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Quantum resonances in the delta-kicked harmonic oscillator

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

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T.P. Billam


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.


Billam, T., & Gardiner, S. (2009). Quantum resonances in the delta-kicked harmonic oscillator. Physical Review A, 80(2),

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
Publisher URL


Published Journal Article (397 Kb)

Copyright Statement
© 2009 by The American Physical Society. All rights reserved.

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