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

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.

Critical exponent of a quantum-noise-driven phase transition: The open-system Dicke model

“…An example is a lattice gas immersed in a BEC of another species of atoms [9], which serves as a zero-temperature reservoir of Bogoliubov excitations. The resulting dissipative Bose-Hubbard model exhibits a dynamical phase transition between a pure superfluid state and a thermal-like mixed state as the onsite interaction is increased [10]. Note that this method for the preparation of strongly correlated quantum states makes dissipation to be a resource for quantum simulation [11] and universal quantum computation [12].…”

Connecting dynamical quantum phase transitions and topological steady-state transitions by tuning the energy gap

“…Considerable effects have been made to the formulation of various notions of nonequilibrium phase transitions [7][8][9][10][11][12][13][14][15][16][17] which are seen as promising attempts to extend elementary equilibrium concepts such as scaling and universality to the nonequilibrium regime. Among these notions there is the concept of a steady-state transition, which is signaled by a nonanalytic change of physical properties as a function of a parameter of the nonequilibrium protocol in the asymptotic long-time state of the system [8,11,12]. An example is the universal logarithmic divergence of the Hall conductance in the steady state of topological insulators after a quench [16,17].…”

Dynamical phases in a one-dimensional chain of heterospecies Rydberg atoms with next-nearest-neighbor interactions

“…However, the MFA is still regarded as a reliable and adequate tool to qualitatively describe the phase diagram and at least to predict the existence of kinds of steady-state phases [15][16][17]. By the MFA we can neglect the intersite quantum correlation and factorize the density matrix into each site ρ = ⊗ j ρ j [32,33]. For atom j, the second term in Eq.…”