Exact results for Schr\"odinger cats in driven-dissipative systems and their feedback control

TL;DR

This paper provides an exact analytical solution for steady-state Schr"odinger cat states in driven-dissipative quantum optical systems, revealing their robustness against losses and proposing feedback control for pure state generation.

Contribution

It introduces an exact steady-state solution including one-photon losses and proposes a feedback protocol to produce pure cat states.

Findings

Steady state is a mixture of two cat-like states despite losses.

Transient dynamics depend on initial conditions and can be long-lived.

Feedback control can generate pure Schr"odinger cat states.

Abstract

In quantum optics, photonic Schr\"odinger cats are superpositions of two coherent states with opposite phases and with a significant number of photons. Recently, these states have been observed in the transient dynamics of driven-dissipative resonators subject to engineered two-photon processes. Here we present an exact analytical solution of the steady-state density matrix for this class of systems, including one-photon losses, which are considered detrimental for the achievement of cat states. We demonstrate that the unique steady state is a statistical mixture of two cat-like states with opposite parity, in spite of significant one-photon losses. The transient dynamics to the steady state depends dramatically on the initial state and can pass through a metastable regime lasting orders of magnitudes longer than the photon lifetime. By considering individual quantum trajectories in photon-counting configuration, we find that the system intermittently jumps between two cats. Finally, we propose and study a feedback protocol based on this behaviour to generate a pure cat-like steady state.