Quantum communication through Jaynes-Cummings-Hubbard arrays

TL;DR

This paper investigates quantum state propagation in a one-dimensional array of Jaynes-Cummings-Hubbard systems, revealing how detuning and coupling configurations affect atomic and photonic excitation dynamics and enabling potential quantum state transmission.

Contribution

It introduces a detailed analysis of excitation propagation in coupled cavity arrays with uniform and nonuniform couplings, including exact correlation functions for specific detuning conditions.

Findings

Atomic excitations propagate without populating field modes at large detuning.

Near-resonance conditions lead to mixing of atomic and photonic states.

Exact quantum state transmission is achievable with parabolic coupling and specific detuning.

Abstract

We study the dynamics of an one dimensional array of Jaynes-Cummings-Hubbard system of arbitrary number of coupled cavities, each containing a two level atom that interacts with a field mode. In particular, we consider propagation of a single excitation quantum state for two different couplings of the photonic modes of the adjacent cavities, namely, a translation invariant closed chain of uniformly coupled cavities, and also a linear chain with nonuniform parabolically varying intercavity coupling where the interaction Hamiltonian is associated with the Jacobi matrix of the Krawtchouk polynomials. Using a description via the delocalized atomic and field modes we observe that for a large detuning of these two degrees of freedom atomic excitations propagate without populating the field modes, and vice versa. For the near-resonance scenario between these modes the atomic excitations, say, while propagating mix with the photonic states. In the context of the parabolic coupling between photons of adjacent cavities an arbitrary element of the time-dependent correlation function between two arbitrary cavities may be expressed in closed form for dominant values of the detuning parameter, when an exact transmission of the quantum state at pre-specified times is realized.