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.
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.
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.
"Spatially modulated ordered states, such as crystals, liquid crystals, and antiferromagnets, are ubiquitous in nature but relatively difficult to realize in ultracold atomic systems. In the present work, we present a scheme for generating controllable cavity-mediated interactions between atoms, and show that these interactions give rise to a crystallization transition in the case of a transversely pumped optical cavity. We focus on the case of multimode cavities, in which the interactions are relatively local and the range of possible ordered configurations (and consequently of low-energy fluctuations) is large; as we show, the crystallization transition for a Bose-Einstein condensate in a multimode cavity is driven first-order by fluctuations, through the Brazovskii effect. The ordered state to which this crystallization transition gives rise is a ""supersolid,"" possessing both superfluid and solid order. We address the crystallization transition and the properties of the ordered state, discuss the experimental feasibility of observing these, and finally show how ordering in layered systems of atoms is geometrically frustrated. We then introduce a more straightforward realization of frustrated cavity-mediated interactions, viz. systems of randomly-positioned spins in multimode cavities. We show by means of a mapping to a variant of the Hopfield associative-memory model that such systems exhibit a spin-glass phase. Finally, we consider a different ultracold-atomic setting---that of spin-orbit-coupled Bose gases---in which the Brazovskii effect has a profound influence on the low-temperature phases, leading to a universal preference for stripe-like ordering at zero temperature and bosonic pair condensation at nonzero temperatures."
In the context of ultracold atoms in multimode optical cavities, the appearance of a quantum-critical glass phase of atomic spins has been predicted recently. Due to the long-range nature of the cavity-mediated interactions, but also the presence of a driving laser and dissipative processes such as cavity photon loss, the quantum optical realization of glassy physics has no analog in condensed matter and could evolve into a ``cavity glass microscope'' for frustrated quantum systems out of equilibrium. Here we develop the nonequilibrium theory of the multimode Dicke model with quenched disorder and Markovian dissipation. Using a unified Keldysh path integral approach, we show that the defining features of a low-temperature glass, representing a critical phase of matter with algebraically decaying temporal correlation functions, are seen to be robust against the presence of dissipation due to cavity loss. The universality class, however, is modified due to the Markovian bath. The presence of strong disorder leads to an enhanced equilibration of atomic and photonic degrees of freedom, including the emergence of a common low-frequency effective temperature. The imprint of the atomic spin-glass physics onto the photon subsystem realizes a ``photon glass'' state and makes it possible to detect the glass state by standard experimental techniques of quantum optics. We provide an unambiguous characterization of the superradiant and glassy phases in terms of fluorescence spectroscopy, homodyne detection, and the temporal photon correlation function ${g}^{(2)}(\ensuremath{\tau})$.
We introduce a near-term experimental platform for realizing an associative memory.It can simultaneously store many memories by using spinful bosons coupled to a degenerate multimode optical cavity.The associative memory is realized by a confocal cavity QED neural network, with the modes serving as the synapses, connecting a network of superradiant atomic spin ensembles,which serve as the neurons.Memories are encoded in the connectivity matrix between the spins and can be accessed through the input and output of patterns of light.Each aspect of the scheme is based on recently demonstrated technology using a confocal cavity and Bose-condensed atoms.Our scheme has two conceptually novel elements.First, it introduces a new form of random spin system that interpolates between a ferromagnetic and a spin glass regime as a physical parameter is tuned-the positions of ensembles within the cavity.Second, and more importantly, the spins relax via deterministic steepest-descent dynamics rather than Glauber dynamics.We show that this nonequilibrium quantum-optical scheme has significant advantages for associative memory over Glauber dynamics: These dynamics can enhance the network's ability to store and recall memories beyond that of the standard Hopfield model.Surprisingly, the cavity QED dynamics can retrieve memories even when the system is in the spin glass phase.Thus, the experimental platform provides a novel physical instantiation of associative memories and spin glasses as well as provides an unusual form of relaxational dynamics that is conducive to memory recall even in regimes where it was thought to be impossible.
We present a novel cavity QED system in which a Bose–Einstein condensate (BEC) is trapped within a high-finesse optical cavity whose length may be adjusted to access both single-mode and multimode configurations. We demonstrate the coupling of an atomic ensemble to the cavity in both configurations and measure that the single-atom, -mode cooperativity exceeds unity. The atoms are confined either within an intracavity far-off-resonance optical dipole trap or a crossed optical dipole trap via transversely oriented lasers. Multimode cavity QED provides fully emergent and dynamical optical lattices for intracavity BECs, in that the process of atomic self-organization may be described as a continuous symmetry breaking phase transition resulting in the emergence of a compliant lattice with phonon-like excitations. Such systems will enable explorations of quantum soft matter, including superfluid smectics, superfluid glasses, and spin glasses as well as neuromorphic associative memory.
By solving the quench dynamics of a frustrated many-body spin-boson problem, we investigate the role of spin size on the dynamical formation of spin-glass order. In particular, we observe that quantum and classical spin glasses exhibit markedly different evolution. The former displays a quick relaxation of magnetization together with an exponential dependence of the spin-glass order parameter on spin size, while the latter has long-lasting prethermal magnetization and a spin-glass order parameter independent of spin size. The quantum-to-classical crossover is sharp and occurs for relatively small spins, highlighting the fragility of the quantum regime. Furthermore, we show that spin-glass order is resonantly enhanced when the frequency of the bosonic mediators of the interactions approaches the value of the transverse field. Our predictions are directly applicable to the nonequilibrium dynamics of all spin-glass systems with SU(2) spins, such as the quantum Sherrington-Kirkpatrick model, and they can be examined in recently developed multimode cavity QED experiments. Published by the American Physical Society 2024