Dissipation-induced pure Gaussian state

TL;DR

This paper establishes simple matrix conditions for Markovian Gaussian master equations to have unique pure steady states, enabling systematic design of dissipative systems for pure Gaussian state preparation, including cluster states.

Contribution

It provides necessary and sufficient matrix conditions for pure steady states in Gaussian systems and a systematic method for engineering such dissipative systems.

Findings

Derived simple matrix equations for pure Gaussian steady states.

Provided a complete parametrization for system design.

Demonstrated examples including Gaussian cluster states.

Abstract

This paper provides some necessary and sufficient conditions for a generalMarkovian Gaussian master equation to have a unique pure steady state. The conditions are described by simple matrix equations; thus the so-called environment engineering problem for pure-Gaussian-state preparation can be straightforwardly dealt with in the linear algebraic framework. In fact, based on one of those conditions, for an arbitrary given pure Gaussian state,we obtain a complete parametrization of the Gaussian master equation having that state as a unique steady state; this leads to a systematic procedure for engineering a desired dissipative system.We demonstrate some examples including Gaussian cluster states.