One of the most exciting applications of quantum computers is turning their gaze inward. So it’s the very quantum rules that drive them. Quantum computers can be used to simulate quantum physics itself, and perhaps even explore areas that exist nowhere else in nature.
But even without a fully functioning large-scale quantum computer, physicists can use easily controlled quantum systems to emulate something more complex or less accessible. Ultracold atoms (atoms cooled to just above absolute zero) are a prime platform for quantum simulations. These atoms can be controlled with laser beams and magnetic fields, and can be induced to perform quantum dance routines choreographed by the experimenter. Also, quantum nature can be easily investigated by extracting information using high-resolution imaging after or while the steps are completed.
Currently, researchers at JQI and the NSF Quantum Leap Challenge Institute for Robust Quantum Simulation (RQS), led by former JQI postdoc Mingwu Lu and graduate student Graham Reid, are teaching ultracold atoms a new dance and developing a growing toolkit. Added to of quantum simulation. In two studies, they bent atoms out of shape, winding up their quantum-mechanical spins in both space and time, then tied them together to create a kind of spatio-temporal quantum pretzel.
They mapped the curvilinear space-time shapes they created and reported the results in an article in the journal titled “Floquet Engineering Topological Dirac Bands.” physical review letter last summer. In follow-up experiments, they observed atoms transitioning between various serpentine shapes and discovered an abundance of structures inaccessible to simple, stationary atoms. They published this result titled “Dynamically induced symmetry breaking and out-of-equilibrium topologies in 1D quantum systems”. physical review letter in September.
The windings they studied relate to the mathematical branch of topology, the classification of objects according to the number of holes. Donuts are topologically identical to hula hoops and coffee mugs because each has a single through hole. But a donut is different from a spectacle frame with two holes or a pretzel with three holes.
This seemingly simple classification of shapes has had an amazing impact on physics. It describes things like the quantum Hall effect, which produces precisely reproducible electrical resistances used to define resistance criteria, and topological insulators, which may one day serve as components of robust quantum computers.
In a physical setting, whether it’s a clump of metal or an ultracold atom, the topology that physicists care about has little to do with the actual shape of matter. Rather, it is the shape that a quantum wave takes as it travels through matter. Physicists often study a unique property of quantum particles called spin and how the spin rotates when the particle accelerates or decelerates within a solid mass.
Most solids are crystalline, consisting of a regular grid extending in all directions with a repeating pattern of evenly spaced atoms. For free floating electrons in this grid, jumping from one atom to another identical atom makes no difference. The landscape is exactly the same as far as the eye can see. A similar grid appears in the electron velocity landscape. Things can change when the electrons start accelerating, but at a certain speed, the landscape looks as if it’s not moving at all.
But position and velocity are just two properties of electrons. Another is spin. Spin can behave somewhat independently with changes in position and velocity, but if position shifts by one site or velocity shifts by one velocity “site”, spin remains unchanged. I have to. This is another reflection of the symmetry that exists in crystals. But anything between two sites or two speed “sites” is fine. The serpentine shape that the spin draws before returning to its original position defines the topology.
In the world of quantum simulation, cryogenic atoms can emulate electrons in crystals. The role of the crystal is played by a laser, creating a repeating pattern of light for the cryogenic atoms to inhabit. Atomic positions and velocities likewise acquire repeating patterns, and atomic spins trace the shape that defines the topology.
In the hoisting experiment, Lu and his lab mates devised a two-dimensional crystal, but not the usual two-dimensional one of a sheet of paper. One dimension was in space, like directions along a thin thread, and the other was time. In this sheet composed of space and time, the spin of the atoms plotted strange shapes as a function of the velocity of the atoms in the spatio-temporal crystal.
“Topology is defined by the surface,” says JQI Fellow Ian Spielman, principal investigator of the study and RQS’s Associate Director of Research. “One of the surface-defining dimensions could be time. This has been known in theory for some time, but is now only being tested experimentally.”
To create a surface that is tortuous in both space and time, the researchers shot lasers from two directions and hit a cloud of ultracold atoms with a radio-frequency magnetic field from above. A combination of lasers and magnetic fields created regions of high and low energy in which atoms were pushed and attracted, like egg packs for atoms to live inside. This carton had a unique shape. He had only one row of slots instead of two rows of slots like the usual dozen you find in the grocery store. Each slot in the carton consisted of two sub-slots (see diagram below). This resulted in a crystal-like pattern that repeated along lines in space.
By adjusting how the laser and magnetic field align with each other, the team was able to move the entire pattern sideways by one subslot. But I didn’t switch just once. They rhythmically shook the egg carton back and forth between the two.
To do this, I had to make sure the laser egg carton and strobe timing was right. “The hardest part was getting the timing right,” says his Graham Reid, a physics graduate student and one of the study’s authors. “This experiment relies on very precise timing that is not known a priori, so we have to make a lot of adjustments.”
However, after much fine-tuning, they experimentally imaged the spins of atoms within this spatio-temporal crystal. They mapped the tortuous spin as it traverses both time and space and returns to its starting point. In this way they directly measured the winding topology they built.
Following this work, they performed very different topology-related experiments using the same laser pattern. Instead of looking at the topology of space and time, they focused on spatial dimensions only. This time they prepared the atoms in different ways. All spin down, all spin up, or mixed.
These weren’t natural and comfortable conditions for the atoms in the laser patterns they created, and eventually the atoms settled into a more natural state, a state of equilibrium. But in the process, the researcher was able to capture his frames of friezes of several different topological shapes. These results reveal new mysteries that researchers are eager to investigate.
“There are two big questions that would be great if we could answer them,” says Spielman. “The first is that the spatial and temporal topology results really only worked with fine-tuned timing. I’m wondering if there’s a way to make it robust. Second. are interested in seeing what happens for non-equilibrium topologies, where we can quickly switch between different topological states.”
In addition to Spielman, who is also a National Institute of Standards and Technology Fellow, Reid, and Lu, who is now at Atom Computing, the authors of the paper include Amilson Fritsch, a former postdoc at JQI and now at the University of JQI, Sao Paulo. San Carlos, and Alina Pinheiro, a JQI physics graduate student.
For more information:
Mingwu Lu et al., Floquet Engineering Topological Dirac Bands, physical review letter (2022). DOI: 10.1103/PhysRevLett.129.040402
GH Reid et al, Dynamically induced symmetry breaking and out-of-equilibrium topologies in 1D quantum systems, physical review letter (2022). DOI: 10.1103/PhysRevLett.129.123202
Courtesy of Joint Quantum Institute
Quote: Twisting Atoms Across Spacetime (23 Jan 2023) Retrieved on 23 Jan 2023 from https://phys.org/news/2023-01-atoms-space.html
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