Beyond mean-field bistability in driven-dissipative lattices: Bunching-antibunching transition and quantum simulation

Mendoza‐Arenas, J. J.; Clark, Stephen R. L.; Felicetti, Simone; Romero, G.; Solano, E.; Angelakis, Dimitris G.; Jaksch, Dieter

doi:10.1103/physreva.93.023821

Cited by 87 publications

(90 citation statements)

References 85 publications

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“…In this section, we investigate the driven-dissipative spin-1/2 XYM in (4). In particular, we study the antibunching-bunching transition of the nearest neighbor correlator as a function of the detuning Δ, which was recently predicted in [52] using large scale MPS simulations. In the following, we (i) provide a simple and analytic explanation of the transition based on a minimal model of two coupled spins (dimer), (ii) reproduce exact numerical results with the self-consistent z 1 method to high accuracy and (iii) go beyond the MPS method by also studying the 2D case.…”

Section: Spin-1/2 Xy Model: Antibunching-bunching Transitionmentioning

confidence: 99%

Spatial correlations in driven-dissipative photonic lattices

et al. 2017

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We study the nonequilibrium steady-state of interacting photons in cavity arrays as described by the driven-dissipative Bose-Hubbard and spin-1/2 XY model. For this purpose, we develop a selfconsistent expansion in the inverse coordination number of the array ( z 1 ) to solve the Lindblad master equation of these systems beyond the mean-field approximation. Our formalism is compared and benchmarked with exact numerical methods for small systems based on an exact diagonalization of the Liouvillian and a recently developed corner-space renormalization technique. We then apply this method to obtain insights beyond mean-field in two particular settings: (i) we show that the gasliquid transition in the driven-dissipative Bose-Hubbard model is characterized by large density fluctuations and bunched photon statistics. (ii) We study the antibunching-bunching transition of the nearest-neighbor correlator in the driven-dissipative spin-1/2 XY model and provide a simple explanation of this phenomenon.

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Section: Spin-1/2 Xy Model: Antibunching-bunching Transitionmentioning

confidence: 99%

Spatial correlations in driven-dissipative photonic lattices

et al. 2017

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“…A recent work [73] showed that collective bistability in the driven-dissipative XY spin-1 2 model vanishes as the Gutzwiller approximation is systematically improved. Our results demonstrate that whileρ ss is indeed unique [74,75], it retains clear signatures of the MF bistability, namely that the system dynamically switches between two macroscopically distinguishable configurations that resemble the MF steady statesρ 1 andρ 2 ; in fact, this is a generic feature of bistable systems [60,61,65,76,77].…”

Section: Collective Bistability and Switchingmentioning

confidence: 99%

Collective phases of strongly interacting cavity photons

Wilson

Mahmud

et al. 2016

Phys. Rev. A

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We study a coupled array of coherently driven photonic cavities, which maps onto a drivendissipative XY spin-1 2 model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify steady state phases with canted antiferromagnetic order, in addition to limit cycle phases, where oscillatory dynamics persist indefinitely. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results to exact quantum trajectories simulations for finite one-dimensional arrays. The exact results exhibit short-range antiferromagnetic order for parameters that have significant overlap with the mean-field phase diagram. In the mean-field bistable regime, the exact quantum dynamics exhibits real-time collective switching between macroscopically distinguishable states. We present a clear physical picture for this dynamics, and establish a simple relationship between the switching times and properties of the quantum Liouvillian.Despite numerous outstanding questions, the study of quantum many-body systems in thermal equilibrium is on relatively solid ground. In particular, very general guiding principles help to categorize the possible equilibrium phases of matter, and predict in what situations they can occur [1][2][3]. In comparison, quantum manybody systems that are far from equilibrium are less thoroughly understood, motivating a large scale effort to explore non-equilibrium dynamics experimentally, in particular using atoms, molecules, and photons [4][5][6][7][8][9]. At the same time, it has become clear that studying nonequilibrium physics in these systems is often more natural than studying equilibrium physics; they are, in general, intrinsically non-equilibrium. For example, thermal equilibrium is essentially never a reasonable assumption in photonic systems, where dissipation must be countered by active pumping [10]. Indeed, the inadequacy of equilibrium descriptions for photonic systems has long been recognized [11], even though close analogies to thermal systems sometimes exist [12][13][14][15][16].Until recently, photonic systems have been restricted to a weakly interacting regime. With notable progress towards generating strong optical nonlinearities at the few-photon level, for example with atoms coupled to small-mode-volume optical devices [17][18][19][20][21][22], Rydberg polaritons [23,24], and circuit-QED devices [25][26][27][28], this situation is rapidly changing. The production of strongly interacting, driven and dissipative gases of photons appears to be feasible [29,30], and affords exciting opportunities to explore the properties of open quantum systems in unique contexts, while studying the applicability of theoretical treatments designed with more weakly interacting systems in mind. For example, it is not fully understood how the steady states of these systems relate to the equilibrium states of their "closed" c...

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“…There have been several recent proposals [8][9][10][11][12] on achieving this model with photons and open systems, such as with photons in coupled cavity arrays, superconducting circuit QED and polaritons. With added drive and dissipation, the Bose-Hubbard model does not exhibit superfluid or Mott insulator phases but gives rise to mixed state nonequilibrium steady states and phases [13][14][15][16], the nature and generation of which are not fully understood.…”

Section: Introductionmentioning

confidence: 99%

Two coupled nonlinear cavities in a driven-dissipative environment

2016

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We investigate two coupled nonlinear cavities that are coherently driven in a dissipative environment. We perform semiclassical, numerical and analytical quantum studies of this dimer model when both cavities are symmetrically driven. In the semiclassical analysis, we find steady-state solutions with different photon occupations in two cavities. Such states can be considered analogs of the closed system double well symmetry breaking states. We analyze the occurrence and properties of these localized states in the system parameter space and examine how the symmetry breaking states, in form of a bistable pair, are associated to the single cavity bistable behavior. In a full quantum calculation of the master equation dynamics that includes quantum fluctuations, the symmetry breaking states and bistability disappear due to the quantum fluctuations. In quantum trajectory picture, we observe enhanced quantum jumps and switching which indicate the presence of the underlying semiclassical symmetry breaking states. Finally, we present a set of analytical solutions for the steady state correlation functions using the complex P-representation and discuss its regime of validity.

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Beyond mean-field bistability in driven-dissipative lattices: Bunching-antibunching transition and quantum simulation

Cited by 87 publications

References 85 publications

Spatial correlations in driven-dissipative photonic lattices

Spatial correlations in driven-dissipative photonic lattices

Collective phases of strongly interacting cavity photons

Two coupled nonlinear cavities in a driven-dissipative environment

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