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arXiv:1609.04159

Steady-state localized-delocalized phase transition of an incoherent-pumped dissipative Bose-Hubbard model

Yuanwei Zhang, Jingtao Fan, Chen, Gang, Wu-Ming Liu

Published Sep 14, 2016• 0 citations
arXivHTMLPDF

Abstract

We investigate steady-state properties of a two-dimensional incoherent-pumped dissipative Bose-Hubbard model, which describes a photon square lattice. This incoherent pumping exhibits an important environment-induced higher-order fluctuation effect, which induces a strong competition between the driven-dissipative channel, the photon-photon interaction, and the photon hopping in multi-photon processes. This new competition gives rise to a spontaneous breaking of the U(1) symmetry of system. As a result, we predict a many-body steady-state localized-delocalized phase transition and an anti-blockade effect, in which the increasing of the repulsive photon-photon interaction promotes the emergence of phase transition. These unconventional many-body steady-state phenomena can be understood by analyzing the single-cavity properties. Our results pave a new way to control many-body dynamics of driven-dissipative systems.

DOI
10.48550/arxiv.1609.04159

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A number of experimental platforms relevant for quantum simulations, ranging from arrays of superconducting circuits hosting correlated states of light to ultracold atoms in optical lattices in the presence of controlled dissipative processes. Their theoretical understanding is hampered by the exponential scaling of their Hilbert space and by their intrinsic nonequilibrium nature, limiting the applicability of many traditional approaches. In this work, we extend the nonequilibrium bosonic dynamical mean-field theory (DMFT) to Markovian open quantum systems. Within DMFT, a Lindblad master equation describing a lattice of dissipative bosonic particles is mapped onto an impurity problem describing a single site embedded in its Markovian environment and coupled to a self-consistent field and to a non-Markovian bath, where the latter accounts for fluctuations beyond Gutzwiller mean-field theory due to the finite lattice connectivity. We develop a nonperturbative approach to solve this bosonic impurity problem, which dresses the impurity, featuring Markovian dissipative channels, with the non-Markovian bath, in a self-consistent scheme based on a resummation of noncrossing diagrams. As a first application of our approach, we address the steady state of a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump. We show that DMFT captures hopping-induced dissipative processes, completely missed in Gutzwiller mean-field theory, which crucially determine the properties of the normal phase, including the redistribution of steady-state populations, the suppression of local gain, and the emergence of a stationary quantum-Zeno regime. We argue that these processes compete with coherent hopping to determine the phase transition toward a nonequilibrium superfluid, leading to a strong renormalization of the phase boundary at finite connectivity. We show that this transition occurs as a finite-frequency instability, leading to an oscillating-in-time order parameter, that we connect with a quantum many-body synchronization transition of an array of quantum van der Pol oscillators.