Quantum entanglement and phase transition in a two-dimensional photon-photon pair model

TL;DR

This paper models a 2D photon-photon pair system, revealing quantum phase transitions and entanglement properties, with potential implications for understanding second harmonic generation.

Contribution

It introduces a novel 2D photon-photon pair model and analytically explores its quantum phase transitions and entanglement characteristics.

Findings

Existence of two condensate phases in the system

Analytical critical coupling line for phase transition

Entanglement linked to phase transition phenomena

Abstract

We propose a two-dimensional model consisting of photons and photon pairs. In the model, the mixed gas of photons and photon pairs is formally equivalent to a two-dimensional system of massive bosons with non-vanishing chemical potential, which implies the existence of two possible condensate phases. Using the variational method, we discuss the quantum phase transition of the mixed gas and obtain the critical coupling line analytically. Moreover, we also find that the phase transition of the photon gas can be interpreted as second harmonic generation. We then discuss the entanglement between photons and photon pairs. Additionally, we also illustrate how the entanglement between photons and photon pairs can be associated with the phase transition of the system.