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arXiv:physics/0411010 · Journal of Optics B Quantum and Semiclassical Optics

Cold collisions in dissipative optical lattices

Jyrki Piilo, Kalle‐Antti Suominen

Published Apr 15, 2005• 4 citations
arXivHTMLPDF

Abstract

In the past, light-assisted cold collisions between laser cooled atoms have been widely studied in magneto-optical atom traps (MOTs). We describe here theoretical studies of dynamical interactions, specifically cold collisions, between atoms trapped in near-resonant, dissipative optical lattices. The developed quantum-mechanical model is based on Monte Carlo wave-function simulations and combines atomic cooling and collision dynamics in a single framework. It turns out, that the radiative heating mechanism affects the dynamics of atomic cloud in a red-detuned lattice in a way that is not directly expected from the MOT studies. The optical lattice and position dependent light-matter coupling introduces selectivity of collision partners. Atoms, which are most mobile and energetic, are strongly favored to participate in collisions, and are more often ejected from the lattice, than the slow ones in the laser parameter region selected for study. For blue-detuned lattices, we study how optical shielding emerges as a natural part of the lattice and look for ways to optimize the effect. The simulations are computationally very demanding and would obviously benefit from the simplification schemes. We present some steps to this direction by showing how it is possible to calculate collision rates in near-resonant lattices in a fairly simple way.

