Classical diffusion in double-delta-kicked particles

Abstract

We investigate the classical chaotic diffusion of atoms subjected to {\em pairs} of closely spaced pulses (`kicks) from standing waves of light (the $2\delta$-KP). Recent experimental studies with cold atoms implied an underlying classical diffusion of type very different from the well-known paradigm of Hamiltonian chaos, the Standard Map. The kicks in each pair are separated by a small time interval $\epsilon \ll 1$, which together with the kick strength $K$, characterizes the transport. Phase space for the $2\delta$-KP is partitioned into momentum `cells' partially separated by momentum-trapping regions where diffusion is slow. We present here an analytical derivation of the classical diffusion for a $2\delta$-KP including all important correlations which were used to analyze the experimental data. We find a new asymptotic ($t\to \infty$) regime of `hindered' diffusion: while for the Standard Map the diffusion rate, for $K\gg 1$, $D\sim K^2/2[1-J_2(K)..]$ oscillates about the uncorrelated, rate $D_0=K^2/2$, we find analytically, that the $2\delta$-KP can equal, but never diffuses faster than, a random walk rate. We argue this is due to the destruction of the important classical `accelerator modes' of the Standard Map. We analyze the experimental regime $0.1\lesssim K\epsilon \lesssim 1$, where quantum localisation lengths $L\sim {\hslash }^{-0.75}$ are affected by fractal cell boundaries. We find an approximate asymptotic diffusion rate $D\propto K^3\epsilon$, in correspondence to a $D\propto K^3$ regime in the Standard Map associated with 'golden-ratio' cantori.

14 pages, 10 figures, error in equation in appendix corrected

References in corpus (5)

• Experimental investigation of early-time diffusion in the quantum kicked rotor using a Bose-Einstein condensate
• 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
• Theory of 2$\delta$-kicked Quantum Rotors

Cited by in corpus (6)

• Floquet topological phases in a spin-1/2 double kicked rotor
• Non-Hermitian Floquet topological phases in the double-kicked rotor
• Directed deterministic classical transport: symmetry breaking and beyond
• Complex dynamics of nano-mechanical membrane in cavity optomechanics
• Classical and Quantum Transport in One-Dimensional Periodically Kicked Systems
• Classical and quantum anomalous diffusion in a system of 2$\delta$-kicked Quantum Rotors