A classical scaling theory of quantum resonances

Abstract

The quantum resonances occurring with delta-kicked particles are studied with the help of a fictitious classical limit, establishing a direct correspondence between the nearly resonant quantum motion and the classical resonances of a related system. A scaling law which characterizes the structure of the resonant peaks is derived and numerically demonstrated.

4 pages, 2 Figs

References in corpus (6)

• Quantum resonances and decoherence for delta-kicked atoms
• Stable Quantum Resonances in Atom Optics
• Experimental observation of high-order quantum accelerator modes
• Observation of sub-Fourier resonances in a quantum-chaotic system
• Quantum Resonances of Kicked Rotor and SU(q) group
• Quantum Resonances and Regularity Islands in Quantum Maps

Cited by in corpus (38)

• Ratchet effect for cold atoms in an optical lattice
• Controlling the Ratchet Effect for Cold Atoms
• Resonant nonlinear quantum transport for a periodically kicked Bose condensate
• Quantum synchronization
• Sub-Fourier characteristics of a $\delta$-kicked rotor resonance
• Atoms in double-delta-kicked periodic potentials: chaos with long-range correlations
• Ballistic and localized transport for the atom optics kicked rotor in the limit of vanishing kicking period
• Experimental Realization of a Quantum Ratchet Through Phase Modulation
• General Quantum Resonances of the Kicked Particle
• Observation of Robust Quantum Resonance Peaks in an Atom Optics Kicked Rotor with Amplitude Noise
• Quantum resonance, Anderson localisation and selective manipulations in molecular mixtures by ultrashort laser pulses
• Experimental verification of a one-parameter scaling law for the quantum and "classical" resonances of the atom-optics kicked rotor
• Current behavior of a quantum Hamiltonian ratchet in resonance
• Delocalized and Resonant Quantum Transport in Nonlinear Generalizations of the Kicked Rotor Model
• Phase Noise in the Delta Kicked Rotor: From Quantum to Classical
• The manifestation of quantum resonances and antiresonances in a finite temperature dilute atomic gas
• Nonlinear resonances in δ-kicked Bose-Einstein Condensates
• Demonstration of perfect coherence preservation for matter-waves perturbed by a delta-kicked rotor
• Quantum Mechanical Cumulant Dynamics near Stable Periodic Orbits in Phase Space: Application to the classical-like dynamics of quantum accelerator modes
• The role of quasi-momentum in the resonant dynamics of the atom-optics kicked rotor
• Cold Atom Optical Lattices as Quantum Analog Simulators for Aperiodic One-Dimensional Localization Without Disorder
• Many-body interference at the onset of chaos
• Pseudo-classical theory for fidelity of nearly resonant quantum rotors
• Power-law behavior in the quantum-resonant evolution of the delta-kicked accelerator
• Fluctuations and Transients in Quantum-Resonant Evolution
• Fidelity for kicked atoms with gravity near a quantum resonance
• Quantum recurrences in the kicked top
• Directed transport and Floquet analysis for a periodically kicked wavepacket at a quantum resonance
• Fractional resonances in the atom-optical delta-kicked accelerator
• Enhancing Quantum Metrology by Quantum Resonance Dynamics
• 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
• Low-energy prethermal phase and crossover to thermalization in nonlinear kicked rotors
• Rotating Accelerator-Mode Islands
• Deviations from early--time quasilinear behaviour for the quantum kicked rotor near the classical limit
• Engineering transport by concatenated maps
• Kicked-rotor quantum resonances in position space: Application to situations of experimental interest
• Classical model for survival resonances close to Talbot time