Researchers realize a driven-dissipative Ising spin glass using a cavity quantum electrodynamics setup

Spin glasses are physical systems in which the small magnetic moments of particles (i.e., spins) interact with each other in a random way. These random interactions between spins make it impossible for all spins to satisfy their preferred alignments; a condition known as ‘frustration.”

Researchers at Stanford University recently realized a new type of spin glass, namely a driven-dissipative Ising spin glass in a cavity quantum electrodynamics (QED) experimental setup. Their paper, published in Physical Review Letters, is the result of over a decade of studies focusing on creating spin glasses with cavity QED.

“Spin glasses are a general model for complex systems, and specifically for neural networks—spins serve as neurons connected by their mutually frustrating interactions,” Benjamin Lev, senior author of the paper, told Phys.org.

“We’ve long wondered what sort of glasses and neuromorphic computational devices one could make by replacing classical spins with atomic spins and allowing them to interact via photons. How might quantum-optical and entangling effects enhance such devices? Our foray into this began in 2010 with a theory paper written with theorists Paul Goldbart and Sarang Gopalakrishnan (now at Stony Brook and Princeton, respectively).”

A promising cavity QED setup

While conducting their earlier theoretical studies, Lev and his colleagues had identified a new promising cavity QED setup, characterized by multiple frequency-degenerate modes. They realized that this setup, dubbed multimode cavity QED, could “wire up” atom-based spins to such an extent that it would frustrate their orientation into a glassy state.

“The new type of cavity QED could be used to realize associative memory, a canonical neuromorphic capability,” said Lev.

“Shortly after this realization, in discussions with Jonathan Keeling, we found that a particular ‘multimode-degenerate’ cavity geometry called a confocal cavity could make the spin glass practicable,” explained Lev. “Meanwhile, we began building the experiment and, in a series of papers beginning in 2015, benchmarked each of the steps needed to learn how multimode cavity QED works in practice.”

After several years of research, the researchers were able to mediate spin interactions in a spin glass leveraging cavity photons in their proposed multimode cavity QED system. This led to the realization of the very first spin glass in a quantum-optical setup.

“We were the first to report the direct experimental observation of replica symmetry breaking and the resulting ultrametric structure of all-to-all connected spin glasses from microscopic spin measurements,” said Lev. “However, we achieved this using a strange form of spin glass—that of XY spins interacting like XX–YY. To connect more directly with the literature of neural networks, we wanted to instead create a spin glass of canonical form, i.e., one that has Ising-interacting spins.”

Notably, the simple confocal cavity that the team used in their previous experiments would not allow them to engineer the photon-mediated interactions necessary to realize this new type of Ising spin glass. They collaborated with Keeling and Rhiannon Lunney, an undergraduate student that he was supervising at University of St. Andrews, to develop an alternative, exotic multimode cavity.

“In a paper published in 2019, we came up with a taxonomy for multimode cavities formed with two mirrors,” said Lev. “This allowed us to show that photon-mediated Ising interactions can be engineered using a multimode cavity configuration that we call a ‘4/7’ cavity (for the particular mode structure that makes up the resonator). A few years later, my team, led by former student Brendan Marsh, tuned the mirrors to this configuration and were able to realize the Ising spin glass reported in PRL.”

The realization of a new Ising spin glass

With the new multimode cavity setup they introduced, the researchers were able to realize a simpler (i.e., Ising) spin glass that was three times larger than the quantum-optical spin glass reported in their earlier work. In addition, they demonstrated the existence of replica symmetry breaking and ultrametricity in this system at a microscopic level as well.

“Moreover, we tripled the size of the spin glass from the n = 8 size of the Science paper to n = 25,” said Lev. “It was already not possible to numerically simulate the driven-dissipative, quantum-optical dynamics of the n = 8 system. However, n = 25 removes exact simulation much further from the realm of possibility, making the experimental system a unique platform for exploring the dynamics of intrinsically non-equilibrium glassy systems, for which no theory yet exists.”

The Ising spin glass realized by the researchers could be a promising platform both for conducting research studies and for developing new brain-inspired hardware components. Recently, the researchers successfully used their spin glass to create a so-called associative memory, which was previously thought to be impossible using glassy systems.

