Continuous-variable entanglement in a two-mode lossy cavity: an exact solution

TL;DR

This paper provides an exact theoretical solution for continuous-variable entanglement generated in a two-mode lossy cavity pumped with a classical pulse, revealing how losses affect entanglement and aiding optimization efforts.

Contribution

It derives an exact solution for the density operator of a two-mode squeezed thermal state in a lossy cavity, including a formula for maximum entanglement considering mode losses.

Findings

Maximum entanglement depends on loss differences between modes

Exact solution models time-dependent squeezing and thermal photon number

Application to microring resonators demonstrates practical relevance

Abstract

Continuous-variable (CV) entanglement is a valuable resource in the field of quantum information. One source of CV entanglement is the correlations between the position and momentum of photons in a two-mode squeezed state of light. In this paper, we theoretically study the generation of squeezed states, via spontaneous parametric downconversion (SPDC), inside a two-mode lossy cavity that is pumped with a classical optical pulse. The dynamics of the density operator in the cavity is modelled using the Lindblad master equation, and we show that the exact solution to this model is the density operator for a two-mode squeezed thermal state, with a time-dependent squeezing amplitude and average thermal photon number for each mode. We derive an expression for the maximum entanglement inside the cavity that depends crucially on the difference in the losses between the two modes. We apply our exact solution to the important example of a microring resonator that is pumped with a Gaussian pulse. The expressions that we derive will help researchers optimize CV entanglement in lossy cavities.