving marks behind.
The carbon atoms in a diamond, by contrast, have been forced together with tremendous pressure, crowding the atoms together in a perfect and complex web. This allows for another unique property: when a nitrogen atom pushes in and displaces two carbon atoms, it creates a tiny defect called a nitrogen vacancy center or NV center.
NV centers behave like tiny compass needles and have been used in quantum sensors that can measure magnetic fields. While quarantining at home during the COVID pandemic, de Leon began wondering what would happen if there were two NV centers, precisely separated within a diamond chip.
It turns out that while its much, much harder to measure two nitrogen vacancies simultaneously, once you do, you can measure new physical quantities, namely correlations in the magnetic field in space and time. With simultaneous measurements of two NV centers, a whole new world of nanoscale measurements is possible, de Leon said.
This is a fundamentally new thing, she said. The world is our oyster. We can use this new technique that measures a completely new physical quantity. So lets clean up! Lets go look at everything that people were trying to do in the 80s and then just got stuck because they didnt have the right tool. Maybe theres some really cool physics that we can learn. That's where Elisabeth comes in.
The voyage from pandemic inspiration to simultaneously measuring two NV centers took years. De Leon and a postdoc in her lab, Jared Rovny, spent 18 months working out the math and longer than that to figure out how to build a tool that lets you shine lasers at two atomic-sized objects and then count the photons flying out. They first demonstrated this technique with a resolution of 500 nanometers. (For comparisons sake, the period at the end of this sentence is about a million nanometers across.) Rlkes senior thesis has focused on improving this resolution from 500 nanometers down to 10 nm or maybe even a single nanometer.
Rlke credits her coursework and her independent research projects at the University with developing her ability to navigate uncertainty and face challenges head-on.
I remember a three-hour physics exam that only had two questions. You have to spend so much time grasping around in the darkness, trying to think of how to do this, which method to start with and building the skills to do that makes you a person with the ability to think really critically and not be afraid if youre going head-on to a problem where you cant really see the end or you dont really know how to solve it.
In high school, I hated those sorts of problems, she said. I liked getting to the answer and getting it right. That growth happened at Princeton.
She and de Leon both enjoyed their weekly thesis advising sessions.
I have enough autonomy to decide what exactly I want to do, Rlke said. But de Leon also provides enough help to make sure that I have the right background knowledge.
She always shows up at my office extremely sunny and very enthusiastic, de Leon said of Rlke. I dont know where she gets all that energy. Even if its the middle of midterm season or application season, she still just shows up and is like, Okay, heres what Ive done. Look at all my data. Lets discuss it. Heres my plan. I think this thing is really interesting.
1
Rlke and her thesis adviser, quantum physicist Nathalie de Leon (right), are measuring two nitrogen vacancy centers simultaneously. De Leon and her postdoc Jared Rovny first demonstrated this technique with a resolution of 500 nanometers, and Rlkes senior thesis has focused on improving this resolution down to 10 nm or maybe even a single nanometer.
Photo by
Denise Applewhite, Office of Communications
2
Rlke gives her parents a tour of Cottage Club in Fall 2022.
Courtesy of Elisabeth Rlke
Outside of her coursework, Rlke is a member of Mathey College and she serves as the diversity, equity and inclusion chair of University Cottage Club. She got involved in entrepreneurship through the Keller Center and the Entrepreneurship Club, and she traveled to California with the Silicon Valley Tiger Track to meet with entrepreneurs, venture capital firms and space related companies.
She received the Manfred Pyka Memorial Prize in Physics, given to outstanding physics undergraduates who have shown excellence in course work and promise in independent research; the Jocelyn Bell Burnell fellowship, aimed at encouraging women to pursue physics; and the Schwarzman Scholarship, which covers the cost of one-year masters program at Tsinghua University in Beijing.
Rlke says she feels a pull towards being a global citizen, having been born in the United Kingdom to a German dad and a Chinese mom.
My cultural identity is complicated, she said. I have family in different parts of the world, and sometimes being mixed race means you dont feel that you fully fit in anywhere. Visiting family in Germany or in China, I never looked like anybody else.
As a kid, that made me feel out of place sometimes, but as Ive grown up, Ive started to enjoy it, Rlke said. I think standing out is much better than disappearing into a crowd.
This elaborate array of mirrors, lenses, and scanning galvonometers route and collect light in this home-built microscope for quantum sensing.
Photo by
Denise Applewhite, Office of Communications
Rlke dons safety safety goggles before firing lasers into single-atom sized defects that are closer together than the wavelength of light.
Photo by
Denise Applewhite, Office of Communications
Rlke (left) visits Cairo with her family in 2009.
Photo by
Courtesy of Elisabeth Rlke
Elisabeth Rlke is a Class of 2023 physics major with a minor inappliedand computational mathematics.
Photo by
Denise Applewhite, Office of Communications
More here:
That flawed diamond could be a quantum physicist's best friend - Princeton University