Phases, collective modes, and non-equilibrium dynamics of dissipative Rydberg atoms

TL;DR

This paper investigates the equilibrium phases and non-equilibrium dynamics of dissipative Rydberg atoms in an optical lattice, analyzing phase boundaries, excitation spectra, and entropy evolution under parameter ramps.

Contribution

It provides a mean-field theoretical framework for understanding phase transitions and dynamics of dissipative Rydberg atoms, including effects of finite dissipation and interactions.

Findings

Identified the MI-SF phase boundary in dissipative Rydberg systems.

Analyzed the excitation spectrum and stability of phases under dissipation.

Showed power-law behavior of entropy deviation during parameter ramps.

Abstract

We use a density matrix formalism to study the equilibrium phases and non-equilibrium dynamics of a system of dissipative Rydberg atoms in an optical lattice within mean-field theory. We provide equations for the fixed points of the density matrix evolution for atoms with infinite on-site repulsion and analyze these equations to obtain their Mott insulator- superfluid (MI-SF) phase boundary. A stability analysis around these fixed points provides us with the excitation spectrum of the atoms both in the MI and SF phases. We study the nature of the MI-SF critical point in the presence of finite dissipation of Rydberg excitations, discuss the fate of the superfluidity of the atoms in the presence of such dissipation in the weak-coupling limit using a coherent state representation of the density matrix, and extend our analysis to Rydberg atoms with finite on-site interaction via numerical solution of the density matrix equations. Finally, we vary the boson (atom) hopping parameter $J$ and the dissipation parameter $\Gamma$ according to a linear ramp protocol. We study the evolution of entropy of the system following such a ramp and show that the deviation of the entropy from its steady state value for the latter protocol exhibits power-law behavior as a function of the ramp time. We discuss experiments which can test our theory.