• Carrie Weidner

Simulating the Quantum World

Carrie Weidner, PhD Aarhus University, Denmark

When her friends ask what I do for a living, my mom tells them that I “freeze atoms.”

She is not too far off from the truth. Indeed, the experiment I work on in the basement of Aarhus University’s physics building could be described as a glorified freezer. I have used these very words when giving lab tours to those outside of the field of cold atom physics.

That’s right, a lab. An experimentalist has invaded the theory girls. (Run!)

I spent a lot of time thinking about what I wanted to write here. In many ways, writing a coherent, informative, and engaging blog post is much harder than writing a research paper. Or is it? For a research paper, my colleagues and I present our idea, its background, and then we describe what we did. Sprinkle in a bit of an outlook and you have a reasonable first draft. Why not do that here?

Let’s start with my background, then we can get to the fun stuff.

Who am I?

I’m a postdoctoral researcher in experimental cold atom physics at Aarhus University in Denmark. I’m originally from Austin, Texas, and I did all of my university education at the University of Colorado at Boulder. Eventually, they gave me a PhD and I found a job out here doing what I would call quantum control and simulation. When people ask me (not my mom) what I do for a living, I typically tell them that I shoot lasers at things, very carefully.

The author, very pleased with how the experiment is functioning.

Wait. What?

Okay. Let’s break this down.

The fun stuff (as promised)

Quantum mechanics deals with things at very small scales. In my particular subfield, I deal mostly with atoms and their interaction with electromagnetic fields. A few decades ago, a lot of work was done to understand how to cool bosonic atoms to within billionths of absolute zero (this is known as a Bose-Einstein condensate, or BEC). Since that wasn’t hard enough, physicists decided to cool fermions too (it turns out the sign problem that fermions give rise to requires folks to be a bit more clever about how to get such atoms to do their bidding). The next logical step is molecules, so researchers are hard at work understanding the intricacies of molecular cooling and trapping (find a description of some of these molecular cooling techniques here).

This is all cool stuff (pun absolutely intended), but it’s not my shtick, at least not right now. I work with one of the simplest atoms, not named hydrogen, one can play with. Rubidium was one of the first atoms condensed into a BEC, and it’s laughably simple to work with compared to the exotic tricks required for more complex atomic and molecular systems. Rubidium is still a super useful atom to play with, though, so it remains one of the workhorses of cold atom physics.

Indeed, what we do in our basement is known as quantum gas microscopy. Simply put, we make BECs of rubidium and trap them in light fields generated by a laser. It’s like a tractor beam for atoms, and that sci-fi analogy never gets old. Even better, if I take a laser beam and reflect it back onto itself, it interferes with itself to make a very nicely ordered pattern of alternating light and dark spots, and I can trap the atoms in the light spots. We call such a trap an optical lattice. Play the same game in three dimensions with three sets of laser beams, and you have a three-dimensional array of atom traps. This takes a lot of precision and control, so I truly do make a living shooting lasers at things very carefully!

An illustration of an optical lattice in one dimension. A laser (wavelength λ, red)

hits a mirror (right side of image) and reflects back on itself, creating a sinusoidal

interference pattern of nodes (no light) and anti-nodes (with light). The period of

the sinusoidal pattern (a) is half of the laser wavelength, and we typically describe

the depth of the resulting atom trap in terms of a parameter labelled here by V.

In a 3D lattice, we overlap these optical lattices created from lasers coming from

all three spatial dimensions.

The atoms can then be trapped in this 3D lattice like eggs in an egg carton, but even that is a bit of an oversimplification. In fact, if we have an infinite lattice, Bloch’s theorem says that the ground state of the system is delocalized in that a trapped atom effectively samples each lattice site. Thus, the atoms act a lot more like broken eggs in an egg carton. We call this a superfluid.

If you make this lattice deep enough and the atoms cold enough, the atoms will start to act more and more localized--like whole, intact eggs. This describes what is known as a Mott insulator, a term lifted from condensed matter physics. If we then trap these atoms close to a microscope objective, we can take incredible images with single-lattice-site resolution. If we build a Mott insulating state with precisely one atom per lattice site, we can get incredible images of single atoms. This enables us to study an incredible variety of systems, and this has given rise to the field of quantum simulation.

An image taken with the Aarhus quantum gas microscope. The purple dots are

single rubidium atoms, and their color is indicated by the number of photons

that we collect from each atom.

What is quantum simulation?

The idea here is straightforward: given a system that is relatively hard to study, like electrons in a solid (here, fermions do a better job of this than our good bosonic friend rubidium) or photons in a light-harvesting complex, we can set up analogous systems in relatively easy to study systems, and ideally, conclusions drawn from experiments with these simpler systems can be mapped onto the more difficult system. Cold atom systems are fantastic for these types of studies. Cold atoms are slower and easier to control than electrons (and certainly slower than photons), and with each passing year, researchers are pushing the technologies and techniques behind this control, allowing for extraordinarily precise experiments that simulate more and more complex systems.

