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

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.

Bose-Einstein condensation of light in a cavity

“…with ω 0 given by formula (6). Therefore, substituting ( 22) into (21), one obtains the expression to determine the necessary amount of photons, which were pumped into the system to observe BEC:…”

“…[12,13] is relatively simple from the viewpoint of implementation and observation of Bose condensation in other many-particle systems (see for example, [2][3][4][5][6]). However, the result is so intriguing that it gives a stimulus to a substantial number of theoretical studies on the subject [14][15][16][17][18][19][20][21][22]. Despite the considerable progress in this area, the phenomenon of BEC of photons needs further study.…”

Bose-Einstein condensation of light: General theory

“…The aim of this paper is to give a detailed description of the theory of Bose-Einstein condensation (BEC) of light in a dye-filled optical microcavity, a new physical phenomenon that was experimentally observed in 2010 [1]. This observation is an important achievement in the study of critical phenomena in optical systems [2][3][4][5][6][7][8][9] and has attracted considerable interest [10][11][12][13][14][15][16][17][18][19]. In the experiment, a microcavity composed of two highly reflecting spherical dielectric mirrors is filled with a dye solution and confines photons, which are repeatedly absorbed and reemitted by dye molecules.…”