Experiments that imitate solid materials with light waves reveal the quantum basis of exotic physical effects

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 graphene—a crystal made of carbon atoms arranged in a hexagonal lattice—produces 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.

TOPOLOGICAL MATERIALS

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 distinct—discrete—energy 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 range—also known as a band gap—that 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 it—allowing 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 shape—to bend or stretch it—without 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-D—its 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 materials—the half-integer quantum Hall effect—and the special kind of tunneling possible within it.

ARTIFICIAL CRYSTALS

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 delocalize—to 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!”

THE SINGULARITY

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 directions—right 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 momentum—in 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 lattice—to change its momentum—and 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 happens—its 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 to—but still does not touch—P2, the state again is unchanged.

Now imagine that we move the arrow from P1 directly through P2—that 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 turn—meaning 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 singularity—a 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.

GEOMETRIC SURPRISES

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 phase—a 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 π.

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 π.

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.

On a late summer afternoon it can seem like sunlight has turned to honey, but could liquid—or even solid—light be more than a piece of poetry? Princeton University electrical engineers say not only is it possible, they’ve already made it happen.

In Physical Review X, the researchers reveal that they have locked individual photons together so that they become like a solid object.

"It's something that we have never seen before," says Dr. Andrew Houck, an associate professor of electrical engineering and one of the researchers. "This is a new behavior for light."

The researchers constructed what they call an “artificial atom” made of 100 billion atoms engineered to act like a single unit. They then brought this close to a superconducting wire carrying photons. In one of the almost incomprehensible behaviors unique to the quantum world, the atom and the photons became entangled so that properties passed between the “atom” and the photons in the wire. The photons started to behave like atoms, correlating with each other to produce a single oscillating system.

As some of the photons leaked into the surrounding environment, the oscillations slowed and at a critical point started producing quantum divergent behavior. In other words, like Schroedinger's Cat, the correlated photons could be in two states at once.

"Here we set up a situation where light effectively behaves like a particle in the sense that two photons can interact very strongly," said co-author Dr. Darius Sadri. "In one mode of operation, light sloshes back and forth like a liquid; in the other, it freezes."

As cool as it is to produce solidified light, the team was not acting out of curiosity alone. When connected together the photons of light behave like subatomic particles, but are in some ways easier to study. Consequently, the team is hoping to use the solid light to simulate subatomic behavior.

Attempts to model the behavior of large numbers of particles usually use statistical mechanics, and often simplify by assuming no interaction between particles and a system at equilibrium. However, in a point we can all relate to, Houck and his colleagues note, “The world around us is rarely in equilibrium.” The solidified light offers a chance to observe a subatomic system as it starts to diverge from equilibrium, with potential for a basic understanding of how these systems operate.

The system created so far is very simple, with the light entangled with the atom at two points. However, it should be possible to increase this, greatly expanding the complexity and range of possibilities of what is being constructed.

As well as providing an easy-to-study model of atomic systems that actually exist, Houck and his team hope the frozen light could be made to behave like materials that do not exist, but have been hypothesised by physicists, allowing them to explore how these things would react if they were real.

Unlike atoms, photons do not normally interact with each other, but here they oscillated almost uniformly and at a critical point, as some photons leaked out into the surrounding environment, these oscillations began to produce quantum divergent behavior. The photons, in other words, could be in two states at once: a liquid and a solid. (Much like the famous Schrödinger's Cat thought experiment, in which a cat in a box is simultaneously both alive and dead.)

The current device has only two sites where light can be entangled with the artificial atom, but the researchers plan on scaling it up to allow more interactions and thus more complex systems – from a simple molecule to entire materials. They hope to then use this technique of solidifying light to study dissipation and decoherence from quantum systems – to simulate subatomic behavior, essentially, with tools developed for quantum computing.

Large numbers of particles are usually modeled statistically under the assumption that there's no interaction between particles and the system is at equilibrium. But, as the researchers note in their popular summary, "the world around us is rarely in equilibrium." The solidified light, by contrast, provides opportunities to observe such systems just as they diverge from equilibrium.

The researchers also hope to make the frozen light behave like more exotic forms of matter (like superfluids) and to mimic materials that have never been observed in nature (only hypothesized by physicists), perhaps leading to the development of room-temperature superconductors and other world-changing hypothetical materials that could have especially-dramatic consequences in computing, power generation, electronic storage, and many other areas.

"There is a lot of new physics that can be done even with these small systems," said James Raftery, a co-author on the study. "But as we scale up, we will be able to tackle some really interesting questions."

The research is described in a paper published in the journal Physical Review X.

Source: Princeton University

Source : https://newatlas.com/solid-light-quantum-mechanics/33865/

It may seem like such optical behavior would require bending the rules of physics, but in fact, scientists at MIT, Harvard University, and elsewhere have now demonstrated that photons can indeed be made to interact — an accomplishment that could open a path toward using photons in quantum computing, if not in light sabers.

