About

Benjamin Lev is a Professor of Physics and Applied Physics at Stanford University. He received his Bachelor’s degree Magna Cum Laude from Princeton University in 1999 and his Ph.D. from the California Institute of Technology in 2005, both in Physics. His academic journey includes a National Research Council postdoctoral position at JILA and an Assistant Professorship at the University of Illinois at Urbana-Champaign before joining Stanford in 2011, where he is now a Full Professor. His research focuses on exploring quantum many-body physics, including quantum neural networks, utilizing techniques at the interface of ultracold atomic physics, quantum optics, and condensed matter physics. Benjamin Lev has been recognized with numerous awards, such as a Packard Foundation Fellowship, the Presidential Early Career Award for Scientists and Engineers (PECASE) from President Obama, NSF CAREER award, and awards from the Air Force Office of Scientific Research, DARPA, and the Office of Naval Research. His research has been funded by various agencies including the NSF, DOE, ARO, AFOSR, ONR, DARPA, NTT, and the Moore Foundation.

Research topics

• Quantum mechanics
• Physics
• Computer Science
• Atomic physics
• Computer architecture
• Condensed matter physics

Selected publications

• Superradiant Charge Density Waves in a Driven Cavity-Matter Hybrid

  arXiv (Cornell University) · 2026-03-30

  preprintOpen access

  Optical cavities enable strong, long-range, light-matter interactions that can drive collective ordering phenomena, such as superradiant self-organization in ultracold atomic gases. Extending these ideas to solid-state electron systems could enable continuous-wave optical control of electronic order, but is impeded by the mismatch between optical wavelengths and electronic length scales. Here, we propose a platform for realizing superradiant charge density waves (sCDWs) in doped, driven transition-metal dichalcogenides coupled to an optical cavity. A nanoscale grating generates electric fields at large in-plane optical momenta, allowing cavity photons to couple efficiently to electronic density fluctuations through exciton-polaron processes. Using a linear-stability analysis, we determine the threshold for superradiant ordering and map out the driven phase diagram. We show that tuning the grating periodicity to match the enhanced electronic density fluctuations - such as those near Wigner crystallization - substantially lowers the required pump intensity. Our results establish a novel route toward cavity-controlled electronic order in quantum materials.

  PublisherDOI

• Mixed-state learnability transitions in monitored noisy quantum dynamics

  Physical review. B./Physical review. B · 2026-01-12 · 1 citations

  articleOpen accessSenior author

  We consider learnability transitions in monitored quantum systems that undergo noisy evolution, subject to a global strong symmetry—i.e., in addition to the measuring apparatus, the system can interact with an unobserved environment, but does not exchange charge with it. As in the pure-state setting, we find two information-theoretic phases—a sharp (fuzzy) phase in which an eavesdropper can rapidly (slowly) learn the symmetry charge. However, because the dynamics is noisy, both phases can be simulated efficiently using tensor networks. Indeed, even when the true dynamics is unitary, introducing noise by hand allows an eavesdropper to efficiently learn the symmetry charge from local measurements, as we demonstrate. We identify the fuzzy phase in this setting as a mixed-state phase that exhibits spontaneous strong-to-weak symmetry breaking.

  PublisherDOI

• Superradiant Charge Density Waves in a Driven Cavity-Matter Hybrid

  arXiv (Cornell University) · 2026-03-30

  articleOpen access

  Optical cavities enable strong, long-range, light-matter interactions that can drive collective ordering phenomena, such as superradiant self-organization in ultracold atomic gases. Extending these ideas to solid-state electron systems could enable continuous-wave optical control of electronic order, but is impeded by the mismatch between optical wavelengths and electronic length scales. Here, we propose a platform for realizing superradiant charge density waves (sCDWs) in doped, driven transition-metal dichalcogenides coupled to an optical cavity. A nanoscale grating generates electric fields at large in-plane optical momenta, allowing cavity photons to couple efficiently to electronic density fluctuations through exciton-polaron processes. Using a linear-stability analysis, we determine the threshold for superradiant ordering and map out the driven phase diagram. We show that tuning the grating periodicity to match the enhanced electronic density fluctuations - such as those near Wigner crystallization - substantially lowers the required pump intensity. Our results establish a novel route toward cavity-controlled electronic order in quantum materials.

