Classical momentum diffusion in double-δ-kicked particles

Abstract

We investigate the classical chaotic diffusion of atoms subjected to pairs of closely spaced pulses ("kicks") from standing waves of light (the 2delta-KP ). Recent experimental studies with cold atoms implied an underlying classical diffusion of a 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 E<<1, which together with the kick strength K, characterizes the transport. Phase space for the 2delta-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 2delta-KP including all important correlations which were used to analyze the experimental data. We find an asymptotic (t-->infinity) regime of "hindered" diffusion: while for the standard map the diffusion rate, for K>>1 , D approximately K(2)/2[1-2J(2)(K)...] oscillates about the uncorrelated rate D(0)=K(2)/2, we find analytically, that the 2delta-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 less or approximately KE less or approximately 1 , where quantum localization lengths L approximately Planck's (-0.75) are affected by fractal cell boundaries. We find an approximate asymptotic diffusion rate D proportional to K(3)E, in correspondence to a D proportional to K(3) regime in the standard map associated with the "golden-ratio" cantori.