Generation of entangled tripartite states in three identical cavities

TL;DR

This paper investigates how to generate and analyze entangled tripartite states in three identical cavities with atoms, focusing on the effects of photon exchange and system constraints to produce maximally entangled states.

Contribution

It introduces a method for deterministic generation of tripartite entanglement in coupled cavities with conserved photon number, providing analytic solutions for large hopping strength.

Findings

Analytic solutions for entanglement states in large hopping limit

Conservation law reduces the state space significantly

Identification of maximally entangled tripartite states

Abstract

The generation of entanglement between three identical coupled cavities, each containing a single three-level atom, is studied when the cavities exchange two coherent photons and are in the N=2, 4, and 6 manifolds, where $N$ represents the maximum number of photons possible in any one cavity. The combined states of the atom and the photon in a cavity is given by a qutrit for N=2, a five-dimensional qudit for N=4, and a seven-dimensional qudit for N=6. The conservation of the operator $\hat{N}$ for the interacting three-cavity system limits the total number of tripartite states to only 6, 18, and 38, rather than the usual $3^3=27$, $5^3=125$, and $7^3 =343$ states for N=2, 4, and 6, respectively. The deterministic generation of entanglement from general initially unentangled tripartite states is studied in the limit of large hopping strength, where all the solutions are analytic and given in terms of exponential functions. Several types of resulting tripartite entanglement are analyzed in order to obtain maximally entangled states.