A simple way to incorporate loss when modelling multimode entangled state generation

TL;DR

This paper introduces a semi-analytic method to model the generation and evolution of multimode entangled states in lossy cavities, simplifying calculations by reducing complexity and enabling analysis of large systems.

Contribution

It presents a scalable, semi-analytic approach to describe multimode entangled states in lossy cavities using coupled differential equations for the first time.

Findings

The method scales linearly with the number of modes.

Correlation variances can be expressed analytically.

Efficiently models large multimode systems with loss.

Abstract

We show that the light generated via spontaneous four-wave mixing or parametric down conversion in multiple, coupled, lossy cavities is a multimode squeezed thermal state. Requiring this state to be the solution of the Lindblad master equation results in a set of coupled first-order differential equations for the time-dependent squeezing parameters and thermal photon numbers of the state. The benefit of this semi-analytic approach is that the number of coupled equations scales linearly with the number of modes but is independent of the number of photons generated. With this analytic form of the state, correlation variances are easily expressed as analytic functions of the time-dependent mode parameters. Thus, our solution makes it computationally tractable and relatively straight forward to calculate the generation and evolution of multimode entangled states in multiple coupled, lossy cavities, even when there are a large number of modes and/or photons.