Quantum light propagation in longitudinally inhomogeneous media as a spatial Lewis-Ermakov physical invariance

TL;DR

This paper investigates quantum light propagation in inhomogeneous media, introducing a Lewis-Ermakov invariant approach that yields physically consistent results and reveals a quantum Gouy's phase relevant for quantum interferometry.

Contribution

It presents a novel method using generalized canonical transformations and Lewis-Ermakov invariants to accurately model quantum light propagation in inhomogeneous media.

Findings

A physical propagator consistent with experiments is derived.

Quantum Gouy's phase is identified as a key effect of propagation.

The approach resolves unphysical noise squeezing issues in previous models.

Abstract

We study the propagation of quantum states of light in separable longitudinally inhomogeneous media. By means of the usual quantization approach this kind of media would lead to the unphysical result of quantum noise squeezing. This problem is solved by means of generalized canonical transformations in a comoving frame. Under these transformations the generator of propagation is a physical Lewis-Ermakov invariant in space which is quantized and, accordingly, a propagator consistent with experiments is obtained. Finally, we show that the net effect produced by propagation in these media is a quantum Gouy's phase with application in quantum interferometry.