Entanglement in parametric down-conversion with phase mismatch at finite temperature

TL;DR

This paper analyzes how temperature and phase mismatch affect entanglement in photon pairs generated by parametric down-conversion, identifying critical conditions for entanglement presence and proposing a dynamical witness.

Contribution

It introduces a model for entanglement in parametric down-conversion considering phase mismatch and temperature, and proposes a new entanglement witness based on a dynamical invariant.

Findings

Entanglement disappears above a critical temperature for each phase mismatch.

The minimum interaction time for entanglement depends on temperature and phase mismatch.

Regions of entangled and separable states are mapped in parameter space.

Abstract

In this work the degree of entanglement of two-photon states generated by parametric-down conversion with a phase mismatch is computed in terms of the temperature of the nonlinear medium where the interaction takes place. The minimum interaction time, named {\it birth time of entanglement}, needed before entanglement is attained, is computed in terms of the temperature and of the phase mismatch. Our results show that, for each value of the phase mismatch, there is a critical temperature above which entanglement disappears. We are able to identify the regions of parameters, temperature and mismatch, where the states are entangled and where they are separable. We also propose a entanglement witness based in a dynamical invariant of the nonlinear interaction.