Photon reflection by a quantum mirror: a wave function approach

TL;DR

This paper derives the photon-mirror momentum exchange from first principles, showing the photon momentum as hk/2π and linking it to the Minkowski momentum in media, contributing to the Abraham-Minkowski debate.

Contribution

It provides a quantum wave function approach to photon reflection, clarifying the photon momentum in media and its relation to the Minkowski momentum.

Findings

Photon momentum is hk/2π upon reflection.

Photon radiation pressure in a medium is proportional to its refractive index n.

The system generally ends in an entangled state unless the mirror is highly localized.

Abstract

We derive from first principles the momentum exchange between a photon and a quantum mirror upon reflection, by considering the boundary conditions imposed by the mirror surface on the photon wave equation. We show that the system generally ends up in an entangled state, unless the mirror position uncertainty is much smaller than the photon wavelength, when the mirror behaves classically. Our treatment leads us directly to the conclusion that the photon momentum has the known value hk/2{\pi}. This implies that when the mirror is immersed in a dielectric medium the photon radiation pressure is proportional to the medium refractive index n. Our work thus contributes to the longstanding Abraham-Minkowski debate about the momentum of light in a medium. We interpret the result by associating the Minkowski momentum (which is proportional to n) with the canonical momentum of light, which appears naturally in quantum formulations.