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arXiv:physics/0009053 · Journal of Physics B Atomic Molecular and Optical Physics

Cold collisions between atoms in optical lattices

Jyrki Piilo, Kalle‐Antti Suominen, Kirstine Berg‐Sørensen

Published Mar 22, 2001• 6 citations
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Abstract

We have simulated binary collisions between atoms in optical lattices during Sisyphus cooling. Our Monte Carlo wavefunction simulations show that the collisions selectively accelerate mainly the hotter atoms in the thermal ensemble, and thus affect the steady state which one would normally expect to reach in Sisyphus cooling without collisions.

DOI
10.1088/0953-4075/34/7/105

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We have simulated binary collisions between atoms in optical lattices during Sisyphus cooling. Our Monte Carlo wavefunction simulations show that the collisions selectively accelerate mainly the hotter atoms in the thermal ensemble, and thus affect the steady state which one would normally expect to reach in Sisyphus cooling without collisions.
We simulate collisions between two atoms, which move in an optical lattice under the dipole-dipole interaction. The model describes simultaneously the two basic dynamical processes, namely the Sisyphus cooling of single atoms, and the light-induced inelastic collisions between them. We consider the $J=1/\stackrel{\ensuremath{\rightarrow}}{2}J=3/2$ laser cooling transition for Cs and Na. We find that the hotter atoms in a thermal sample are selectively lost or heated by the collisions, which modifies the steady-state distribution of atomic velocities, reminiscent of the evaporative cooling process.
We have simulated the dynamics of interacting atoms in optical lattices. The periodic lattice structure is produced with laser beams detuned a few linewidths to the red from the atomic transition. The atoms localize in lattice sites as a steady state is reached during the cooling, but they can still to some extent move between the sites. Our Monte Carlo Wave Function simulations show that in such situations the interactions can lead to evaporative cooling of the atoms as the hotter ones are ejected from the lattice.
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 study the dynamics of the cooling of a gas of caesium atoms in an optical lattice, both experimentally and with 1D full-quantum Monte Carlo simulations. We find that, contrary to the standard interpretation of the Sisyphus model, the cooling process does not work by a continuous decrease of the average kinetic energy of the atoms in the lattice. Instead, we show that the momentum of the atoms follows a bimodal distribution, the atoms being gradually transferred from a hot to a cold mode. We suggest that the cooling mechanism should be depicted in terms of a rate model, describing the transfer between the two modes along with the processes occurring within each mode.
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.
The purpose of our master thesis is to present an original synthesis of various works dealing with the Monte-Carlo wavefunction (MCWF) method in quantum optics and its applications to laser cooling of atoms with a particular focus on Doppler and Sisyphus cooling mechanisms. We introduce the MCWF method which is used to solve master equations describing the dynamics of open quantum systems in quantum optics. This method turns out to be much more efficient than a method based on the full integration of the density matrix. We perform laser cooling simulations in 1D both with a classical and a quantum treatment of the atomic centre-of-mass motion and investigate Doppler and Sisyphus cooling. Our numerical results turn out to be in very good agreement with those predicted by semiclassical theories, except for large detuning and/or low intensity laser where semiclassical theories fail. For such cases, our method provides a good alternative and predicts temperatures much larger than the recoil temperature. Finally, we also consider a classical treatment of the centre-of-mass motion and we compare the subsequent results with those obtained with a full quantum approach.