Human spatial sense does not extend outside the well-known three dimensions, but that does not prevent researchers from exploring whatever lies outside.
Physicists at Rice University are attempting to extend spatial boundaries in new experiments. They have learned to regulate electrons in massive Rydberg atoms with such precision they can form “synthetic dimensions,” vital tools for quantum simulations.
The Rice team formulated a method to engineer the Rydberg states of ultracold strontium atoms by using resonant microwave electric fields to couple numerous states together. A Rydberg state happens when one electron in the atom is energetically bumped up to an extremely excited state, supersizing its orbit to transform the atom thousands of times larger than usual.
Ultracold Rydberg atoms are approximately a millionth of a degree above absolute zero. By precisely and flexibly working the electron motion, Rice Quantum Initiative scientists coupled lattice-like Rydberg levels in ways that mimic characteristics of real materials. The methods could also help develop systems that cannot be realized in real three-dimensional space, forming a robust new platform for quantum studies.
Rice physicists Barry Dunning, Tom Killian and Kaden Hazzard, all members of the initiative, explain the research along with lead author and graduate student Soumya Kanungo in an article published in the journal Nature Communications. The study is founded on earlier work on Rydberg atoms that Killian and Dunning first investigated in 2018.
Rydberg atoms comprise numerous recurrently spaced quantum energy levels, which can be coupled by microwaves that enable the highly excited electron to travel from level to level. Dynamics in this “synthetic dimension” are mathematically corresponding to a particle traveling between lattice sites in a real crystal.
“In a typical high school physics experiment, one can see light emission lines from atoms that correspond to transitions from one energy level to another,” said Hazzard, an associate professor of physics and astronomy who proved the theoretical basis for the research in several earlier articles. “One can even see this with a very primitive spectrometer: a prism,” Hazzard continued.
What is new here is that we think of each level as a location in space. By sending in different wavelengths of light, we can couple levels. We can make the levels look like particles that just move around between locations in space. That’s hard to do with light—or nanometer-wavelength electromagnetic radiation—but we’re working with millimeter wavelengths, which makes it technically much easier to generate couplings.
Kaden Hazzard, Associate Professor of Physics and Astronomy, Rice University
“We can set up the interactions, the way particles move and capture all the important physics of a much more complicated system,” said Killian, a Rice professor of physics and astronomy and dean of the Wiess School of Natural Sciences.
“The really exciting thing will be when we bring multiple Rydberg atoms together to create interacting particles in this synthetic space,” he said. “With this, we’ll be able to do physics that we can’t simulate on a classic computer because it gets complicated very quickly.”
The scientists showed their methods by engineering a 1D lattice referred to as a Su-Schrieffer-Heeger system. To create it, they employed lasers to cool strontium atoms and applied microwaves with alternating weak and strong couplings to form the appropriate synthetic landscape. A second set of lasers was employed to stimulate atoms to the manifold of coupled, high-lying Rydberg states.
The experiment exposed how particles travel through the 1D lattice or, in certain cases, are frozen at the edges even though they have sufficient energy to travel, Killian said. This relates to material features that can be illustrated in terms of topology.
It is much easier to have control over coupling amplitudes when using millimeter waves to couple Rydberg atomic states. When we achieve that 1D lattice, with all the couplings in place, we can try to see what dynamics would result from exciting a Rydberg electron into that synthetic space.
Soumya Kanungo, Study Lead Author and Graduate Student, Rice University
“Using a quantum simulator is kind of like using a wind tunnel to isolate the small but important effects that you care about among the more complicated aerodynamics of a car or airplane,” Killian said. “This becomes important when the system is governed by quantum mechanics, where as soon as you get more than a couple of particles and a few degrees of freedom, it becomes complicated to describe what’s going on.
“Quantum simulators are one of the low-hanging fruits that people think will be early, useful tools to come out of investments in quantum information science,” he said, noting that this experiment integrated methods that are now fairly regular in labs that investigate atomic physics.
All the technologies are well-established. You could even conceive of this becoming almost a black box experiment that people could use, because the individual pieces are very robust.
Tom Killian, Professor of Physics and Astronomy and Dean of Wiess School of Natural Sciences, Rice University
Co-authors of the study are postdoctoral researcher Joseph Whalen and graduate students Yi Lu and Sohail Dasgupta of Rice, and graduate student Ming Yuan of Rice and the University of Chicago. Dunning is the Sam and Helen Worden Professor in the Department of Physics and Astronomy.
This research was supported by the Air Force Office of Scientific Research (FA9550-17-1-0366), the National Science Foundation (1904294, 1848304), and the Robert A. Welch Foundation (C-0734, C-1844, C-1872).
Kanungo, S., et al. (2022) Realizing topological edge states with Rydberg-atom synthetic dimensions. Nature Communications. doi.org/10.1038/s41467-022-28550-y.