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arXiv:1003.2071 · Physical Review Letters

Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems

Sebastian Diehl, Andrea Tomadin, Andrea Micheli, Rosario Fazio, P. Zoller

Published Jul 1, 2010• 350 citations
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Abstract

We discuss an open driven-dissipative many-body system, in which the competition of unitary Hamiltonian and dissipative Liouvillian dynamics leads to a nonequilibrium phase transition. It shares features of a quantum phase transition in that it is interaction driven, and of a classical phase transition, in that the ordered phase is continuously connected to a thermal state. We characterize the phase diagram and the critical behavior at the phase transition approached as a function of time. We find a novel fluctuation induced dynamical instability, which occurs at long wavelength as a consequence of a subtle dissipative renormalization effect on the speed of sound.

DOI
10.1103/physrevlett.105.015702

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We study the nonequilibrium dynamics of a many-body bosonic system on a lattice, subject to driving and dissipation. The time evolution is described by a master equation, which we treat within a generalized Gutzwiller mean field approximation for density matrices. The dissipative processes are engineered such that the system, in the absence of interaction between the bosons, is driven into a homogeneous steady state with off-diagonal long-range order. We investigate how the coherent interaction affects the properties of the steady state of the system qualitatively and derive a nonequilibrium phase diagram featuring a phase transition into a steady state without long-range order. The phase diagram also exhibits an extended domain where an instability of the homogeneous steady state gives rise to a persistent density pattern with spontaneously broken translational symmetry. In the limit of low particle density, we provide a precise analytical description of the time evolution during the instability. Moreover, we investigate the transient following a quantum quench of the dissipative processes and we elucidate the prominent role played by collective topological variables in this regime.
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Quantum phases and their transitions play a pivotal role to characterize macroscopic matter. Recent studies have revealed that critical transitions reminiscent of equilibrium phase transitions can occur even out of equilibrium, as a singularity of dynamical counterpart of free energy. In this paper, we report a novel mechanism of dynamical phase transitions caused by spontaneous hidden antiunitary-symmetry breaking in periodically driven unitary dynamics. We characterize dynamical phases in such systems with nonunitary many-body operator obtained by switching space and time and find that its symmetry constrains the nature of phases and their transitions. In particular, at some parameters of stroboscopic Ising models, dynamical free energy density exhibits a critical transition with novel singularity absent in equilibrium. The criticality and its universal exponent originate from a many-body exceptional point of the nonunitary operator associated with spontaneous antiunitary-symmetry breaking. We also show that the generalized correlation function has the divergent correlation length at transition and exhibits oscillatory long-range order after symmetry breaking. Our results open up a quest for hitherto unknown phases with their hidden connection to nonunitary physics in macroscopic nonequilibrium systems, which can be tested in state-of-the-art quantum simulators.