Quantum resonances in an atom-optical delta-kicked harmonic oscillator

TL;DR

This paper investigates quantum resonances in an atom-optical delta-kicked harmonic oscillator, providing theoretical predictions, numerical simulations, and an analytic framework for understanding observable effects and state evolution at resonance.

Contribution

It offers a detailed theoretical analysis of quantum resonances in an atom-optical system, including resonance conditions, physical explanations, and analytic solutions for state evolution.

Findings

Quantum resonances occur at specific parameter values.

Numerical simulations confirm observable resonance effects.

Analytic expressions describe coherent state evolution at resonance.

Abstract

Under certain conditions, the quantum delta-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the delta-kicked harmonic oscillator, and present a theoretical discussion of the quantum resonances that could be observed in such a system. Having outlined our model of the physical system we derive the values at which quantum resonances occur and relate these to potential experimental parameters. We discuss the observable effects of the quantum resonances, using the results of numerical simulations. We develop a physical explanation for the quantum resonances based on symmetries shared between the classical phase space and the quantum-mechanical time evolution operator. We explore the evolution of coherent states in the system by reformulating the dynamics in terms of a mapping over an infinite, two-dimensional set of coefficients, from which we derive an analytic expression for the evolution of a coherent state at quantum resonance.