Dicke-like models can describe a variety of physical systems, such as atoms in a cavity or vibrating ion chains. In equilibrium these systems often feature a radical change in their behavior when switching from weak to strong spin-boson interaction. This usually manifests in a transition from a "dark" to a "superradiant" phase. However, understanding the out-of-equilibrium physics of these models is extremely challenging, and even more so for strong spin-boson coupling. Here we show that the nonequilibrium strongly interacting multimode Dicke model can mimic some fundamental properties of an associative memory-a system which permits the recognition of patterns, such as letters of an alphabet. Patterns are encoded in the couplings between spins and bosons, and we discuss the dynamics of the spins from the perspective of pattern retrieval in associative memory models. We identify two phases, a "paramagnetic" and a "ferromagnetic" one, and a crossover behavior between these regimes. The "ferromagnetic" phase is reminiscent of pattern retrieval. We highlight similarities and differences with the thermal dynamics of a Hopfield associative memory and show that indeed elements of "machine learning behavior" emerge in the strongly coupled multimode Dicke model.
Dicke-like models can describe a variety of physical systems, such as atoms in a cavity or vibrating ion chains. In equilibrium these systems often feature a radical change in their behavior when switching from weak to strong spin-boson interaction. This usually manifests in a transition from a "dark" to a "superradiant" phase. However, understanding the out-of-equilibrium physics of these models is extremely challenging, and even more so for strong spin-boson coupling. Here we show that the nonequilibrium strongly interacting multimode Dicke model can mimic some fundamental properties of an associative memory-a system which permits the recognition of patterns, such as letters of an alphabet. Patterns are encoded in the couplings between spins and bosons, and we discuss the dynamics of the spins from the perspective of pattern retrieval in associative memory models. We identify two phases, a "paramagnetic" and a "ferromagnetic" one, and a crossover behavior between these regimes. The "ferromagnetic" phase is reminiscent of pattern retrieval. We highlight similarities and differences with the thermal dynamics of a Hopfield associative memory and show that indeed elements of "machine learning behavior" emerge in the strongly coupled multimode Dicke model.
Open quantum Dicke models are paradigmatic systems for the investigation of light-matter interaction in out-of-equilibrium quantum settings. Albeit being structurally simple, these models can show intriguing physics. However, obtaining exact results on their dynamical behavior is challenging, since it requires the solution of a many-body quantum system with several interacting continuous and discrete degrees of freedom. Here, we make a step forward in this direction by proving the validity of the mean-field semiclassical equations for open multimode Dicke models, which, to the best of our knowledge, so far has not been rigorously established. We exploit this result to show that open quantum multimode Dicke models can behave as associative memories, displaying a nonequilibrium phase transition toward a pattern-recognition phase.
Nowadays, the research field of Machine Learning (ML) is undergoing a rapid expansion. In addition, in the last decades, within the research area of quantum computation, several quantum protocols and algorithms have shown the ability to outperform their classical counterparts. In the light of these twofold advances, a frontier field investigating the potentiality of quantum implementations of ML architectures arose. Among the latter, many efforts are concentrated on Artificial Neural Networks (ANNs), which represent a highly successful ML architecture. This thesis focuses on characterizing and understanding the role of quantum effects on the behavior of an instance of ANN, the so-called Hopfield Neural Network (HNN). The HNN is an example of an associative memory model and it permits the recognition, or retrieval, of patterns, such as letters of an alphabet. Formally, it can be described in terms of a classical spin network with an all-to-all interaction, ruled by a stochastic dynamics. Its relatively intuitive behavior, and its physical description make the HNN being a good candidate for a theoretical investigation of its possible quantum generalizations. In the first part of our work we deal with the implementation of fully connected Ising models, such as the HNN one, in terms of quantum systems. To this end, we refer to the cases where the theory of Open Quantum System (OQS) is exploited for engineering steady states of out-of-equilibrium dynamics. This paradigm allows us to build a dissipative - yet quantum - dynamics which encodes in its stationary state the thermal state of the original (classical) problem. Such a construction gives us the chance to address the question as to whether the quantum description could lead to a speed-up in reaching the shared stationary state with respect to the classical counterpart. We show that a suitable choice of the parameters allows the system to switch between a classical regime and a quantum one, the latter being characterized by an accelerated approach towards the long-time limit state. In the second part of our work we focus on practically relevant implementations of quantum systems that can show analogies with the HNN model. To this end, we consider spin-boson models as described by the Dicke Hamiltonian. Indeed, at strong spin-boson interaction couplings, and when the latter are additionally characterized by disorder, the equilibrium Dicke model is able to reproduce the retrieval mechanism typical of HNNs. When dissipation is included, the theoretical description becomes more challenging. We analyze the open, disordered Dicke model by employing some perturbative techniques in order to deal with the out-of-equilibrium dynamics at strong coupling. As a result, we are able to highlight similarities and differences between the quantum model and HNNs.
