A von Neumann Entropy Measure of Entanglement Transfer in a Double Jaynes-Cummings Model

TL;DR

This paper investigates how entanglement is transferred between atoms and photons in a double Jaynes-Cummings system using von Neumann entropy, revealing conditions that preserve total entanglement and effects of detuning.

Contribution

It introduces a von Neumann entropy-based measure to analyze entanglement transfer in a double Jaynes-Cummings model with non-interacting atoms and photon modes.

Findings

Total entanglement sum remains constant under certain conditions.

Detuning reduces maximum entanglement and shortens entanglement times.

Von Neumann entropy bounds negativity in the system.

Abstract

We study the entanglement in a system consisting of two non-interacting atoms located in separate cavities, both in their ground states. A single incoming photon has a non-zero probability of entering either of the two cavities. The Jaynes-Cummings interaction in the rotating wave approximation describes the coupling of each atom with the radiation field. We compute and analyze the atom-atom entanglement, the entanglement between the two photon modes, and also the entanglement between each atom and each photon mode. The measure of entanglement is the von Neumann entropy. For the case in which the two atom-photon systems have identical properties, but allowing for non-resonant conditions, the sum of the atom-atom and photon-modes-entanglement is time independent. The effect of detuning is to decrease the strength of the largest entanglement achieved and to shorten the time for it to occur. The results support the fact that the state of the photons after emergence from cavities is entangled, notwithstanding its single-particle nature. In addition, for the case of resonance and identical cavity parameters, we demonstrate that von Neumann entropy is always greater than or equal to the measure of entanglement known as negativity.