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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

How to characterize the dynamics of cold atoms in non dissipative optical lattices?

Daniel Hennequin, Philippe Verkerk

Published Jun 1, 2009• 0 citations
Publisher

Abstract

The aim of this paper is to study experimentally the dynamics of atoms in various 2D or 3D optical potentials. In particular, we would like to be able to detect the existence of chaotic individual trajectories. We access the collective signatures through simulations of the atomic dynamics in different optical lattices: a standard square potential, which is either red or blue detuned, and a lattice developed in our group, made of a stack of ring traps.

DOI
10.1109/cleoe-eqec.2009.5192468

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The aim of this paper is to study experimentally the dynamics of atoms in various 2D or 3D optical potentials. In particular, we would like to be able to detect the existence of chaotic individual trajectories. We access the collective signatures through simulations of the atomic dynamics in different optical lattices: a standard square potential, which is either red or blue detuned, and a lattice developed in our group, made of a stack of ring traps.
We examine here the classical dynamics of cold atoms in square optical lattices, i.e. lattices obtained with two orthogonal stationary plane waves. Contrary to many of the past studies in this domain, the potential here is time independent and non-dissipative. We show that, as a function of the experimental parameters, very different behaviours are obtained, both for the dynamics of atoms trapped inside individual sites and for atoms travelling between sites: inside the sites, chaos may be the main regime or, on the contrary, it may be negligible; outside the sites, chaos sometimes coexists with other regimes. We discuss the consequences of these differences on the macroscopic behaviour of the atoms in the lattice, and we propose experimental measurements able to characterize these dynamics and to distinguish between the different cases.
We propose an optical lattice for cold atoms made of a one-dimensional stack of dark ring traps. It is obtained through the interference pattern of a standard Gaussian beam with a counterpropagating hollow beam obtained using a setup with two conical lenses. The traps of the resulting lattice are characterized by a high confinement and a filling rate much larger than unity, even if loaded with cold atoms from a magneto-optical trap. We have implemented this system experimentally, and demonstrated its feasibility. Applications in statistical physics, quantum computing, and Bose-Einstein condensate dynamics are conceivable.
The possibility of experimental observation of chaotic motion of cold atoms in a one-dimensional rigid optical lattice without any modulation of its parameters and additional impact is demonstrated theoretically and numerically. This effect of deterministic chaos arises near the optical resonance due to the nonlinear coupling of electronic and mechanical degrees of freedom in the atom. In a certain range of resonance detunings, at each crossing of the lattice-forming standing wave node by the atom, the atomic dipole moment changes pseudorandomly in a step-like manner, accompanied by an appropriate change in the atom momentum. This leads to the effect of chaotic wandering of atoms, possessing the properties of the classical deterministic chaos, namely, to the exponential sensitivity of atomic trajectories to small variations of the initial conditions and/or the control parameters. With time, part of atoms from the initial cloud changes the direction of their motion to the opposite one, which can be detected in a real experiment. Numerical experiments with lithium atoms with the spontaneous emission taken into account show that by varying the laser radiation intensity (normalised detuning of resonance) in the rigid optical lattice, one can implement the transition from the regular regime of the atomic motion to the chaotic wandering in a real experiment.
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.
We study the dynamics of non interacting thermal atoms embedded in structured optical lattices with non trivial geometry. The lattice would be generated by two counter propagating modes with parabolic cylindrical symmetry and we concentrate on the quasi conservative red detuned far-off-resonance regime. The system exhibits quasi periodic and chaotic behaviors whose probability can be controlled by varying the intensity of the beams. The spectral density of the trajectories is used as a chaos signature. An analysis of permanency times for chaotic trajectories that visit more than one potential well reveals a distribution with a long tail.