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Journal of the Optical Society of America B

Calculations on cooling of fast, multilevel atoms by intense laser fields

Ejvind Bonderup, Klaus Mølmer

Published Nov 1, 1989• 8 citations
Publisher

Abstract

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.

DOI
10.1364/josab.6.002125

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Bulletin of the American Physical Society•May 1, 1993•0 citations
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.
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.
Splitting of the atomic wave packet in velocity space due to the action of ultrashort laser pulses in the coherent regime of interaction was obtained in @2,9,10#. The transient regime of cooling by a sequence of short laser pulses of the narrowband traveling-wave field under the condition that the atoms decay completely between pulses was investigated in @11# .I t was shown in @12# that more deceleration of neutral atoms may be achieved with the train of ultrashort p pulses separated by a few radiative lifetimes than would be achived with the same average intensity used for cw generation. Laser cooling on transitions with a linewidth narrower than the recoil shift was studied by the Monte Carlo method using broadband excitation in @13#. The force of the stimulated light pressure on an atom arising from the action of two near-resonant standing waves with different frequencies modeling two counterpropagating waves with modulated in time amplitudes was studied in @14#.
The dressed atom approach is used to investigate the evolution of atoms moving in an intense standing wave laser field. When coherences between the dressed states can be neglected, a simple expression is obtained for the radiative force acting on the atoms. The Landau-Zener model, well-known in the theory of slow atomic collisions, is here used to include coherences in an analytic treatment. At high velocities, where the simplest approach breaks down, the results are in good agreement with exact numerical calculations. Applications outside the field of laser cooling are discussed.
The effect of the dipole force and its fluctuation on the motion of Li atoms in an intense, one-dimensional, near-resonant standing light wave has been investigated, both theoretically and experimentally. The duration of the interaction of the atoms with the standing wave was varied from several tens of spontaneous emission lifetimes to several hundred. For a standing wave frequency blue-detuned from resonance, diffusive heating can dominate the time-averaged dissipative dipole force so that there is no steady-state momentum distribution. However, for sufficiently large blue detunings the rate of diffusion is so slow that the resulting distribution approaches a quasi-steady state. For red detunings the diffusion is balanced with the force and a true steady-state is achieved. A Monte Carlo method based on the density matrix equations in the dressed-state representation is applied to simulate the atomic motion. The dynamics of atom channeling is studied. One of the important applications of this investigation is adiabatic laser cooling of atoms. Lithium atoms channeled in the nodes of an intense standing wave radiation field are cooled to near the recoil limit, a single photon's momentum hbark\\hbar{k}hbark, by adiabatically reducing the radiation intensity. The final momentum distribution has a narrow component with a root mean squared momentum of 2 hbark\\hbar{k}hbark in one-dimension. The data are compared with the results obtained by the Monte Carlo method. This process may be useful for cooling and increasing the phase-space density of atoms confined in a magnetic trap.
This work discusses the effect of a high-intensity standing wave laser field on the motion of neutral atoms moving with a relatively high velocity. The analysis involves a detailed calculation of the force acting on the atoms and the calculation of the diffusion tensor associated with the fluctuations of the quantum force operator. The high-intensity laser field limit corresponds to a Rabi frequency much greater than the natural rate of the atom. The general results are valid for any atomic velocity. Results are then specialized to the case of slow and fast atoms where the Doppler shift of the laser frequency due to the atomic motion is either smaller or larger than the natural decay rate of the atom. The results obtained for the force and diffusion tensor are applied to a particular ideal experiment that studies the evolution of a fast atomic beam crossing a high-intensity laser beam. The theories developed previously, for a similar laser configuration, discuss only the low atomic velocities case and not the more realistic case of fast atoms. Here, an approximate solution of the equation for the distribution is obtained. Starting from the approximate distribution function, the deflection angle and dispersion angle for themore » atomic beam with respect to the free motion are calculated.« less
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.