Steady Schr\"odinger cat state of a driven Ising chain

TL;DR

This paper demonstrates that a driven Ising chain coupled to non-equilibrium environments can stabilize a Schr"odinger cat state, a superposition of macroscopically distinct states, which is impossible in thermal equilibrium.

Contribution

It introduces a model where a steady Schr"odinger cat state emerges in a driven Ising chain coupled to non-equilibrium reservoirs, highlighting the role of symmetry in stabilizing such states.

Findings

Steady cat states can be stabilized in non-equilibrium conditions.

The system's symmetry between Hamiltonian and environment coupling is crucial.

Pure superpositions of all-spin-up and all-spin-down states are achievable at low temperatures.

Abstract

For short-range interacting systems, no Schr\"odinger cat state can be stable when their environment is in thermal equilibrium. We show, by studying a chain of two-level systems with nearest-neighbour Ising interactions, that this is possible when the surroundings consists of two heat reservoirs at different temperatures, or of a heat reservoir and a monochromatic field. The asymptotic state of the considered system can be a pure superposition of mesoscopically distinct states, the all-spin-up and all-spin-down states, at low temperatures. The main feature of our model leading to this result is the fact that the Hamiltonian of the chain and the dominant part of its coupling to the environment obey the same symmetry.