Squeezed state evolution and entanglement in lossy coupled resonator optical waveguides

TL;DR

This paper provides a theoretical analysis of how squeezed states evolve and become entangled in lossy coupled resonator optical waveguides, offering analytical insights into photon dynamics and quantum correlations.

Contribution

It introduces a general formalism for analyzing squeezed state evolution in lossy coupled cavities and derives analytical expressions for key quantum properties.

Findings

Loss affects photon number, squeezing, and entanglement over time.

Analytical expressions for maximum photon number, squeezing, and entanglement.

Quantum entanglement persists despite system losses.

Abstract

We investigate theoretically the temporal evolution of a squeezed state in lossy coupled-cavity systems. We present a general formalism based upon the tight binding approximation and apply this to a two-cavity system as well as to a coupled resonator optical waveguide in a photonic crystal. We derive analytical expressions for the number of photons and the quadrature noise in each cavity as a function of time when the initial excited state is a squeezed state in one of the cavities. We also analytically evaluate the time dependant cross correlation between the photons in different cavities to evaluate the degree of quantum entanglement. We demonstrate the effects of loss on the properties of the coupled-cavity systems and derive approximate analytic expressions for the maximum photon number, maximum squeezing and maximum entanglement for cavities far from the initially excited cavity in a lossless coupled resonator optical waveguide.