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arXiv:physics/0510268 · Physical Review A

Predictions of laser-cooling temperatures for multilevel atoms in three-dimensional polarization-gradient fields

Josh W. Dunn, Chris H. Greene

Published Mar 31, 2006• 4 citations
arXivHTMLPDF

Abstract

We analyze the dynamics of atom-laser interactions for atoms having multiple, closely spaced, excited-state hyperfine manifolds. The system is treated fully quantum mechanically, including the atom's center-of-mass degree of freedom, and motion is described in a polarization gradient field created by a three-dimensional laser configuration. We develop the master equation describing this system, and then specialize it to the low-intensity limit by adiabatically eliminating the excited states. We show how this master equation can be simulated using the Monte Carlo wave function technique, and we provide details on the implementation of this procedure. Monte Carlo calculations of steady state atomic momentum distributions for two fermionic alkaline earth isotopes, $^{25}\mathrm{Mg}$ and $^{87}\mathrm{Sr}$, interacting with a three-dimensional lin-\ensuremath{\perp}-lin laser configuration are presented, providing estimates of experimentally achievable laser-cooling temperatures.

DOI
10.1103/physreva.73.033421

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We analyze the dynamics of atom-laser interactions for atoms having multiple, closely spaced, excited-state hyperfine manifolds. The system is treated fully quantum mechanically, including the atom's center-of-mass degree of freedom, and motion is described in a polarization gradient field created by a three-dimensional laser configuration. We develop the master equation describing this system, and then specialize it to the low-intensity limit by adiabatically eliminating the excited states. We show how this master equation can be simulated using the Monte Carlo wave function technique, and we provide details on the implementation of this procedure. Monte Carlo calculations of steady state atomic momentum distributions for two fermionic alkaline earth isotopes, 25Mg^{25}\mathrm{Mg}25Mg and 87Sr^{87}\mathrm{Sr}87Sr, interacting with a three-dimensional lin-\ensuremath{\perp}-lin laser configuration are presented, providing estimates of experimentally achievable laser-cooling temperatures.
A theoretical discussion of laser cooling of multilevel atomic systems using intense, blue detuned laser beams is given. A method based on matrix continued fractions is presented, which enables the efficient calculation of the semi-classical force on a multilevel system. The method is applied to a three-level system driven by one standing wave and one travelling wave. The force curves obtained exhibit strong cooling features. Cooling of the three-level system is simulated using the fully quantum mechanical Monte Carlo wave function technique. The simulation predicts efficient cooling to sub-Doppler temperatures. The three-level model is related to a multilevel cooling experiment performed on sp7\\sp7sp7Li. The experimental results are found to be in reasonable agreement with the three-level model. However, a comparison of the simulation and experiment for a two-level atomic system reveals significant discrepancies, which raises questions about the model and experiment.
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.
Two distinct lasers are shown to permit controlled cooling of a three-level atomic system to a regime particularly useful for group-II atoms. Alkaline-earth-metal atoms are difficult to laser cool to the micro- or nanokelvin regime, but this technique exhibits encouraging potential to circumvent current roadblocks. Introduction of a sparse-matrix technique permits efficient solution of the master equation for the stationary density matrix, including the quantized atomic momentum. This overcomes long-standing inefficiencies of exact solution methods, and it sidesteps inaccuracies of frequently implemented semiclassical approximations. The realistic theoretical limiting temperatures are optimized over the full parameter space of detunings and intensities. A qualitative interpretation based on the phenomenon of electromagnetically induced transparency reveals dynamical effects due to photon-atom dressing interactions that generate non-Lorentzian line shapes. Through coherent engineering of an asymmetric Fano-type profile, the temperature can be lowered down to the recoil limit range.
As a theoretical background for an ongoing experiment on longitudinal cooling of an energetic atomic beam by an intense laser field, we generalize the dressed-atom description of the atom–laser interaction from a two-level to a multilevel system. Expressions are presented for the average force on the atom, in particular in the limits of high and low velocities with respect to a standing wave, and the influence of fluctuations is studied through a Monte Carlo simulation. Appreciable cooling is predicted for a beam of 200-eV neon atoms traversing a 75-cm-long resonator in which the energy density is maintained by two 0.5-W cw lasers.
In the limit of asymptotically small photon momentum, a Fokker–Planck equation for the center-of-mass Wigner function suffices to describe laser cooling of an atom. We have devised a procedure to compute the light pressure force and the diffusion tensor for an atom with an arbitrary level structure, traveling with an arbitrary velocity in any given three-dimensional light field. The scheme is based on solving a set of differential equations closely related to the density matrix equations of motion encountered in conventional recoilless laser spectroscopy. Computer programs have been written that automatically construct and solve the required equations from broad specifications of the problem, such as energies and angular momenta of the atomic levels. A Langevin equation stochastic simulation has been implemented to solve the Fokker-Planck equation of laser cooling using the computed force and diffusion. Comparisons of optical-molasses experiments and simulations carried out for a model sodium atom with a J = 2→J = 3 transition show qualitative similarities such as sub-Doppler limit temperatures, but the quantitative agreement of theory and experiment is not satisfactory.