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 investigate a generalized Dicke model by introducing two interacting spin ensembles coupled with a single-mode bosonic field. Apart from the normal to superradiant phase transition induced by the strong spin-boson coupling, interactions between the two spin ensembles enrich the phase diagram by introducing ferromagnetic, antiferromagnetic and paramagnetic phases. The mean-field approach reveals a phase diagram comprising three phases: paramagnetic-normal phase, ferromagnetic-superradiant phase, and antiferromagnetic-normal phase. Ferromagnetic spin-spin interaction can significantly reduce the required spin-boson coupling strength to observe the superradiant phase, where the macroscopic excitation of the bosonic field occurs. Conversely, antiferromagnetic spin-spin interaction can strongly suppress the superradiant phase. To examine higher-order quantum effects beyond the mean-field contribution, we utilize the Holstein-Primakoff transformation, which converts the generalized Dicke model into three coupled harmonic oscillators in the thermodynamic limit. Near the critical point, we observe the close of the energy gap between the ground and the first excited states, the divergence of entanglement entropy and quantum fluctuation in certain quadrature. These observations further confirm the quantum phase transition and offer additional insights into critical behaviors.
Quantum many-body systems driven far from equilibrium can exhibit phase transitions, chaos and entanglement, but probing these phenomena in large, nearly closed systems remains challenging. The Dicke model, which couples an ensemble of two-level systems collectively to a single bosonic mode, provides a fundamental framework for exploring these phenomena in light-matter interactions. Here we show that a two-dimensional crystal of approximately 100 trapped ions realizes this model and accesses integrable dynamical phase transitions, signatures of chaotic dynamics and fluctuation-driven spin-phonon excitation growth. Adiabatic elimination of the vibrational mode reveals ferromagnetic and paramagnetic dynamical spin phases, whereas strong spin-phonon coupling produces irregular trajectories and local relaxation consistent with quantum thermalization. Following a quench from an unstable fixed point, correlated excitation growth precedes generalized vacuum Rabi collapses and revivals; calibrated calculations identify two-mode squeezing 2.6 dB below the standard quantum limit, supported by reconstruction from spin measurements. By connecting collective dynamical instabilities to experimentally accessible signatures of quantum correlations, these results establish large ion crystals as a scalable platform for investigating non-equilibrium light-matter dynamics and generating resources for quantum-enhanced sensing.
The Dicke model describes the collective behavior of a subwavelength-size ensemble of two-level atoms (i.e., spin-1/2) interacting identically with a single quantized radiation field of a cavity. Across a critical coupling strength it exhibits a zero-temperature phase transition from the normal state to the superradiant phase where the field is populated and the collective spin acquires a nonzero x component, which can be imagined as ferromagnetic ordering of the atomic spins along x. Here we introduce a variant of this model where two subwavelength-size ensembles of spins interact with a single quantized radiation field with different strengths. Subsequently, we restrict ourselves to a special case where the coupling strengths are opposite (which is unitarily equivalent to equal-coupling strengths). Because of the conservation of the total spin in each ensemble individually, the system supports two distinct superradiant states with x-ferromagnetic and x-ferrimagnetic spin ordering, coexisting with each other in a large parameter regime. The stability and dynamics of the system in the thermodynamic limit are examined using a semiclassical approach, which predicts nonstationary behaviors due to the multistabilities. At the end, we also perform small-scale full quantum-mechanical calculations, with results consistent with the semiclassical ones.