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Dipole force cooling of multilevel atoms

Charles A. Sackett

Published Jan 1, 1994• 0 citations
OpenAlex

Abstract

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 $\\sp7$Li. 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.

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arXiv:physics/0510268•Physical Review A•Mar 31, 2006•4 citations
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.
We have examined the mechanical effects of light on a three level atom. A single excited state decays to two long-lived ground states. One of the transitions is driven by an intense standing wave, while the other is driven by a traveling wave. We examine this system using analytical and computational techniques, and compare with experimental observations of {sup 7}Li. In the absence of the second ground state and laser field, the atom can be cooled by the familiar two level dipole force. In the three level system, the dipole force cooling mechanism is still present, and can be considerably enhanced. As in the two level system, the cold three level atoms are channeled, or localized in space with respect to the standing wave. In the three level case, the atoms can be channeled in the second ground state, even though that state interacts only with the traveling wave laser, which has no spatial structure. We will discuss applications of the three level cooling force to atomic beam slowing experiments, and the attainment of ultra-cold final temperatures using adiabatic cooling.
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.
We extend the kinetic theory of the laser cooling of atoms to four multilevel atomic schemes: (3+5)-, (5+7)-, (7+9)-, and (9+11)-level atom. In all four atomic schemes the atoms are considered to be excited by two counterpropagating circularly polarized laser waves. A comparison of four multilevel atomic schemes shows that the even-order multiphoton processes are responsible for the narrow structures near zero velocity in the atomic coherences, atomic populations, dipole radiation forces, and the diffusion coefficients. The even-order multiphoton processes in a multilevel atom with a big number of magnetic sublevels are shown to produce the velocity structures, which are much narrower than that produced by the two-photon processes in a (3+5)-level atom. It is found that the multiphoton processes enhance the radiation force at low velocities and the friction produced by the force at a negative detuning. The even-order multiphoton processes caused by the laser waves are identified as the basic physical mechanism responsible for the sub-Doppler laser cooling of atoms. The temperature of laser-cooled atoms is derived for all four models and found to be lower for atomic schemes with a larger number of magnetic sublevels.
We propose an efficient method of cooling atoms in a strong Gaussian standing wave. The steep gradients of the atomic potential energy give rise to large dipole forces, which can be much stronger than the maximum radiation pressure force and can therefore stop atoms in a much shorter distance. We have simulated the cooling process using a semi-classical Monte- Carlo method, which includes the radial motion, in addition to the motion along the beams. Both motions are calculated directly without separation the dynamics into force and diffusion terms. To cool a large range of atomic velocities the frame in which the standing wave is at rest was swept by changing the frequencies of the counter-propagating beams, in a similar way to the well-known chirp cooling technique using the radiation pressure force. If the curvature of Gaussian beams far from beam waist is employed the radial motion and velocities can be reduced even for the blue detuning comparing to the near waist case. The simulations show that it is possible to stop caesium atoms in a distance of several centimeters (the exact value depends on the laser power, beam waist radius and acceptable chirping force) starting from the most probable velocity at room temperature. Narrower radial and wider axial velocity distribution was obtained for red detuning comparing with the blue one.
We examine the laser cooling of three-level (Lambda) -atoms in the field of two standing waves when frequency detunings are considerably greater than natural width of the excited state as well as the Rabi frequencies in the system. It is shown that at the difference of frequency detunings is small when compared to the Rabi frequencies sub-Doppler cooling of the (Lambda) -atom is possible. We present the dependence of the light pressure force on the atoms velocity and dependence of cooled atoms temperature on the parameters of the exciting waves.
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.