Twisting atoms through space and time

Twisting of atoms through space and time

In two experiments with ultracold atoms, the researchers explored the landscape of different topological shapes they could create in space and time. Credit: with edits by Dina Genkina/JQI

One of the most exciting applications of quantum computers will be to direct their gaze inward, to the very quantum rules that make them work. Quantum computers can be used to simulate quantum physics itself, and perhaps even explore areas that do not exist anywhere in nature.

But even in the absence of a fully functional large-scale quantum computer, physicists can use a quantum system they can easily control to emulate a more complicated or less accessible system. Ultracold atoms – atoms that are cooled to temperatures slightly above absolute zero – provide a state-of-the-art platform for quantum simulation. These atoms can be controlled with laser beams and magnetic fields, and persuaded to perform a quantum dance routine choreographed by an experimenter. It’s also quite easy to peer into their quantum nature using high-resolution imaging to extract information after or while they complete their stages.

Now, researchers from JQI and the NSF Quantum Leap Challenge Institute for Robust Quantum Simulation (RQS), led by former JQI postdoctoral fellow Mingwu Lu and graduate student Graham Reid, have trained their ultracold atoms to do a new dance, adding to the growing toolbox of quantum simulation. In a pair of studies, they warped their atoms, coiling their quantum mechanical spins in space and time before linking them together to create a kind of space-time quantum pretzel.

They mapped the meandering shape of spacetime they created and reported their results in a paper titled “Floquet Engineering Topological Dirac Bands” in the journal Physical examination letters last summer. In a follow-up experiment, they watched their atoms transition between different coiling shapes and found a rich structure inaccessible to single, stationary atoms. They published this result, entitled “Dynamically Induced Symmetry Breaking and Out-of-Equilibrium Topology in a 1D Quantum System”, in Physical examination letters in September.

The windings they studied are related to the mathematical field of topology – the classification of objects according to the number of holes they have. Donuts are topologically identical to hula hoops and coffee mugs since they each have a through hole. But donuts are distinct from eyeglass frames, which have two holes, or pretzels, which have three.

This deceptively simple classification of shapes has had a surprising impact in physics. He explained things like the quantum Hall effect, which produces a precisely repeatable electrical resistance used to set the resistance standard, and topological insulatorsthat could one day serve as components of robust quantum computers.

In physical environments, whether solid pieces of metal or ultracold atoms, the topology that physicists are interested in is not really related to the shape of the actual material. Rather, it is the shape taken by the quantum waves traveling through the material. Often physicists look at an intrinsic property of quantum particles called spin and how it twists as a particle speeds up or slows down in the solid piece.

Most solids are crystals, consisting of a regular grid extending in all directions in a repeating pattern of equidistant atoms. For free-floating electrons inside this grid, jumping from one identical atom to another makes no difference – the landscape is exactly the same as far as the eye can see. A similar grid appears in the velocity landscape of electrons – things may change as the electron starts to accelerate, but at certain speeds the landscape will look the same as if it weren’t moving at all.

But position and velocity are only two properties of the electron. Another is the spin. Spin can behave somewhat independently when position and velocity change, but when position is shifted by one site or velocity is shifted by one “site” of velocity, spin should remain unchanged – another reflection of the symmetry present in the crystal. But between two sites or two “sites” of speed, everything is allowed. The curvy shape that the spin draws before returning to its starting point is what defines the topology.

In the world of quantum simulation, ultracold atoms can emulate electrons in a crystal. The role of the crystal is played by the lasers, creating a repeating pattern of light for the ultracold atoms. The location and velocity of atoms similarly acquire a repeating pattern, and atomic spins trace shapes that define topology.

In their winding experiment, Lu and his lab mates designed a two-dimensional crystal, but not in the usual two dimensions of a sheet of paper. One of the dimensions was in space, like direction along a thin wire, while the other was time. In this sheet composed of space and time, the spin of their atoms drew a curious shape depending on the speed in the space-time crystal.

Twisting of atoms through space and time

Two laser configurations between which the researchers rhythmically switched to wrap their atoms in space and time. Credit: Mingwu Lu/JQI

“Topology is defined on surfaces,” says Ian Spielman, JQI Fellow, Principal Research Investigator and Associate Director of Research at RQS. “One of the surface-defining dimensions may be time. This has been known theoretically for some time, but only now is it being tested experimentally.”

To create a surface that would wrap in both space and time, the researchers shone lasers in two directions and a radiofrequency magnetic field from above onto their cloud of ultracold atoms. The lasers and magnetic field combined to create areas of higher and lower energy from which the atoms were repelled or attracted, like an egg box in which the atoms live. This carton had a special shape: instead of two rows of slots like in a normal dozen that you would find in a grocery store, there was only one row. And each box slot was made up of two sub-slots (see photo below). This gave the repeating crystal pattern along a line in space.

By adjusting how the lasers and magnetic fields align with each other, the team was able to move the entire pattern to the side of a sub-slit. But they didn’t just change it once. They rhythmically shook the egg carton back and forth in between. This rhythmic jolt created a repeating pattern over time, similar to the repeating spatial pattern of nuclei in a crystal.

To do this, they had to make sure their laser egg carton, as well as the timing of the strobe, was perfect. “The hardest part was finding the right time,” says Graham Reid, a graduate student in physics and one of the book’s authors. “This experience really relies on very precise timing of things that you don’t know a priori, so you just have to do a lot of tweaking.”

After many adjustments, however, they experimentally imagined the spin of the atoms in this spacetime crystal. They mapped the winding of the spinning as he traveled through both time and space to return to his starting point. In this way, they directly measured the sinuous topology they had constructed.

Following this work, they used the same laser pattern to do a very different experiment related to topology. Instead of looking at a topology in space and time, they focused only on the spatial dimension. This time, they prepared their atoms in different ways: all spinning, all spinning, or a mixture.

These were not natural, comfortable states for the atoms in the laser pattern they created, and eventually the atoms settled into their most natural states – their equilibrium states. But along the way, the researchers were able to capture still images of several different topological shapes, some of which would only occur for a moment. These results have revealed new mysteries that researchers are eager to investigate.

“There are two big questions that I think would be good to answer,” Spielman said. “The first is that the spatial and temporal topology result only really worked at a specific time. I wonder if there is a way to make this robust. Second, for the non-equilibrium topology, I I’m interested to see what happens when we quickly switch between a wider variety of topological states.”

In addition to Spielman, who is also a fellow at the National Institute of Standards and Technology, Reid, and Lu, who is now at Atom Computing, authors of the papers included Amilson Fritsch, a former postdoctoral fellow at JQI now at the University of Sao Paulo Sao Carlos, and Alina Piñeiro, graduate student in physics at JQI.

More information:
Mingwu Lu et al, Floquet Engineering Topological Dirac Bands, Physical examination letters (2022). DOI: 10.1103/PhysRevLett.129.040402

GH Reid et al, Dynamically induced symmetry breaking and non-equilibrium topology in a 1D quantum system, Physical examination letters (2022). DOI: 10.1103/PhysRevLett.129.123202

Quote: Torsion of Atoms Through Space and Time (2023, Jan 23) Retrieved Jan 23, 2023 from

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