Dissipative spin chains: Implementation with cold atoms and steady-state properties

TL;DR

This paper presents a method to implement dissipative spin models with cold atoms in optical lattices, enabling the study of their dynamics and steady-states, including critical phenomena related to Hamiltonian degeneracies.

Contribution

It introduces a quantum optical scheme for simulating dissipative spin systems with tunable parameters using ultra-cold atoms, expanding experimental capabilities.

Findings

Steady-state expectation values show peaks at critical parameters.

Degeneracies in the Hamiltonian are linked to these peaks.

Numerical simulations confirm the theoretical predictions.

Abstract

We propose a quantum optical implementation of a class of dissipative spin systems, including the XXZ and Ising model, with ultra-cold atoms in optical lattices. Employing the motional degree of freedom of the atoms and detuned Raman transitions we show how to obtain engineerable dissipation and a tunable transversal magnetic field, enabling the study of the dynamics and steady-states of dissipative spin models. As an example of effects made accessible this way, we consider small spin chains and weak dissipation and show by numerical simulation that steady-state expectation values display pronounced peaks at certain critical system parameters. We show that this effect is related to degeneracies in the Hamiltonian and derive a sufficient condition for its occurrence.