Homodyne versus photon-counting quantum trajectories for dissipative Kerr resonators with two-photon driving

TL;DR

This paper compares homodyne and photon-counting quantum trajectories in a driven Kerr resonator, revealing distinct switching behaviors between cat states and coherent states, respectively, in the context of dissipative quantum state generation.

Contribution

It introduces a comparative analysis of homodyne and photon-counting quantum trajectories for a two-photon driven Kerr resonator, highlighting their different state-switching dynamics.

Findings

Photon-counting trajectories show switches between odd and even cat states.

Homodyne trajectories reveal switches between coherent states of opposite phase.

Steady state is a mixture of two states with equal weight.

Abstract

We investigate two different kinds of quantum trajectories for a nonlinear photon resonator subject to two-photon pumping, a configuration recently studied for the generation of photonic Schroedinger cat states. In the absence of feedback control and in the strong-driving limit, the steady-state density matrix is a statistical mixture of two states with equal weight. While along a single photon-counting trajectory the systems intermittently switches between an odd and an even cat state, we show that upon homodyne detection the situation is different. Indeed, homodyne quantum trajectories reveal switches between coherent states of opposite phase.