2008/09/30 by T. P. Billam, S. A. Gardiner · 1 citation
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Chemistry #Coherent states #Cold Atom Physics and Bose-Einstein Condensates #Harmonic oscillator #Mathematics #Nonlinear Dynamics and Pattern Formation #Observable #Open quantum system #Operator (biology) #Phase space #Physics #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Quantum simulator #Realization (probability) #Resonance (particle physics) #quant-ph
paper · pdf · doi:10.1103/physreva.80.023414
published as Phys. Rev. A 80, 023414 (2009) · 10 pages, 6 figures. Manuscript revised and extended
arxiv created 2009/05/22 · openalex publication_date 2009/08/20 · arxiv updated 2010/08/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Under certain conditions, the quantum \ensuremathδ-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the \ensuremathδ-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.