Theory of 2$\delta$-kicked Quantum Rotors

Abstract

We examine the quantum dynamics of cold atoms subjected to {\em pairs} of closely spaced $\delta$-kicks from standing waves of light, and find behaviour quite unlike the well-studied quantum kicked rotor (QKR). Recent experiments [Jones et al, {\em Phys. Rev. Lett. {\bf 93}, 223002 (2004)}] identified a regime of chaotic, anomalous classical diffusion. We show that the corresponding quantum phase-space has a cellular structure, arising from a unitary matrix with oscillating band-width. The corresponding eigenstates are exponentially localized, but scale with a fractional power, $L\sim {\hslash }^{-0.75}$, in contrast to the QKR for which $L\sim {\hslash }^{-1}$. The effect of inter-cell (and intra-cell) transport is investigated by studying the spectral fluctuations with both periodic as well as `open' boundary conditions.

12 pages with 14 figures

References in corpus (5)

• Entanglement Across a Transition to Quantum Chaos
• The Anderson transition in quantum chaos
• Atoms in double-delta-kicked periodic potentials: chaos with long-range correlations
• $2\delta$-Kicked Quantum Rotors: Localization and `Critical' Statistics
• Chaotic quantum ratchets and filters with cold atoms in optical lattices: properties of Floquet states

Cited by in corpus (14)

• Differences between mean-field dynamics and N-particle quantum dynamics as a signature of entanglement
• Floquet topological phases in a spin-1/2 double kicked rotor
• Proposal of a Cold-atom Realization of Quantum Maps with Hofstadter's Butterfly Spectrum
• Non-Hermitian Floquet topological phases in the double-kicked rotor
• Quantum Ratchet Accelerator without a Bichromatic Lattice Potential
• Quantum Control of Ultra-cold Atoms: Uncovering a Novel Connection between Two Paradigms of Quantum Nonlinear Dynamics
• Directed deterministic classical transport: symmetry breaking and beyond
• Fractional photon-assisted tunneling in an optical superlattice: large contribution to particle transfer
• Classical diffusion in double-delta-kicked particles
• Fractional $\hslash$-scaling for quantum kicked rotors without cantori
• Classical and Quantum Transport in One-Dimensional Periodically Kicked Systems
• Bose-Einstein condensates in a double well: mean-field chaos and multi-particle entanglement
• Classical and quantum anomalous diffusion in a system of 2$\delta$-kicked Quantum Rotors
• Quantum Effects In Low Temperature Bosonic Systems