  PublisherOA PDF

• Effects of intertube dipole-dipole interactions in nearly integrable one-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mi>Dy</mml:mi> <mml:mprescripts/> <mml:none/> <mml:mn>162</mml:mn> </mml:mmultiscripts> </mml:math> gases

  Physical review. A/Physical review, A · 2026-01-15

  articleOpen access

  We study the effects of the intertube dipole-dipole interactions (DDI) in recent experiments with arrays of nearly integrable one-dimensional (1D) dipolar Bose gases of $^{162}$Dy atoms. An earlier theoretical modeling ignored those interactions, which we include here via a modification of the 1D confining potentials. We investigate the effects of the intertube DDI both during the state preparation and during the measurements of the rapidity distributions. We explore how the strength of the contact interactions and the magnetic field angles modify the intertube DDI corrections. We find that those corrections slightly change both the properties of the equilibrium state and the rapidity measurements. Remarkably, however, the changes nearly cancel each other, resulting in measured rapidity distributions that are very close to those predicted in the absence of the intertube DDI.

  PublisherOA PDFDOI

• Multimode Cavity QED Ising Spin Glass

  Physical Review Letters · 2025-10-15 · 1 citations

  articleOpen accessSenior author

  We realize a driven-dissipative Ising spin glass using cavity QED in a novel "4/7" multimode geometry. Gases of ultracold atoms trapped within the cavity by optical tweezers serve as effective spins. They are coupled via randomly signed, all-to-all Ising cavity-mediated interactions. Networks of up to n=25 spins are holographically imaged via cavity emission. The system is driven through a frustrated transverse-field Ising transition, and we show that the entropy of the spin glass states depends on the rate at which the transition is crossed. Despite being intrinsically nonequilibrium, the system exhibits phenomena associated with Parisi's theory of equilibrium spin glasses, namely, replica symmetry breaking (RSB) and ultrametric structure. For system sizes up to n=16, we measure the Parisi function q(x), Edwards-Anderson overlap q_{EA}, and ultrametricity K correlator; all indicate a deeply ordered spin glass under RSB. The system can serve as an associative memory and enable aging and rejuvenation studies in driven-dissipative spin glasses at the microscopic level.

  PublisherOA PDFDOI

• Directly observing replica symmetry breaking in a vector quantum-optical spin glass

  Science · 2025-08-14 · 8 citations

  articleSenior authorCorresponding

  Spin glasses are quintessential examples of complex matter. Although their ordering lacks complete theoretical understanding, abstract models of spin glasses inform problems in other fields, such as combinatorial optimization and artificial intelligence-where they form a mathematical basis for neural network computing. We demonstrate the ability to realize a spin glass of a distinct driven-dissipative and vector form. By microscopically visualizing its glassy spin states, the technique allows us to directly measure replica symmetry breaking and the resulting ultrametric hierarchical structure. Ultrametricity is known to be emergent in models of evolution, protein folding, and climate change; this work shows it to be directly observable in a physically realized system.

  PublisherDOI

• High-capacity associative memory in a quantum-optical spin glass

  ArXiv.org · 2025-09-15

  preprintOpen accessSenior author

  The Hopfield model describes a neural network that stores memories using all-to-all-coupled spins. Memory patterns are recalled under equilibrium dynamics. Storing too many patterns breaks the associative recall process because frustration causes an exponential number of spurious patterns to arise as the network becomes a spin glass. Despite this, memory recall in a spin glass can be restored, and even enhanced, under quantum-optical nonequilibrium dynamics because spurious patterns can now serve as reliable memories. We experimentally observe associative memory with high storage capacity in a driven-dissipative spin glass made of atoms and photons. The capacity surpasses the Hopfield limit by up to seven-fold in a sixteen-spin network. Atomic motion boosts capacity by dynamically modifying connectivity akin to short-term synaptic plasticity in neural networks, realizing a precursor to learning in a quantum-optical system.

  PublisherOA PDFDOI

• Raman-phonon-polariton condensation in a transversely pumped cavity

  npj Quantum Materials · 2024-10-17 · 3 citations

  articleOpen access

  Abstract Phonon polaritons are hybrid states of light and matter that are typically realised when optically active phonons couple strongly to photons. We suggest a new approach to realising phonon polaritons, by employing a transverse-pumping Raman scheme, as used in experiments on cold atoms in optical cavities. This approach allows hybridisation between an optical cavity mode and any Raman-active phonon mode. Moreover, this approach enables one to tune the effective phonon–photon coupling by changing the strength of the transverse pumping light. We show that such a system may realise a phonon-polariton condensate. To do this, we find the stationary states and use Floquet theory to determine their stability. We thus identify distinct superradiant and lasing states in which the polariton modes are macroscopically populated. We map out the phase diagram of these states as a function of pump frequencies and strengths. Using parameters for transition metal dichalcogenides, we show that realisation of these phases may be practicably obtainable. The ability to manipulate phonon mode frequencies and attain steady-state populations of selected phonon modes provides a new tool for engineering correlated states of electrons.

