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Physical Review A

Two-peaked probability distribution in laser cooling

Massimo Brambilla, G. Broggi, Federico Casagrande, L. A. Lugiato, E. Arimondo

Published Apr 1, 1992• 1 citation
Publisher

Abstract

We analyze the time evolution of the velocity distribution of a collection of atoms decelerated by two laser beams propagating in the direction opposite to that of the atomic beam. The laser frequencies are chirped and the velocity distribution is analyzed in the appropriate moving frame. Starting from a Maxwellian configuration, the distribution evolves toward a two-peaked configuration, in which it remains for all observable times. The same phenomenon arises when the atoms are decelerated by a single laser beam which interacts simultaneously with two nearly degenerate atomic transitions.

DOI
10.1103/physreva.45.4768

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We analyze the time evolution of the velocity distribution of a collection of atoms decelerated by two laser beams propagating in the direction opposite to that of the atomic beam. The laser frequencies are chirped and the velocity distribution is analyzed in the appropriate moving frame. Starting from a Maxwellian configuration, the distribution evolves toward a two-peaked configuration, in which it remains for all observable times. The same phenomenon arises when the atoms are decelerated by a single laser beam which interacts simultaneously with two nearly degenerate atomic transitions.
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We explore the possibility of decelerating and Doppler cooling an ensemble of two-level atoms by a coherent train of short, nonoverlapping laser pulses. We derive analytical expressions for mechanical force exerted by the train. In frequency space the force pattern reflects the underlying frequency comb structure. The pattern depends strongly on the ratio of the atomic lifetime to the repetition time between the pulses and pulse area. For example, in the limit of short lifetimes, the frequency-space peaks of the optical force wash out. We propose to tune the carrier-envelope offset frequency to follow the Doppler-shifted detuning as atoms decelerate; this leads to compression of atomic velocity distribution about comb teeth and results in a ``velocity comb''---a series of narrow equidistant peaks in the velocity space.
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.
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.
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.