Resonant Population Transfer in the Time-Dependent Quantum Elliptical Billiard

TL;DR

This paper investigates quantum dynamics in a time-dependent elliptical billiard, revealing resonant energy transfer phenomena driven by specific frequencies, supported by numerical and simplified models.

Contribution

It introduces a numerical method for simulating quantum billiards with time-dependent boundaries and identifies resonance conditions for energy transfer.

Findings

Resonances occur when driving frequency matches energy differences between states.

Higher or lower energy states are periodically populated at resonances.

A few-level Rabi-like model reproduces key numerical results.

Abstract

We analyze the quantum dynamics of the time-dependent elliptical billiard using the example of a certain breathing mode. A numerical method for the time-propagation of an arbitrary initial state is developed, based on a series of transformations thereby removing the time-dependence of the boundary conditions. The time-evolution of the energies of different initial states is studied. The maximal and minimal energy that is reached during the time-evolution shows a series of resonances as a function of the applied driving frequency. At these resonances, higher (or lower) lying states are periodically populated, leading to the observed change in energy. The resonances occur when the driving frequency or a multiple of it matches exactly the mean energetic difference between the two involved states. This picture is confirmed by a few-level Rabi-like model with periodic couplings, reproducing the key results of our numerical study.