New Glasses, More Memories

By Benjamin Lev

Professor of Physics and Applied Physics

Among the grand unsolved challenges of physics—quantum gravity, dark matter and energy, and high-temperature superconductivity—the glassy ordering and aging of frustrated and disordered systems seems out of place. Glasses are, after all, an everyday material. Yet they relate to a bigger question regarding how the physics of complex systems can be generally described from microscopic details. This is no idle inquiry: Concepts from (spin-)glass theory helped shape large language models like ChatGPT. Indeed, for this past year’s Nobel Prize in Physics, John Hopfield showed that a frustrated network of spins, acting as a recurrent neural network, can exhibit a brain-like function, associative memory. Certainly the humble glass belongs among the grand mysteries of physics.

A key glass problem concerns order. We normally think that rigidity—the hallmark of order—arises because of a broken symmetry. When a liquid crystallizes, it forms an ordered lattice that breaks translational symmetry; the resulting solid resists deformation. However, a glass defies this expectation: While it becomes rigid like a solid, its molecules remain in random locations like a liquid. What symmetry is broken?

Some progress was made starting in the late 70’s when Giorgio Parisi, among others, considered not the structural glass, but a magnetic version composed of spins. The network of spins (pointing up or down) interact via the magnetic field they cast upon each other. A ferromagnet arises at low temperature if all spins are coupled so that they want to mutually align. However, if some pairs want to align while others want to antialign, then one obtains a spin glass due to frustration—not all bonds can be satisfied. The configuration of spins is a random string of up and down orientations. Unlike the paramagnet, these orientations are “frozen” in place (though in reality they may very slowly evolve—another mystery). While spin glasses are not very exotic—they can be made by doping copper with manganese—Parisi found that their order is very strange. It cannot be fully discerned from a single sample’s random spin configuration. Rather, one must compare exact copies, or “replicas” of the sample, and observe correlations among their spin configurations.

Sketch of the quantum-optical spin glass and memory recall process. a) Transverse and longitudinal fields (light blue) pump the cavity. A digital micromirror device (DMD) scatters the longitudinal pump into 16 beams that program an initial (stimulus) spin pattern. Each atomic gas within the cavity midplane can carry an either up (blue) or down (orange) spin. (Optical tweezer traps not shown.) A camera holographically images the state of the spins from the emitted cavity field. b) Example stimulus field pattern. Spin-flip errors compared to memory 1 are circled in red. c) Memory recall dynamics in a low-dimensional representation of a spin-glassy energy landscape versus spin configuration. Red arrow indicates gradient descent from the corrupted stimulus pattern (red dot) in panel (b) to the memory pattern 1 at the bottom of the memory 1 valley. d) Cavity output image showing spins after successful recall of memory 1, starting from the stimulus field in panel (b). This figure adapted from Marsh et al., 2025.

Imagine each spin configuration residing at the bottom of a valley like in the figure. The height of the peaks are the energy barriers between each valley and spatial distances measure spin configuration differences. While a ferromagnet has only two valleys (all up or all down), a spin glass has an exponential number of valleys. A system may be initialized at the same peak, but noise—thermal or quantum—will cause it to evolve into different valleys as one lowers the temperature. Thus, exact replicas may yield different spin configurations, or states of the glass. This illustrates Parisi’s famous discovery that replica symmetry breaking” (RSB) is the broken symmetry—low-energy replica states are not the same. He won 2021’s Nobel Prize in Physics for showing that RSB results in a peculiar order: Spin pattern correlations between these replicas arise in an “ultrametric” fashion that can be visualized as a family-tree-like structure. While crystals exhibit lattice order, spin glasses have ultrametric order among replicas. Although this is a very abstract concept, ultrametric organization appears in models and data analyses beyond spin glasses—e.g., in turbulence cascade models and in certain ecological and biological hierarchies. Ultrametric concepts have also been applied to climate-indicator datasets. (Parisi’s co-winners are climate scientists.)

However, ultrametric structure has never been experimentally seen from microscopic spin measurements. Our group has now done so, by creating a spin glass made of atoms and photons in our lab. Arrays of tightly focused laser “tweezers” trap up to 25 separate ultracold gases of atoms at locations between two mirrors. Each gas serves as a spin. The mirrors trap photons by forming an optical cavity. The cavity supports many spatial photon modes all at the same frequency, allowing compact wavepackets of photons to bounce between atomic clumps via mirrors. The photons implement network weights by connecting the atoms and causing them to interact like spins coupled with magnetic fields. Spin frustration ensues, creating a glass. We can directly measure spin configurations (and thus ultrametric correlations) by taking holographic images of cavity light emission.

Capitalizing on the close connection between spin glasses and neural networks, we used this system to create the first quantum-optical associative memory. Such devices allow one to recall a memory based on imperfect input information. For example, one may want to remember the face of a friend based on a blurry photograph. Successful associative memory outputs the unblurred image. We discovered that a quantum-optical neural network (i.e., one made with atoms and photons) improves upon Hopfield’s model by allowing memory capacity to be increased at least seven-fold. Moreover, because the atoms can be pushed around by the photons, our device naturally realizes a form of plasticity, akin to the neural “rewiring” that allows our brains to learn.

The abovementioned spin glasses are networks with every spin affecting every other spin. But tangible spin glasses are nearest-neighbor in coupling. The jury is still out on whether Parisi’s RSB explains how these “short-range” spin glasses order, or whether completely different theories apply, like those of Daniel Fisher here at Stanford. We hope to shine (quantum-optical) light on this decades-old mystery.

Meanwhile, our spin glass has (driven-dissipative) dynamics like none other—it is truly a new form of complex matter. Does it age like a normal glass, or does it evolve under rules we have yet to discover? And can we scale up our 25-bit associative memory to one that is technologically competitive? What happens when quintessentially quantum effects like spin entanglement come into play? Would they further enhance memory capacity and recall fidelity? Stay tuned…

For more: LevLab.Stanford.edu. Professor Benjamin Lev is a quantum physicist, with primary research interests at the interface of ultracold atomic physics, quantum optics, and condensed matter physics.