DOI
10.1088/1464-4266/7/5/r01

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In the past, light-assisted cold collisions between laser cooled atoms have been widely studied in magneto-optical atom traps (MOTs). We describe here theoretical studies of dynamical interactions, specifically cold collisions, between atoms trapped in near-resonant, dissipative optical lattices. The developed quantum-mechanical model is based on Monte Carlo wave-function simulations and combines atomic cooling and collision dynamics in a single framework. It turns out, that the radiative heating mechanism affects the dynamics of atomic cloud in a red-detuned lattice in a way that is not directly expected from the MOT studies. The optical lattice and position dependent light-matter coupling introduces selectivity of collision partners. Atoms, which are most mobile and energetic, are strongly favored to participate in collisions, and are more often ejected from the lattice, than the slow ones in the laser parameter region selected for study. For blue-detuned lattices, we study how optical shielding emerges as a natural part of the lattice and look for ways to optimize the effect. The simulations are computationally very demanding and would obviously benefit from the simplification schemes. We present some steps to this direction by showing how it is possible to calculate collision rates in near-resonant lattices in a fairly simple way.
We report Monte Carlo wave-function simulation results for two colliding atoms in a blue-detuned near-resonant $J=\stackrel{\ensuremath{\rightarrow}}{1}J=1$ optical lattice. Our results show that complete optical shielding of collisions can be achieved within the lattice with suitably selected and realistic laser field parameters. More importantly, our results demonstrate that the shielding effect does not interfere with the actual trapping and cooling process, and it is produced by the lattice lasers themselves, without the need to use additional laser beams.
We present a simple method for calculating the binary collision rate between atoms in near-resonant optical lattices. The method is based on Monte Carlo wave-function simulations, and the collision rate is obtained by monitoring the quantum flux beyond the average distance between the atoms. To illustrate the usefulness of the method, we calculate the collision rates for a wide range of occupation densities and various modulation depths of the lattice. The method presented here, combined with the semiclassical calculations accounting for intrawell collisions, can simplify the study of the effects of binary collisions on the dynamics of atomic clouds trapped in near-resonant optical lattices.
In red-detuned magneto-optical traps (MOTs) of molecules, sub-Doppler heating competes with Doppler cooling, resulting in high temperature and low density. A solution is offered by the blue-detuned MOT where sub- Doppler cooling dominates and the cloud is compressed. Several blue-detuned molecular MOTs have been implemented. A recent implementation relies on a pair of orthogonally polarized components whose frequency separation is smaller than the transition linewidth. We identify the trapping force in these MOTs. At a certain magnetic field, there is a state that is dark to the laser propagating in one direction, but not to the counterpropagating one. This Zeeman-induced dark state (ZIDS) sets up an imbalance in the photon scattering rate, leading to a restoring force. We also study the role of the moving lattices generated by the closely spaced frequency components of the light. We show that there is a velocity-dependent force that drives the molecules toward the speeds of these moving lattices, and that over a relevant range of magnetic fields this combines with the ZIDS force to transport molecules toward the center of the MOT. Here, gray molasses cooling, assisted by nonadiabatic transitions driven by the time-varying polarization of the light field, cools the molecules toward zero velocity. We study these mechanisms for model systems with simple level structures and then extend them to molecules with ground-state hyperfine structure.
This thesis gives an account of work done on semi-classical and quantum Monte Carlo simulations in far-detuned optical lattices. Firstly, the basic principles of laser cooling of atoms are presented including a short introduction to optical lattices in the near and far-detuned regime. A detailed analysis is made of the band-structure of optical lattices, using the Bloch formalism, and of the bound-state population distribution appropriate for a thermal sample of trapped atoms. Secondly, a general overview is given of the quantum Monte Carlo method for simulating the dynamics of atom-light interactions. This is followed by a detailed study of the concept of Raman cooling, which is a useful tool to prepare atoms in the ground motional state of the lattice and an important first step to achieving quantum state control with ultra-cold atoms. A simplified model of Raman cooling is introduced and simulated using the quantum Monte Carlo wave-function approach. Then the implementation of simulations of resolved-sideband Raman cooling based on this model is discussed as is how the results were used to optimize the experimental work done by our group. The results of these simulations show for the first time that the quantum Zeno effect has a crucial impact on the efficiency of Raman cooling experiments. Also the experimental measurements of the temperature of Raman sideband cooled atoms for a range of parameters are compared with theoretical results and shows a good qualitative agreement. Thirdly, the results of semi-classical numerical simulations of parametric excitation in optical lattices are presented. It is shown that the modulation of the potential can result in selective parametric excitation of trapped atoms. The theoretical results show good qualitative agreement with experiment. The thesis is concluded with a description of possible avenues for future studies on quantum state control in optical lattices.
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.
It has been more than 30 years since the first demonstration of a magneto-optical trap (MOT) using sodium atoms. Since then the MOT has revolutionised the field of atomic physics by facilitating the emergence of a broad range of productive avenues of research using atoms prepared at low temperatures and high densities. This thesis describes the development of a novel kind of magneto-optical trap: the blue-detuned MOT. Unlike in all previous MOTs the light is blue detuned from atomic resonances and drives "type-II" transitions that have dark ground-state sub-levels. A discussion of the position-dependent and velocity-dependent forces experienced by an atom or molecule in a MOT is first used to consolidate recent theoretical work and, in particular, to introduce the concept of a blue-detuned MOT. The design and construction of an experiment that has been built to demonstrate a blue-detuned MOT using \Rb{87} is described. A thorough characterisation of this novel MOT has been performed. At high magnetic field gradients, radiation-pressure-limited densities exceeding 101110^{11}1011~cm−3^{-3}−3 have been reached whilst temperatures are cooled below 30~\si{\micro K} by the efficient and robust sub-Doppler cooling mechanisms. The maximum phase-space density measured is 6×10−66\times10^{-6}6×10−6, which is higher than in most normal atomic MOTs, comparable to the best dark SPOTs, and a million times higher than that reported for red-detuned type-II MOTs. This makes the blue-detuned MOT particularly attractive for molecules where laser cooling and trapping always uses type-II transitions. For the first time, a study of trap loss due to ultra-cold collisions between atoms occurring in the presence of near-resonant blue-detuned light is undertaken. Finally, the experiment is used to demonstrate many new and unreported configurations of MOT for \Rb{87}, showing that a comprehensive understanding of complicated MOTs is now possible, and presenting a clear direction for further research.