Obtaining pure steady states in nonequilibrium quantum systems with strong dissipative couplings

TL;DR

This paper demonstrates that in the Zeno regime of infinitely strong dissipation, pure steady states in nonequilibrium quantum systems can be achieved through non-commutative coherent and dissipative dynamics, with practical criteria and examples.

Contribution

It introduces a Zeno regime pureness criterion and shows how to generate pure steady states via non-commutative dynamics in strongly dissipative quantum systems.

Findings

Pure steady states can be generated in the Zeno regime.

A criterion for pureness in the Zeno regime is derived.

Effective dissipative strengths for near-target pure states are calculated.

Abstract

Dissipative preparation of a pure steady state usually involves a commutative action of a coherent and a dissipative dynamics on the target state. Namely, the target pure state is an eigenstate of both the coherent and dissipative parts of the dynamics. We show that working in the Zeno regime, i.e. for infinitely large dissipative coupling, one can generate a pure state by a non commutative action, in the above sense, of the coherent and dissipative dynamics. A corresponding Zeno regime pureness criterion is derived. We illustrate the approach, looking at both its theoretical and applicative aspects, in the example case of an open $XXZ$ spin-$1/2$ chain, driven out of equilibrium by boundary reservoirs targeting different spin orientations. Using our criterion, we find two families of pure nonequilibrium steady states, in the Zeno regime, and calculate the dissipative strengths effectively needed to generate steady states which are almost indistinguishable from the target pure states.