Quantum Mechanical Cumulant Dynamics near Stable Periodic Orbits in Phase Space: Application to the classical-like dynamics of quantum accelerator modes

Abstract

We formulate a general method for the study of semiclassical-like dynamics in stable regions of a mixed phase-space, in order to theoretically study the dynamics of quantum accelerator modes. In the simplest case, this involves determining solutions, which are stable when constrained to remain pure-state Gaussian wavepackets, and then propagating them using a cumulant-based formalism. Using this methodology, we study the relative longevity, under different parameter regimes, of quantum accelerator modes. Within this attractively simple formalism, we are able to obtain good qualitative agreement with exact wavefunction dynamics.

20 pages, 4 figures. Very substantially revised and expanded version

References in corpus (17)

• Transport equations including many-particle correlations for an arbitrary quantum system. General formalism
• Quantum resonances and decoherence for delta-kicked atoms
• A microscopic quantum dynamics approach to the dilute condensed Bose gas
• Stable Quantum Resonances in Atom Optics
• A classical scaling theory of quantum resonances
• Experimental investigation of early-time diffusion in the quantum kicked rotor using a Bose-Einstein condensate
• Experimental observation of high-order quantum accelerator modes
• Observation of sub-Fourier resonances in a quantum-chaotic system
• Nonlinear atom-optical delta-kicked harmonic oscillator using a Bose-Einstein condensate
• Signatures of quantum stability in a classically chaotic system
• Semiclassical Dynamics with Exponentially Small Error Estimates
• Observation of Robust Quantum Resonance Peaks in an Atom Optics Kicked Rotor with Amplitude Noise
• Revivals of Coherence in Chaotic Atom-Optics Billiards
• Gravity-Sensitive Quantum Dynamics in Cold Atoms
• Analysis of dynamical tunnelling experiments with a Bose-Einstein condensate
• Experimental evidence for the role of cantori as barriers in a quantum system
• An accelerator mode based technique for studying quantum chaos

Cited by in corpus (12)

• A number-conserving approach to a minimal self-consistent treatment of condensate and non-condensate dynamics in a degenerate Bose gas
• Quantum Accelerator Modes from the Farey Tree
• Quantum random walks using quantum accelerator modes
• The manifestation of quantum resonances and antiresonances in a finite temperature dilute atomic gas
• Coherent acceleration of material wavepackets in modulated optical fields
• Atom interferometry using $\delta$-kicked and finite duration pulse-sequences
• Power-law behavior in the quantum-resonant evolution of the delta-kicked accelerator
• Fractional resonances in the atom-optical delta-kicked accelerator
• Resonant transfer of large momenta from finite duration pulse sequences
• An $\epsilon$-pseudoclassical model for quantum resonances in a cold dilute atomic gas periodically driven by finite-duration standing-wave laser pulses
• Lattice-depth measurement using multi-pulse atom diffraction in and beyond the weakly diffracting limit
• Lattice-depth measurement using continuous grating atom diffraction