M. M. A. Stocklin | Searcharxiv

arXiv2006

Quantum chaos with spin-chains in pulsed magnetic fields

Recently it was found that the dynamics in a Heisenberg spin-chain subjected to a sequence of periodic pulses from an external, parabolic, magnetic field can have a close correspondence with the quantum kicked rotor (QKR). The QKR is a key paradigm of quantum chaos; it has as its classical limit the well-known Standard Map. It was found that a single spin excitation could be converted into a pair of non-dispersive, counter-propagating spin coherent states equivalent to the accelerator modes of the Standard Map. Here we consider how other types of quantum chaotic systems such as a double-kicked quantum rotor or a quantum rotor with a double-well potential might be realized with spin chains; we discuss the possibilities regarding manipulation of the one-magnon spin waves.

quant-ph↗

arXiv2006

Classical diffusion in double-delta-kicked particles

We investigate the classical chaotic diffusion of atoms subjected to {\em pairs} of closely spaced pulses (`kicks) from standing waves of light (the $2δ$-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 $ε\ll 1$, which together with the kick strength $K$, characterizes the transport. Phase space for the $2δ$-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 $2δ$-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 $2δ$-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 $0.1\lesssim Kε\lesssim 1$, where quantum localisation lengths $L \sim \hbar^{-0.75}$ are affected by fractal cell boundaries. We find an approximate asymptotic diffusion rate $D\propto K^3ε$, in correspondence to a $D\propto K^3$ regime in the Standard Map associated with 'golden-ratio' cantori.

physics.atom-ph↗