We call these types of quantum simulators analog quantum simulators. This is in comparison to digital quantum simulators. You may know the latter of these by their more popular name, quantum computers. That’s right. Given enough qubits (the quantum analog to a bit) with low enough noise, quantum computers are universal in that they can simulate any quantum system. This could lead to serious advances in the understanding of high-temperature superconductivity and quantum chemistry, among many others. I chose the above two examples because they have potentially deep technological implications that could help us improve sustainability and health. Of course, concrete solutions are a long way off, but it’s always fun to dream. Personally, knowing potential applications of my research, even if the road is long, winding, and bumpy, has always been a huge motivator for me.

Okay, I just spent the whole last paragraph telling you about how cool digital quantum simulation is, but I only have an analog quantum simulator. Analog simulators are not (necessarily) universal, and indeed, systems like the one we have in Aarhus are limited in terms of the systems that can be simulated. Why on Earth would we study these sub-par simulators?

Well, right now, they’re not sub-par at all. Currently, the best quantum computers that we have exist firmly in the noisy, intermediate-scale qubit (NISQ) regime. Basically, we don’t have a lot of qubits to play with, and the ones we have are riddled with errors. As such, it’s really hard to get useful results out of these systems, even though researchers are becoming increasingly clever at getting these systems to perform as well as possible. Analog quantum simulators are great tools because they are relatively robust to errors. Basically, if you have a good enough analog simulator that captures the important bits of what you are trying to model, you can set the system up and let it run. What you get out when you make appropriate measurements (e.g. of where your atoms are) should be what you expect, given that your lasers and atoms are behaving the way they should. This will allow researchers to make great headway on relevant problems in the field (like high-Tc superconductivity) while we simultaneously work to make quantum computers better and better.

What do we do?

In Aarhus, our experiment is still young. It’s still a bit of a teenager--moody and temperamental. We’re working hard to bring it to the maturity that we need to study the systems that we are interested in. We have wonderful pictures of single atoms in a 3D lattice that were taken with our microscope, and, when everything is complete, we want to study how atoms behave in two- and three-dimensional systems. We want to watch atoms hop around in our lattice, and we want to control how they move and interact. To do this, we will project light (another tractor beam!) up through our microscope objective and onto the atoms. The atoms will “see” this light as an additional potential, and this additional potential will affect how the atoms interact with one another and move through the lattice. These are the knobs we have to turn when we build our simulations, and until we have a quantum computer that can simulate any system we want, these types of analog quantum simulators will get a lot of use in laboratories around the world.

How does this additional tractor beam work? How do we shape the traps that the atoms experience? To do this, we use a digital mirror device, or DMD. DMDs are a special example of experimental tools known as spatial light modulators. Other spatial light modulators work by using sound waves to change how light moves through crystals (these are known as acousto-optic deflectors), and some use liquid crystal technology to manipulate the polarization and amplitude of light. A DMD is basically an array of very small mirrors, about 10 µm in size (smaller than the width of a human hair). Each of these mirrors is individually controllable and can be set to be either on or off, so we basically have a binary image that we can load onto the mirrors. Then, we hit the mirrors with our laser light, and the mirrors that are set to the on state reflect the light, and the reflected light then travels up through the microscope objective and into the system. By controlling the mirror pattern, we can control what gets projected through the microscope objective. Incidentally, this is exactly how projectors work!

A schematic showing how we collect light from the atoms and use the DMDs to project

potentials onto the atom. (a) A cartoon of the experiment, showing the science chamber, the

high-resolution microscope objective (oddly colored like a cigarette), and the digital mirror

device. Light from the atoms l(called fluorescence light) bounces off of a dichroic (two-color)

mirror and goes to a camera that records how many photons hit each pixel. Projection light

from a laser hits the DMD, passes through the dichroic mirror, land is projected onto the

atoms. The DMD pattern is controlled by a black-and-white llbitmap that we upload to the

DMD chip. (b) Zoom-in on the DMD, showing the individual mirrors that can be individually

manipulated to pointl in one of two directions (corresponding to an on state and an off state).

(c) The pattern shown on the computer in (a) produces the image shown here, which we like

to call atomic luv. You can see single atoms in this image too!

Our DMD patterns are limited by the size of the beam that we can project onto the atoms, but we still have a massive range of potential systems that we can simulate. Most of these possible systems are ones that we probably haven’t even thought about yet, and that’s okay! As we make our experiment better and better, we will uncover more and more systems that it is capable of simulating, and there will be no end to the science that we can produce.

In conclusion...

The work that my colleagues and I do isn’t limited to experiments. We like to play with theoretical quantum control. We’ve even shown recently that AlphaZero, a state-of-the-art machine learning algorithm, can be used to optimize gates for quantum computers. We like to play games with science, both inside and outside the quantum world, including an awesome project where we opened our laboratory up for citizens and experts to play in--remotely!

To me, this versatility is one of the best things about working as a physicist. With a physics degree, you have learned the skills to think and work through difficult problems. Physicists can learn to work and play in any environment, inside or outside of academia. This post has illustrated a bit of the playground that I have chosen, but it is only one option in an infinite space of interesting and useful arenas where a physicist can ply their trade.

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