Quantum resonances and decoherence for delta-kicked atoms

Abstract

The quantum resonances occurring with delta-kicked atoms when the kicking period is an integer multiple of the half-Talbot time are analyzed in detail. Exact results about the momentum distribution at exact resonance are established, both in the case of totally coherent dynamics and in the case when decoherence is induced by Spontaneous Emission. A description of the dynamics when the kicking period is close to, but not exactly at resonance, is derived by means of a quasi-classical approximation where the detuning from exact resonance plays the role of the Planck constant. In this way scaling laws describing the shape of the resonant peaks are obtained. Such analytical results are supported by extensive numerical simulations, and explain some recent surprising experimental observations.

51 pages, 13 figures; KEYWORDS: quantum chaos, decoherence, kicked rotor, dynamical localization, atom optics; submitted to Nonlinearity

References in corpus (8)

• Non-dispersive wave packets in periodically driven quantum systems
• Stable Quantum Resonances in Atom Optics
• Observation of sub-Fourier resonances in a quantum-chaotic system
• Signatures of quantum stability in a classically chaotic system
• Quantum Resonances of Kicked Rotor and SU(q) group
• An accelerator mode based technique for studying quantum chaos
• Diffusion Resonances in Action Space for an Atom Optics Kicked Rotor with Decoherence
• Quantum Resonances and Regularity Islands in Quantum Maps

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