In a paper published today in the journal Science, the team, led by Vladan Vuletic, the Lester Wolfe Professor of Physics at MIT, and Professor Mikhail Lukin from Harvard University, reports that it has observed groups of three photons interacting and, in effect, sticking together to form a completely new kind of photonic matter.

In controlled experiments, the researchers found that when they shone a very weak laser beam through a dense cloud of ultracold rubidium atoms, rather than exiting the cloud as single, randomly spaced photons, the photons bound together in pairs or triplets, suggesting some kind of interaction — in this case, attraction — taking place among them.

While photons normally have no mass and travel at 300,000 kilometers per second (the speed of light), the researchers found that the bound photons actually acquired a fraction of an electron’s mass. These newly weighed-down light particles were also relatively sluggish, traveling about 100,000 times slower than normal noninteracting photons.

Vuletic says the results demonstrate that photons can indeed attract, or entangle each other. If they can be made to interact in other ways, photons may be harnessed to perform extremely fast, incredibly complex quantum computations.

“The interaction of individual photons has been a very long dream for decades,” Vuletic says.

Vuletic’s co-authors include Qi-Yung Liang, Sergio Cantu, and Travis Nicholson from MIT, Lukin and Aditya Venkatramani of Harvard, Michael Gullans and Alexey Gorshkov of the University of Maryland, Jeff Thompson from Princeton University, and Cheng Ching of the University of Chicago.

Biggering and biggering

Vuletic and Lukin lead the MIT-Harvard Center for Ultracold Atoms, and together they have been looking for ways, both theoretical and experimental, to encourage interactions between photons. In 2013, the effort paid off, as the team observed pairs of photons interacting and binding together for the first time, creating an entirely new state of matter.

In their new work, the researchers wondered whether interactions could take place between not only two photons, but more.

“For example, you can combine oxygen molecules to form O2 and O3 (ozone), but not O4, and for some molecules you can’t form even a three-particle molecule,” Vuletic says. “So it was an open question: Can you add more photons to a molecule to make bigger and bigger things?”

To find out, the team used the same experimental approach they used to observe two-photon interactions. The process begins with cooling a cloud of rubidium atoms to ultracold temperatures, just a millionth of a degree above absolute zero. Cooling the atoms slows them to a near standstill. Through this cloud of immobilized atoms, the researchers then shine a very weak laser beam — so weak, in fact, that only a handful of photons travel through the cloud at any one time.

The researchers then measure the photons as they come out the other side of the atom cloud. In the new experiment, they found that the photons streamed out as pairs and triplets, rather than exiting the cloud at random intervals, as single photons having nothing to do with each other.

In addition to tracking the number and rate of photons, the team measured the phase of photons, before and after traveling through the atom cloud. A photon’s phase indicates its frequency of oscillation.

“The phase tells you how strongly they’re interacting, and the larger the phase, the stronger they are bound together,” Venkatramani explains. The team observed that as three-photon particles exited the atom cloud simultaneously, their phase was shifted compared to what it was when the photons didn’t interact at all, and was three times larger than the phase shift of two-photon molecules. “This means these photons are not just each of them independently interacting, but they’re all together interacting strongly.”

Memorable encounters

The researchers then developed a hypothesis to explain what might have caused the photons to interact in the first place. Their model, based on physical principles, puts forth the following scenario: As a single photon moves through the cloud of rubidium atoms, it briefly lands on a nearby atom before skipping to another atom, like a bee flitting between flowers, until it reaches the other end.

If another photon is simultaneously traveling through the cloud, it can also spend some time on a rubidium atom, forming a polariton — a hybrid that is part photon, part atom. Then two polaritons can interact with each other via their atomic component. At the edge of the cloud, the atoms remain where they are, while the photons exit, still bound together. The researchers found that this same phenomenon can occur with three photons, forming an even stronger bond than the interactions between two photons.

“What was interesting was that these triplets formed at all,” Vuletic says. “It was also not known whether they would be equally, less, or more strongly bound compared with photon pairs.”

The entire interaction within the atom cloud occurs over a millionth of a second. And it is this interaction that triggers photons to remain bound together, even after they’ve left the cloud.

“What’s neat about this is, when photons go through the medium, anything that happens in the medium, they ‘remember’ when they get out,” Cantu says.

This means that photons that have interacted with each other, in this case through an attraction between them, can be thought of as strongly correlated, or entangled — a key property for any quantum computing bit.

“Photons can travel very fast over long distances, and people have been using light to transmit information, such as in optical fibers,” Vuletic says. “If photons can influence one another, then if you can entangle these photons, and we’ve done that, you can use them to distribute quantum information in an interesting and useful way.”

Going forward, the team will look for ways to coerce other interactions such as repulsion, where photons may scatter off each other like billiard balls.

“It’s completely novel in the sense that we don’t even know sometimes qualitatively what to expect,” Vuletic says. “With repulsion of photons, can they be such that they form a regular pattern, like a crystal of light? Or will something else happen? It’s very uncharted territory.”

This research was supported in part by the National Science Foundation.

Jennifer Chu | MIT News Office

Source : https://news.mit.edu/2018/physicists-create-new-form-light-0215