“This was predicted in our earlier theory work led by Marsh, and we showed that our spin glass can outperform the classic Hopfield model’s memory capacity by virtue of being made of atoms and photons,” said Lev. “But also—in an experimental surprise—we found that our quantum-optical Ising spin glass enables a form of short-term learning plasticity akin to what neuroscientists suggest might occur in our brains.”

In the Ising spin glass realized by the researchers, atoms are strongly coupled to each other by the light inside the multimode cavity and can be moved around by this light. The changing positions of these atoms enable the emission of light patterns that represent stored information from the cavity with far greater fidelity than if atoms were unable to move.

“A multimode cavity supports thousands of different spatial patterns of photons bouncing between the two mirrors,” explained Lev. “Normal cavities support just one, and that usually looks like a Gaussian wavepacket for the photons transverse to the cavity axis. In a multimode cavity, these spatial patterns superimpose to form a much more tightly localized wavepacket for the photons—whereas the Gaussian can be tens of microns wide for the photon, a multimode cavity supports modes that are less than two microns wide.”

An ideal platform for initiating spin interactions

The local mode that can be realized with the team’s setup, referred to as a “synthetic” or “supermode,” can prompt Bose Einstein condensates (BECs) that are trapped inside the cavity to behave as a collective spin-up or spin-down particle. The team was able to realize the desired spins leveraging this supermode.

“Microscopically, the ‘spin’ is just one of two checkerboard states—black or red—of a density wave that the atoms in the BEC form when light from the side of the cavity is shown upon them,” clarifies Lev.

After they realized the Ising spins, the researchers had to “wire them up,” prompting them to interact with each other. The multimode cavity they developed is ideal for initiating these spin interactions.

“These interactions naturally occur in a multimode cavity, because in addition to the tight-spot component of the supermodes, the modes also spread out every other round trip of the cavity to illuminate all the spins at once,” said Lev.

“Depending on the phase of this light at each spin, the spins are forced to either align or anti-align with all the other spins. That phase can be random if the BECs are spaced away from the cavity center, yielding a network of spin connectivity where every spin is coupled to every other spin with a randomly signed weight (due to the random light phases).”

The random spin interactions that emerge in the team’s cavity QED setup ultimately result in the geometric frustration of the spin states, producing a glass. The light illuminating the system then leaks out of the cavity and can be used to produce an image, employing the same strategy used to create holograms.

“The phase of the supermode spots emanated from each BEC tell us the ‘spin’ state of that BEC,” said Lev. “This means that we can read out the spin configuration of the entire network as it organizes into a glass.”

Informing research and neuromorphic hardware development

The team’s ability to read out the spin configuration of a glassy system in a cavity QED system is remarkable, as it has never been reported before.

“The key breakthroughs here are the two aspects of this new multimode cavity QED w/BECs instrument we created in the last few years, an active quantum gas microscope,” explained Lev. “This is like traditional quantum gas microscopes in that high NA optics (in our case these are mirrors rather than lenses) allow one to image quantum atomic gases on the length scale at which they interact but at the same time, the cavity mirrors reflect the photons back onto the atoms to engineer the interactions that drive system organization. In that sense, it’s active.”

Glasses are typically not in a state of equilibrium, as they can get stuck in metastable configurations (i.e., states that can remain stable for a long time but are not the lowest-energy states of a system). The cavity QED setup developed by the researchers enables the realization of glasses that are driven by photons and dissipate photons into the environment, thus extending even further from a state of equilibrium.

The new experimental platform introduced by Lev and his colleagues could soon advance the study of spin glasses, potentially shedding new light onto their underlying physics and how they are formed. In addition, the researchers plan to explore the potential of the driven-dissipative Ising spin glass introduced in their paper for the development of brain-inspired technologies.

“We uncovered a brand-new form of spin glass that hasn’t been explored before, even theoretically,” added Lev. “Our work now allows us to ask questions about its unique properties and capabilities for neuromorphic computation. We’re also moving toward making the spins behave more quantum mechanically so that we can create and explore a quantum-entangled spin glass.”

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