  PublisherOA PDFDOI

• Raman-phonon-polariton condensation in a transversely pumped cavity

  arXiv (Cornell University) · 2024-05-08

  preprintOpen access

  Phonon polaritons are hybrid states of light and matter that are typically realised when optically active phonons couple strongly to photons. We suggest a new approach to realising phonon polaritons, by employing a transverse-pumping Raman scheme, as used in experiments on cold atoms in optical cavities. This approach allows hybridisation between an optical cavity mode and any Raman-active phonon mode. Moreover, this approach enables one to tune the effective phonon-photon coupling by changing the strength of the transverse pumping light. We show that such a system may realise a phonon-polariton condensate. To do this, we find the stationary states and use Floquet theory to determine their stability. We thus identify distinct superradiant and lasing states in which the polariton modes are macroscopically populated. We map out the phase diagram of these states as a function of pump frequencies and strengths. Using parameters for transition metal dichalcogenides, we show that realisation of these phases may be practicably obtainable. The ability to manipulate phonon mode frequencies and attain steady-state populations of selected phonon modes provides a new tool for engineering correlated states of electrons.

  PublisherOA PDFDOI

• Entanglement and Replica Symmetry Breaking in a Driven-Dissipative Quantum Spin Glass

  Physical Review X · 2024-02-22 · 36 citations

  articleOpen accessSenior author

  We describe simulations of the quantum dynamics of a confocal cavity QED system that realizes an intrinsically driven-dissipative spin glass. A close connection between open quantum dynamics and replica symmetry breaking is established, in which individual quantum trajectories are the replicas. We observe that entanglement plays an important role in the emergence of replica symmetry breaking in a fully connected, frustrated spin network of up to 15 spin-1/2 particles. Quantum trajectories of entangled spins reach steady-state spin configurations of lower energy than that of semiclassical trajectories. Cavity emission allows monitoring of the continuous stochastic evolution of spin configurations, while backaction from this projects entangled states into states of broken Ising and replica symmetry. The emergence of spin glass order manifests itself through the simultaneous absence of magnetization and the presence of nontrivial spin overlap density distributions among replicas. Moreover, these overlaps reveal incipient ultrametric order, in line with the Parisi replica symmetry breaking solution for the Sherrington-Kirkpatrick model. A nonthermal Parisi order parameter distribution, however, highlights the driven-dissipative nature of this quantum optical spin glass. This practicable system could serve as a test bed for exploring how quantum effects enrich the physics of spin glasses.

  PublisherOA PDFDOI

Recent grants

• E2CDA: Type I: Collaborative Research: Energy Efficient Computing with Chip-Based Photonics

  NSF · $242k · 2016–2019

• One-Dimensional Gases of Dysprosium

  NSF · $487k · 2017–2020

• Synthetic Gauge Fields in Quantum Gases of Dysprosium

  NSF · $445k · 2014–2017

• CAREER: Exploring exotic matter through the quantum manipulation of dipolar atoms

  NSF · $490k · 2009–2012

• CAREER: Exploring exotic matter through the quantum manipulation of dipolar atoms

  NSF · $202k · 2011–2014

Frequent coauthors

• Jun Ye

  University of Colorado Boulder

  41 shared

• Sarang Gopalakrishnan

  35 shared

• Brian C. Sawyer

  Georgia Tech Research Institute

  34 shared

• Eric R. Hudson

  27 shared

• Nathaniel Burdick

  Stanford University

  23 shared

• Jonathan Keeling

  University of St Andrews

  23 shared

• Benjamin Stuhl

  Energy Dynamics (Norway)

  23 shared

• Mingwu Lu

  22 shared

Education

• B.S., Physics

  Princeton

  1999

• Ph.D., Physics

  Caltech

  2005

Awards & honors

• Packard Foundation Fellowship
• Presidential Early Career Award for Scientists and Engineers…
• NSF CAREER award
• Air Force Office of Scientific Research, DARPA, and Office o…
• APS Fellow