Dynamical phases and intermittency of the dissipative quantum Ising model

Abstract

We employ the concept of a dynamical, activity order parameter to study the Ising model in a transverse magnetic field coupled to a Markovian bath. For a certain range of values of the spin-spin coupling, magnetic field and dissipation rate, we identify a first order dynamical phase transition between active and inactive dynamical phases. We demonstrate that dynamical phasecoexistence becomes manifest in an intermittent behavior of the bath quanta emission. Moreover, we establish the connection between the dynamical order parameter that quantifies the activity, and the longitudinal magnetization that serves as static order parameter. The system that we consider can be implemented in current experiments with Rydberg atoms and trapped ions.

Spatial correlations of one-dimensional driven-dissipative systems of Rydberg atoms

“…This is because the laser is originally on resonance with the Rydberg transition, but the more-excited sublattice shifts the other sublattice off resonance due to the blockade effect [31]. When ∆ ∼ V , there is bistability, meaning that there are two steady states: one with low Rydberg population and one with high Rydberg population [13,14]. The intuition for bistability is as follows.…”

“…Figure 1 shows the mean-field phase diagram as a function of Ω and ∆, showing the antiferromagnetic and bistable regions. The phase diagram as a function of Ω and V is given in [14].…”

“…The Hamiltonian can be mapped to a spin-1/2 Ising model with both transverse and longitudinal fields [14]. In the corresponding Ising model, the coupling V corresponds to spin-spin coupling along z-axis, the drive Ω corresponds to a transverse magnetic field along the x-axis, and ∆ − V corresponds to a longitudinal field along the z-axis.…”

“…Simulations of the all-to-all coupling model in the bistable region found strong temporal correlations between the atoms: the system collectively jumps between the two stable states [13]. Simulations of the 1D model found strong temporal correlations in the bistable region, but the simulation was for a large coupling (V = 100γ) and a system of N = 12 lattice sites [14]. Recently, two experiments have observed bistability in a gas of Rydberg atoms [21,22], although the atoms are not fixed on a lattice, and they are not perfect two-level systems.…”

Spatiotemporal dynamics of quantum jumps with Rydberg atoms

“…Recent works have shown that the Rydberg interaction greatly affects how a group of atoms fluoresce [14][15][16]. When the atoms are laser excited from the ground state to a Rydberg state and spontaneously decay back to the ground state, there are strong temporal correlations between photon emissions of different atoms.…”