Adiabatic transfer of light in a double cavity and the optical Landau-Zener problem

TL;DR

This paper investigates how to deterministically transfer photons between two coupled cavities by changing their length difference, using a mapping to a Landau-Zener problem to identify adiabatic transfer conditions.

Contribution

It introduces a method to analyze adiabatic light transfer in double cavities via a mapping to a Landau-Zener problem, highlighting the limitations of this approach.

Findings

Photon transfer can be controlled by cavity length adjustments.

The Landau-Zener model applies under weak coupling conditions.

Caution is needed when modeling cavity dynamics with time-dependent boundaries.

Abstract

We analyze the evolution of an electromagnetic field inside a double cavity when the difference in length between the two cavities is changed, e.g. by translating the common mirror. We find that this allows photons to be moved deterministically from one cavity to the other. We are able to obtain the conditions for adiabatic transfer by first mapping the Maxwell wave equation for the electric field onto a Schroedinger-like wave equation, and then using the Landau-Zener result for the transition probability at an avoided crossing. Our analysis reveals that this mapping only rigorously holds when the two cavities are weakly coupled (i.e. in the regime of a highly reflective common mirror), and that, generally speaking, care is required when attempting a hamiltonian description of cavity electrodynamics with time-dependent boundary conditions.