Quantum resonances in the delta-kicked harmonic oscillator

Billam, T.P.; Gardiner, S.A

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.

Citation

Billam, T., & Gardiner, S. (2009). Quantum resonances in the delta-kicked harmonic oscillator. Physical Review A, 80(2), https://doi.org/10.1103/physreva.80.023414

• Journal Article Type: Article
• Publication Date: Aug 1, 2009
• Deposit Date: Jun 30, 2010
• Publicly Available Date: Jul 1, 2010
• Journal: Physical Review A
• Print ISSN: 1050-2947
• Electronic ISSN: 1094-1622
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 80
• Issue: 2
• DOI: https://doi.org/10.1103/physreva.80.023414
• Publisher URL: http://link.aps.org/doi/10.1103/PhysRevA.80.023414