Down the Escher staircase and into the quantum realm

Scientists at the University of Illinois Urbana-Champaign have built a cutting-edge quantum simulator using synthetic dimensions that are represented by internal states of an atom, such as angular momentum or spin. Illinois Physics Professor Jacob Covey and his team are applying this novel approach to reproduce small-scale quantum phenomena, enabling the study of previously unobserved quantum systems. Their work has strong implications for quantum information science.

Covey’s team—Illinois Physics postdoctoral student Chenxi Huang, Illinois Physics Professor Bryce Gadway, now a Professor at Penn State, and Illinois Physics postdoctoral researcher Tao Chen, now a postdoctoral student at Penn State—has published its findings in the journal Physical Review Letters.

Quantum simulation gives scientists insights into the properties of quantum systems too complex to model by hand or on a classical computer. Physicists build special-purpose simulators that allow them to observe dynamics analogous to the quantum phenomena of interest.

“It is not always easy to calculate the properties a quantum system might have, so it is helpful to emulate that physical system with another physical system that you can control,” explains Covey.

The team’s work takes advantage of synthetic dimensions. Through a mathematical perspective, the motion of a particle through real space can be mapped to that of a particle moving through a synthetic space. In Covey’s experiment, the synthetic dimensions are the excited states of the Rydberg atom—which can be thought of as discrete orbits around the nucleus of the atom. An electron moving up an energy level is analogous to an electron moving over a site in real space on a lattice. The team uses microwaves to add energy to the system, which gives them precise control over which sites the electron moves between.

Covey notes, “You could imagine having four sites in synthetic dimensions labeled 1, 2, 3, and 4.  In real space you can move an electron between nearest neighbors, for example from site 1 to 2. In synthetic space, we have the ability to drive any microwave field we want, so we can move an electron from site 1 to 3 or site 1 to 4.”

At the frontier of quantum simulation, this experimental setup uses two optical traps that each contain one atom, and each atom uses up to nine Rydberg states.

“In this new experimental platform, using more than two Rydberg states in an atom is fairly new,” says Covey. “Especially in this controlled way where we can have more than one atom very well characterized and held in an array of optical traps.”

Typically, quantum simulation involves particles that do not interact strongly, such as photons, because they are easier to control. In this experiment, the use of two Rydberg atoms, which do strongly interact, allows the team to capture the more complex dynamics of strongly interacting quantum particles. These dynamics diverge significantly from single-particle physics.

“A major breakthrough of this work is that we are able to go to the strong interaction regime,” says Chen, who is first author on the study.

As proof of principle, in the first step of the experiment, the team verified that in the single-particle case, the quantum properties in synthetic dimensions exactly match previously observed results in real dimensions. For example, the team found that the dynamics of a quantum walk—where an electron explores all the discrete sites of a space—matched experimental observations.

Next, the team took advantage of synthetic dimensions to create geometries that cannot exist in real space. One such geometry is the Escher staircase, an optical illusion where a particle continuously steps down a staircase but stays on the same plane (Escher depicted the illusion in his 1960 lithography “Upstairs and Downstairs”). In real space, there is a gap between the top and bottom stair that is hidden to the eye. In synthetic dimensions, particles move down excited states of the Rydberg atom—“steps”—losing some fixed energy each time they take a step down. The geometry is warped such that moving from the bottom step to the top step requires the same amount of energy as moving down a single step. Thus, the particle can perpetually step down while staying in a closed loop.

Having explored single-particle dynamics in the synthetic lattice, the team turned their focus to correlated dynamics—quantum phenomena emerging from the strong interactions of particles.

For each Rydberg atom, the team shifted the energy—or detuned—the excited states such that they are slightly greater than their original energy levels. Using only a single Rydberg atom, the electron is not able to move up the excited states, because it cannot reach the heightened energy level. However, when two Rydberg atoms interact and their interaction energy is near the energy of the detuning, the electrons are able to hop up the excited states together. The team coined a term for this new phenomenon: “pair-hopping.”

As their next step, the Covey group aims to further improve their experiment to observe more correlated quantum physics.

“We want to make some technical upgrades that will allow us to go to even larger synthetic dimensions. We currently use up to twelve. In principle, it should be possible to go an order of magnitude larger than that,” says Covey. The group also plans to speed up the rate at which electrons hop through sites in their simulation.

With these future upgrades, the team plans to further explore complex quantum phenomena by simulating these emergent systems for the first time.

This work was supported by National Science Foundation under grant No. 1945031 and the AFOSR MURI program under agreement number FA9550-22-1-0339. The findings presented are those of the researchers and not necessarily those of the funding agencies.