Complex dynamics of photon entanglement in two-mode Jaynes-Cummings model

TL;DR

This paper investigates the complex, quasi-periodic dynamics of photon entanglement in a two-mode Jaynes-Cummings model, revealing how indistinguishability and non-linear frequency dependence generate intricate entanglement evolution.

Contribution

It provides a detailed analysis of photon entanglement dynamics in the two-mode Jaynes-Cummings model, highlighting the role of superimposed incommensurate oscillations and photon indistinguishability.

Findings

Entanglement dynamics are quasi-periodic and highly dependent on photon number.

Indistinguishability of photons induces entanglement despite independent atomic transitions.

Complex entanglement profiles result from superimposed oscillations with incommensurate frequencies.

Abstract

We study the dynamics of the photon entanglement, $E_{\mathrm{N}}(t)$, for the two-mode Jaynes-Cummings model in the few-photon case. The atomic transitions associated with the photons with different polarizations are assumed to be independent and, hence, the evolution of the "+"- and "-"-polarized photons is formally separable. However, due to the photons indistinguishability such interaction still leads to entanglement of initially disentangled states owing to the non-linear dependence of the characteristic frequencies on the photon population numbers. The time dependence of entanglement is the result of superimposing oscillations with incommensurate frequencies. Therefore, $E_{\mathrm{N}}(t)$ is a quasi-periodic function of time with the complex profile strongly depending on the number of photons.