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arXiv:0904.4437 · Physical Review A

Signatures of the superfluid-insulator phase transition in laser-driven dissipative nonlinear cavity arrays

Andrea Tomadin, Vittorio Giovannetti, Rosario Fazio, Dario Gerace, Iacopo Carusotto, Hakan E. Türeci, Ataç İmamoğlu

Published Jun 11, 2010• 120 citations
arXivHTMLPDF

Abstract

We analyze the nonequilibrium dynamics of a gas of interacting photons in an array of coupled dissipative nonlinear cavities when driven by a pulsed external coherent field. Using a mean-field approach, we show that the response of the system is strongly sensitive to the underlying (equilibrium) quantum phase transition from a Mott insulator to a superfluid state at commensurate filling. We find that the coherence of the cavity emission after a quantum quench can be used to determine the phase diagram of an optical many-body system even in the presence of dissipation.

DOI
10.1103/physreva.81.061801

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In recent years, the control of photon-photon interactions in optical nonlinear media has led to the realization of quantum fluids of light. One of the current challenges is to increase the strength of these interactions and enter the so-called strongly correlated regime. To achieve this goal, arrays of nonlinear cavities are a very promising candidate. In this thesis, theoretical results on arrays of nonlinear cavities described by a driven-dissipative Bose-Hubbard model are presented. In particular, a general method to compute the mean-field phase diagram of this model is described. Due to the finite life time of photons, the system is intrinsically dissipative: cavity losses must be compensated by an external driving field. This nonequilibrium nature gives rise to interesting features, such as a transition between monostable and bistable phases induced by tunneling. In the limit of weak dissipation and weak driving, analytical results describing generalized Mott insulating phases are derived. These states survive up to a critical tunneling strength, above which a crossover to a classical coherent state takes place. Finally, the issue of how to go beyond the mean-field approximation is addressed by performing exact numerical simulations. Large arrays of cavities were simulated by implementing a new method specifically tailored for driven-dissipative systems.
We study the features of superfluid and Mott-insulator states in a two-dimensional array of cavities with a two-level atom embedded in each cavity which is strongly coupled to the cavity field and immersed in a bosonic bath. Employing a different quasiboson approach, we show analytically how the dissipation and decoherence influence the quantum phase transitions from two aspects and find a localized tendency. For the superfluid state, a dynamical instability will lead to a sweeping to a localized state of photons. For the Mott-insulator state, a dissipation-induced fluctuation will suppress the restoring of long-range phase coherence driven by interaction.
Abstract We investigated the superfluid Mott-insulator phase transition within an open coupled cavity optomagnonic array system. Based on the quasibosonic approach and employing perturbation approximation and mean-field theory, we obtain the time-dependent analytical superfluid order parameter. Our analysis revealed that dissipation induces decoherence within the system, while a strong magnon-cavity coupling enhances coherence significantly. Moreover, we explored the mechanisms by which increasing the magnon-cavity coupling strength drives the system towards the superfluid phase. The work holds significant guidance for the study of superfluidMott insulator phase transition under dissipative conditions, and providing a reliable reference for experimental implementation in open quantum systems.
We investigate the nonlinear light-matter interaction of a Bose-Einstein condensate trapped in an external periodic potential inside an optical cavity which is weakly coupled to vacuum radiation modes and driven by a transverse pump field. Based on a generalized Bose-Hubbard model which incorporates a single cavity mode, we include the collective backaction of the atoms on the cavity light field and determine the nonequilibrium quantum phases within the nonperturbative bosonic dynamical mean-field theory. With the system parameters adapted to recent experiments, we find a quantum phase transition from a normal phase to a self-organized superfluid phase, which is related to the Hepp-Lieb-Dicke superradiance phase transition. For even stronger pumping, a self-organized Mott insulator phase arises.