Analysis of resonant population transfer in time-dependent elliptical quantum billiards

TL;DR

This paper derives a Fermi's Golden Rule for elliptical quantum billiards with oscillating boundaries, explaining observed resonant population transfers and providing criteria for experimental resolvability, supported by numerical simulations.

Contribution

It introduces a new theoretical framework for understanding resonant population transfer in time-dependent elliptical quantum billiards, linking experimental observations with predictive criteria.

Findings

Resonant population transfer occurs when driving frequency matches mean energy differences.

Derived a criterion for the resolvability of resonances in experiments.

Numerical simulations confirm the theoretical resonance spectra predictions.

Abstract

A Fermi's Golden Rule for population transfer between instantaneous eigenstates of elliptical quantum billiards with oscillating boundaries is derived. Thereby, both the occurrence of the recently observed resonant population transfer between instantaneous eigenstates [F. Lenz et al. New J. Phys., {\bf 13}, 103019, 2011] and the empirical criterion stating that these transitions occur when the driving frequency matches the mean difference of the latter are explained. As a second main result a criterion judging which resonances are resolvable in a corresponding experiment of certain duration is provided. Our analysis is complemented by numerical simulations for three different driving laws. The corresponding resonance spectra are in agreement with the predictions of both criteria.