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arXiv:0801.4264

Transporting cold atoms in optical lattices with ratchets: Symmetries and Mechanisms

S. I. Denisov, Sergej Flach A, Peter Hänggi A

Published Jan 28, 2008• 0 citations
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Abstract

The objective of this work is to provide a general introduction into the symmetry analysis of the rachet effect using a simple, non-interacting one-particle dynamics. Despite its simplicity, this model contains all the basic aspects of classical and quantum ratchet dynamics, and may be used also as a starting point of incorporating atom-atom interactions.

DOI
10.48550/arxiv.0801.4264

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The objective of this work is to provide a general introduction into the symmetry analysis of the rachet effect using a simple, non-interacting one-particle dynamics. Despite its simplicity, this model contains all the basic aspects of classical and quantum ratchet dynamics, and may be used also as a starting point of incorporating atom-atom interactions.
Cold atoms in optical lattices are an ideal test bed to explore ratchet physics. This is largely due to the extreme tunability of optical lattice systems, which allows one to precisely control the shape of the potential and of any applied force, as well as to vary at will the level of dissipation. Since the very first demonstration of directed motion in a cold atom system by Mennerat-Robilliard et al. (1999), a number of experimental investigations with cold atoms in optical lattices have explored different aspects of the physics of ratchets. Here, the focus is first on the experiments in the classical regime which explored the relationship between symmetry and transport in a.c. driven ratchets. Experiments in the full quantum Hamiltonian regime are then described, and the unique features of such a regime highlighted. Ratchets in dissipative optical lattices Dissipative optical lattices Optical lattices are periodic potentials for atoms created by the interference of two or more laser fields.The detuning between the laser fields and the nearest atomic transition will emerge as a key parameter to describe the light–atom interaction. It is thus important to distinguish two very different situations: the case of fardetuned laser fields, and the case of near-resonant laser fields. For far-detuned laser fields, a purely conservative potential is produced. As will be discussed in the following sections, far-detuned optical lattices are ideal to model Hamiltonian systems. In the case of near-resonant laser fields, the interaction between the laser and the atoms may lead, under appropriate conditions, to dissipative dynamics. That is, for an appropriately arranged set of near-resonant optical lattices, a dissipative optical lattice, is produced, where the set of laser fields produce at once the periodic potential acting on the atoms and the cooling mechanism, which decreases their kinetic energy and lead to the trapping of the atoms at the bottom of potential wells. The principles behind the cooling mechanism, termed Sisyphus cooling for reasons which will become apparent in the following discussion, can be captured by considering the minimal configuration of a one-dimensional optical lattice and a J g = 1 / 2 → J e = 3 / 2 atomic transition. This is the simplest configuration in which Sisyphus cooling takes place.
This thesis reports the theoretical study of several cold atom ratchet systems. In particular the focus of the work is the determination of the ratchet current as a function of the ratchet parameters through analysis of the system symmetries and through numerical simulation. Ratchets are devices that exhibit directed motion in the absence of net forces. It is necessary to drive them away from thermal equilibrium so as to not violate the second law of thermodynamics. Currents are generated when the symmetries of the ratchet do not forbid it, a consequence of Curie's principle. An analysis of the symmetries will help determine for what parameters currents will be generated we perform such analyses in our investigations. The ratchets studied are modelled on the experimentally realised implementation of cold atoms in a driven optical lattice. Through the parameters of the driving and the optical lattice itself, we control the breaking of the symmetries and thus the generation of atomic currents. The precise relationship between current and ratchet parameters is explored by numerical simulation. In experiments the driving is achieved through a phase-modulation of the optical lattice beams. In numerical simulations we include the driving force directly in the equations of motion. We verify theoretically and numerically that the two approaches are equivalent. We have modelled the dynamics of atoms in light-fields through semiclassical and quantum treatments. The semiclassical treatment results in stochastic differential equations for the external degrees of freedom. These are simulated using the Monte-Carlo technique. For the fully quantum treatment we apply a stochastic trajectory method to simulate the master equation. We perform a comparison between different treatments for an over-damped ratchet.
Ratchets are devices that operate away from thermal equilibrium and can rectify zero-mean perturbations to achieve directed transport. We implement a ratchet system by using cold atoms in a driven optical lattice. This ratchet system can be precisely controlled experimentally, by adjusting either the driving parameters or the characteristics of the optical lattice. Directed transport in our ratchet is caused by rectification of either the driving force or fluctuations. We demonstrate under which conditions these types of rectification occur. Rectification of the driving force is a deterministic process, while rectification of fluctuations implies that the atoms act as Brownian motors. We show that resonant activation is the underlying mechanism of operation of these Brownian motors. The ratchet transport is controlled by symmetries of the system. The temporal symmetry of the system is normally broken by a time- asymmetric driving force. Here we show that for a system with symmetric driving and a symmetric potential, directed transport can also be caused by dissipation-induced breaking of time-reversal symmetry. This happens in the limit of small driving amplitude and large dissipation. We also study quasiperiodic driving of a cold atom ratchet and examine the relationship between symmetries and transport in this case. When mapping the route to quasiperiodicity we find a characteristic peak spectrum with transport occurring for certain ratios of frequencies. We characterize these peaks spectroscopically, and conclude that their shape is determined by the duration of driving. Finally, we investigate the coherency of transport with quasiperiodic driving and find large coherencies for certain driving parameters.