Generation of quantum entanglement between three level atoms via $n$ coupled cavities

TL;DR

This paper investigates the generation of entanglement among three-level atoms in coupled cavities via two-photon exchange interactions, generalizing previous models to n cavities and analyzing state transfer and entanglement dynamics.

Contribution

It extends the model of quantum state transfer and entanglement generation to n coupled cavities with three-level atoms, reducing computational complexity through symmetry and basis transformations.

Findings

Maximal entanglement times depend on hopping strength 

Hamiltonian reduction simplifies analysis from 3^n to 2n dimensions

Block-diagonalization facilitates explicit evolution of initial states

Abstract

Based on two-photon exchange interaction between $n$ coupled optical cavities each of them containing a single three level atom, the $n$-qubit and $n$-photonic state transfer is investigated. In fact, following the approach of Ref.\cite{Alex1}, we consider $n$ coupled cavities instead of two cavities and generalize the discussions about quantum state transfer, photon transition between cavities and entanglement generations between $n$ atoms. More clearly, by employing the consistency of number of photons (the symmetry of Hamiltonian), the hamiltonian of the system is reduced from $3^n$ dimensional space into 2n dimensional one. Moreover, by introducing suitable basis for the atom-cavity state space based on Fourier transform, the reduced Hamiltonian is block-diagonalized, with 2 dimensional blocks. Then, the initial state of the system is evolved under the corresponding Hamiltonian and the suitable times $T$ at which the initially unentangled atoms, become maximally entangled, are determined in terms of the hopping strength $\xi$ between cavities.