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Physical Review A

Cold collisions in a laser field: Quantum Monte Carlo treatment of radiative heating

Murray Holland, Kalle‐Antti Suominen, Keith R. Burnett

Published Aug 1, 1994• 33 citations
Publisher

Abstract

We give a full quantum treatment of the radiative heating mechanism which arises in atomic clouds at low temperatures due to the collisions in the presence of a light field. The time scale of these collisions is comparable to the time scale of spontaneous decay, hence one needs to combine excitation and decay processes with the quantum motion of the colliding atoms into a single model, which we have done. Our study produces a statistical approximate to the full density matrix by combining wave-packet dynamics with the Monte Carlo state-vector method. We also present a quantitative semiclassical treatment based on the Landau-Zener model, and show that it agrees with the quantal results in certain parameter regimes. However, for low temperatures and strong laser fields the full quantum treatment is needed. We describe our numerical procedures and the statistical aspects of the Monte Carlo state-vector method in detail. Our main result is that the low-energy collisions can produce appreciable heating of the cloud.

DOI
10.1103/physreva.50.1513

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We give a full quantum treatment of the radiative heating mechanism which arises in atomic clouds at low temperatures due to the collisions in the presence of a light field. The time scale of these collisions is comparable to the time scale of spontaneous decay, hence one needs to combine excitation and decay processes with the quantum motion of the colliding atoms into a single model, which we have done. Our study produces a statistical approximate to the full density matrix by combining wave-packet dynamics with the Monte Carlo state-vector method. We also present a quantitative semiclassical treatment based on the Landau-Zener model, and show that it agrees with the quantal results in certain parameter regimes. However, for low temperatures and strong laser fields the full quantum treatment is needed. We describe our numerical procedures and the statistical aspects of the Monte Carlo state-vector method in detail. Our main result is that the low-energy collisions can produce appreciable heating of the cloud.
We derive and apply an optical Bloch equation (OBE) model for describing collisions of ground and excited laser cooled alkali atoms in the presence of near-resonant light. Typically these collisions lead to loss of atoms from traps. We compare the results obtained with a quantum mechanical complex potential treatment, semiclassical Landau-Zener models with decay, and a quantum time-dependent Monte Carlo wave packet (MCWP) calculation. We formulate the OBE method in both adiabatic and diabatic representations. We calculate the laser intensity dependence of collision probabilities and find that the adiabatic OBE results agree quantitatively with those of the MCWP calculation, and qualitatively with the semiclassical Landau-Zener model with delayed decay, but that the complex potential method or the traditional Landau-Zener model fail in the saturation limit.
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.
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.
Inelastic collision rates between two very cold ground-state atoms can be strongly decreased by using an optical shielding laser to repel the colliding atoms at very large internuclear separation so that they never get close to each other. This can be achieved by using a sufficiently intense laser to excite a repulsive state of the quasimolecule formed by the two colliding atoms. We study a simple two-state model and compare the predictions of fully quantum-mechanical close coupling and time-dependent wave packet methods with semiclassical approximations based on the concept of a Landau-Zener curve crossing of field-dressed states. The effect of spontaneous emission in the excited state is treated by the Monte Carlo wave-function method. Calculations are given for a model sodium system at 250 \ensuremath{\mu}K. Strong optical shielding, without significant heating due to the quasimolecular excitation, can be achieved at relatively modest laser power. We find that Landau-Zener models give near quantitative agreement with the fully quantum calculations in spite of the extremely low temperature.
We show that in the cold collisions between laser-cooled and trapped atoms the probability to survive in the excited state during the collision can be obtained, in the weak-field limit, from a simple Landau-Zener approach. This is shown by comparing the method with a fully quantum and time-dependent wave-packet treatment. We also show that the optical Bloch equation method is not the proper semiclassical tool to use at low energies, at least in its present form. The unexpectedly low quantum survival probability reported by Boesten et al. [Phys. Rev. A 48, 1428 (1993)] is in fact predicted by the semiclassical Landau-Zener approach. This in turn shows that off-resonant excitation is not important in the low-energy regime.