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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Atomic beam slowing and cooling: Discrete velocity model

C. Reitshammer, Ferdinand Schürrer, Alberto Rossani

Published Sep 1, 1998• 3 citations
Publisher

Abstract

A discrete velocity model of the Boltzmann equation is established to investigate the effect of atomic beam slowing and cooling by means of laser light. Due to momentum transfer, caused by absorption and emission processes of photons, atoms are slowed. The Doppler effect, however, allows only selected atoms within a certain resonance range to interact with the laser field. To overcome this problem an external electric field is maintained. Semianalytical results of the velocity distribution as a function of the deceleration path of both ground level atoms and excited atoms are presented in detail and studied explicitly for various values of the laser intensity. A cooling limit is given and compared with quantum mechanical results.

DOI
10.1103/physreve.58.3964

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Journal of the Optical Society of America B•Jul 1, 1992•61 citations
A discrete velocity model of the Boltzmann equation is established to investigate the effect of atomic beam slowing and cooling by means of laser light. Due to momentum transfer, caused by absorption and emission processes of photons, atoms are slowed. The Doppler effect, however, allows only selected atoms within a certain resonance range to interact with the laser field. To overcome this problem an external electric field is maintained. Semianalytical results of the velocity distribution as a function of the deceleration path of both ground level atoms and excited atoms are presented in detail and studied explicitly for various values of the laser intensity. A cooling limit is given and compared with quantum mechanical results.
A production of low velocity and monoenergetic atomic beams would increase the resolution in spectroscopic studies and many other experiments in atomic physics. Laser Cooling uses the radiation pressure to decelerate and cool atoms. The effusing from a glow discharge metastable argon atomic beam is affected by a counterpropagating laser light tuned to the cycling transition in argon. The Zeeman shift caused by a spatially varying magnetic field compensates for the changing Doppler shift that takes the atoms out of resonance as they decelerated. Deceleration and velocity bunching of atoms to a final velocity that depends on the detuning of the laser relative to a frequency of the transition have been observed. Time-of-Flight (TOF) spectroscopy is used to examine the velocity distribution of the cooled atomic beam. These TOF studies of the laser cooled atomic beam demonstrate the utility of laser deceleration for atomic-beam "velocity selection".
Theoretical analysis of sub-Doppler laser cooling of 24Mg atoms using 33 P2 → 33 D3 transition in the field of two counterpropagating light waves with opposite circular polarizations is presented. The standard semi-classical approach based on the Fokker-Plank equation is exploited for numerical modeling of laser cooling. The problem is solved out of limits of slow atom approximation and for arbitrary light intensity. The dependences of light force and diffusion on an atomic velocity are studied for various frequency detuning and Rabi frequency. Also, to obtain optimal parameters of laser cooling, the atomic velocity distributions are investigated for various conditions and the dependence of average atomic kinetic energy on the light field intensity and frequency detuning is calculated. In the case of strong field a multi-spike velocity distribution profile is observed. It results from various nonlinear effects accompany absorption of laser photons by atoms. In conclusion we make additional recommendations to increase atoms in metastable state 33 P2, what is necessary for effective laser cooling
The high velocity of free atoms associated with the thermal motion, together with the velocity distribution of atoms has imposed the ultimate limitation on the precision of ultrahigh resolution spectroscopy. A sample consisting of low velocity atoms would provide a substantial improvement in spectroscopy resolution. To overcome the problem of thermal motion, atomic physicists have pursued two goals; first, the reduction of the thermal motion (cooling); and second, the confinement of the atoms by means of electromagnetic fields (trapping). Cooling carried sufficiently far, eliminates the motional problems, whereas trapping allows for long observation times. In this work the laser cooling and trapping of an argon atomic beam will be discussed. The experiments involve a time-of-flight spectroscopy on metastable argon atoms. Laser deceleration or cooling of atoms is achieved by counter propagating a photon against an atomic beam of metastable atoms. The solution to the Doppler shift problem is achieved using spatially varying magnetic field along the beam path to Zeeman shift the atomic resonance frequency so as to keep the atoms in resonance with a fixed frequency cooling laser. For trapping experiments a Magnetooptical trap (MOT) will be used. The MOT is formed by three pairs of counter-propagating laser beams with mutual opposite circular polarization and a frequency tuned slightly below the center of the atomic resonance and superimposed on a magnetic quadrupole field.
In sub-Doppler laser cooling of atoms, the lowest temperatures are known to occur at low (but not too low) excitation, and the temperature increases roughly linearly with laser intensity. However, under conditions for which the lowest temperatures are obtained, the small velocity capture range and low optical pumping rate limit the number of atoms that can be collected into the cold sample. In this study, we present measurements for laser cooling of Rb and metastable He atoms for two counterpropagating laser beams with orthogonal linear polarization (lin\ensuremath{\perp}lin) over a wide range of saturation parameters and laser detunings, together with results of semiclassical (Fokker-Planck) and quantum density matrix calculations. We find that at higher laser intensity, a larger number of atoms can be collected into a final velocity distribution that is significantly narrower than that given by a linear extrapolation vs the square root of laser intensity. Two cooling mechanisms are at work: the sub-Doppler Sisyphus mechanism and also Doppler cooling. Under certain conditions that we discuss, Doppler cooling aids Sisyphus cooling by collecting high-velocity atoms beyond the Sisyphus capture range. He∗{\mathrm{He}}^{*}He∗ presents a rather unusual situation in that the minimum average kinetic energy (Eav){(E}_{\mathrm{av}})(Eav​) for purely Sisyphus cooling is comparable to the minimum value of Eav{E}_{\mathrm{av}}Eav​ with Doppler cooling alone.
The thermal velocity distribution of a calcium atomic beam was compressed into a narrow velocity distribution with selectable velocities. Subsequently these slow atoms were deflected by an angle of 30° by a one-dimensional optical molasses. In the deflected beam we obtained an estimated flux of several 1010 atoms/s at mean longitudinal velocities near 35 m/s and a velocity width of approximately 13 m/s. The transverse velocities of the deflected atoms were close to the one-dimensional Doppler limit. We have observed saturated absorption signals in the deflected laser-cooled beam. The reduced transit time broadening allowed us to resolve the recoil splitting in saturated absorption.