Spatial correlations in driven-dissipative photonic lattices

Biondi, Matteo; Lienhard, Saskia; Blatter, G.; Türeci, Hakan E.; Schmidt, Sebastian

doi:10.1088/1367-2630/aa99b2

Cited by 18 publications

(25 citation statements)

References 54 publications

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“…Coupling different sites will inevitably mix the different regimes, leading to novel quantum phenomena [34,60,62,63], including more exotic physics with hysteresis and large collective fluctuations [34,64,65]. Needless to say, no exact solution of the steady state of the many-site problem is currently available, even in one dimension.…”

Section: Modelmentioning

confidence: 99%

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Fully quantum scalable description of driven dissipative lattice models

Deuar,

Ferrier,

Matuszewski

et al. 2020

Preprint

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Section: Modelmentioning

confidence: 99%

“…The crossover regime that mixes all three regimes mentioned in Sec. II, and is often studied [32,34,62,63,65,69], is shown in Fig. 3…”

Section: B Typical Behaviormentioning

confidence: 99%

Fully quantum scalable description of driven dissipative lattice models

Deuar,

Ferrier,

Matuszewski

et al. 2020

Preprint

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“…Including correlations ρ c ij , ρ c ijk and solving iteratively allows for a systematic improvement of the mean-field solution. This self-consistent approach is described in the Appendix A and it has been shown to yield accurate results when compared to exact methods [43].…”

Section: /Z Expansionmentioning

confidence: 99%

“…We now go beyond the mean-field description and study site-site correlations to first order in 1/z using the selfconsistent scheme developed in [43]. The main steps of the method are briefly outlined in Appendix A.…”

Section: Quantum Fluctuations Beyond Mean-fieldmentioning

confidence: 99%

Quantum stabilization of photonic spatial correlations

Biondi¹,

Lienhard²,

Blatter³

et al. 2018

Phys. Scr.

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The driven, dissipative Bose-Hubbard model (BHM) provides a generic description of collective phases of interacting photons in cavity arrays. In the limit of strong optical nonlinearities (hard-core limit), the BHM maps on the dissipative, transverse-field XY model (XYM). The steady-state of the XYM can be analyzed using mean-field theory, which reveals a plethora of interesting dynamical phenomena. For example, strong hopping combined with a blue-detuned drive, leads to an instability of the homogeneous steady-state with respect to antiferromagnetic fluctuations. In this paper, we address the question whether such an antiferromagnetic instability survives in the presence of quantum correlations beyond the mean-field approximation. For that purpose, we employ a self-consistent 1/z expansion for the density matrix, where z is the lattice coordination number, i.e., the number of nearest neighbours for each site. We show that quantum fluctuations stabilize a new homogeneous steady-state with antiferromagnetic correlations in agreement with exact numerical simulations for finite lattices. The latter manifests itself as short-ranged oscillations of the first and second-order spatial coherence functions of the photons emitted by the array. arXiv:1806.11067v1 [cond-mat.quant-gas]

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“…A large number of studies concern one-dimensional (1D) lattices (mostly with nearest-neighbor interactions), finding that the MF AF phase is replaced by a uniform phase stabilized by AF correlations [47,55,58,59], and bistability is replaced by a smooth crossover accompanied by large quantum fluctuations [52,[60][61][62][63]. These conclusions rely on accurate numerical methods that can be applied to large 1D systems, such as matrix product operator (MPO) simulations, but an experimental investigation is still lacking.…”

Section: Introductionmentioning

confidence: 99%

Correlation-induced steady states and limit cycles in driven dissipative quantum systems

Landa,

Schiró,

Misguich

2020

Preprint

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We study a driven-dissipative model of spins one-half (qubits) on a lattice with nearest-neighbor interactions. Focusing on the role of spatially extended spin-spin correlations in determining the phases of the system, we characterize the spatial structure of the correlations in the steady state, as well as their temporal dynamics. In dimension one we use essentially exact matrix-product-operator simulations on large systems, and pushing these calculations to dimension two, we obtain accurate results on small cylinders. We also employ an approximation scheme based on solving the dynamics of the mean field dressed by the feedback of quantum fluctuations at leading order. This approach allows us to study the effect of correlations in large lattices with over one hundred thousand spins, as the spatial dimension is increased up to five. In dimension two and higher we find two new states that are stabilized by quantum correlations and do not exist in the mean-field limit of the model. One of these is a steady state with mean magnetization values that lie between the two bistable mean-field values, and whose correlation functions have properties reminiscent of both. The correlation length of the new phase diverges at a critical point, beyond which we find emerging a new limit cycle state with the magnetization and correlators oscillating periodically in time.

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Spatial correlations in driven-dissipative photonic lattices

Cited by 18 publications

References 54 publications

Fully quantum scalable description of driven dissipative lattice models

Fully quantum scalable description of driven dissipative lattice models

Quantum stabilization of photonic spatial correlations

Correlation-induced steady states and limit cycles in driven dissipative quantum systems

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