Laser collimation of a chromium beam R. E. Scholten,* R. Gupta, J. J. McClelland, and R. J. Celotta Electron Physics Group, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 M. S. Levenson and M. G. Vangel Statistical Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 Received 19 August 1996 We have studied laser collimation of a chromium atomic beam using a transverse polarization gradient cooling scheme. We present detailed measurements of the angular distribution of atoms on the beam axis, over a broad range of laser intensities and detunings, including those that produce significant excitation, and observe collimation angles as small as 0.160.01 mrad 50% quantile. We compare our results with existing calcu- lations based on assumptions of steady-state conditions and low excited-state population. S1050-29479709402-X PACS numbers: 32.80.Pj, 42.50.Vk I. INTRODUCTION Collimated atomic beams play an important role in many applications of current interest, from atom interferometers 1 and atomic clocks 2 to collision studies 3 and direct- write nanofabrication 4. While collimation can be achieved in a very straightforward way using nozzles and/or collimat- ing apertures 5,6, these approaches generally result in a great loss of flux. Recently, laser cooling techniques, which utilize dissipative forces to increase the brightness of atomic beams, have arisen as an alternative that provides high de- grees of collimation without significant loss of flux 7–9. We report here results on laser collimation of a thermal chromium atomic beam using one-dimensional transverse sub-Doppler polarization-gradient laser cooling. We have measured angular distributions of atoms on the beam axis for a range of laser intensities and detunings. We have also de- termined the conditions under which a minimum angular spread is obtained within the constraints of our experimental configuration. Many of the measurements are made under conditions of high excited-state fraction and non-steady-state conditions, so our data cover a relatively unexplored area. As a result, there is no theoretical work available for direct com- parison. We compare our results with theoretical calculations based on assumptions of low-excited-state fraction and steady-state conditions, in order to contrast this work with other laser cooling studies. A. Background Since the first experiments on cooling free atoms with near-resonant laser light 10, many cooling mechanisms have been identified, including Doppler-limited, sub- Doppler, and sub-recoil cooling 11. These techniques have been applied in one, two, and three dimensions, to slow and trap atoms and to transversely cool and therefore collimate and brighten an atomic beam. The fundamentals of laser cooling have been thoroughly described by several authors 11. In the simplest scheme, atoms are cooled in a region of counterpropagating laser beams, sometimes referred to as optical molasses, where the lasers are detuned below the atomic resonance. Due to the Doppler shift, it is more likely that atoms absorb light, and hence momentum, from the laser beam that is propagating opposite to their own motion. Enhanced cooling can be obtained by employing polariza- tion gradients in the laser field 12. In particular, the lin lin configuration uses two counterpropagating lasers with orthogonal linear polarizations to create a superposition with continually varying polarization. Atoms with the appropriate transitions angular momentum J →J +1, J 0 experience laser forces that depend on the polarization, such that motion against the polarization gradients results in additional velocity-dependent forces and the associated cooling effects. In recent years, the understanding of polarization-gradient laser cooling has evolved to the point where it appears to follow near-universal behavior if one concentrates on the limit of low excited-state fraction and assumes that steady- state conditions have been attained. These circumstances can be found, for example, in a three-dimensional atom trap or when slow atoms are cooled in one dimension over a long interaction distance. Given these conditions, the temperature of the cooled at- oms or, equivalently the rms velocity spread or the average kinetic energy E k ) is found to depend for a given J →J +1 transition only on the light shift potential U 0 12– 16. This quantity, which incorporates the essential laser pa- rameters of intensity and detuning, represents in a single number the effective depths of an array of light-shift poten- tials associated with the different magnetic substates of the atom and their differing interactions with the varying polar- ization state of the laser. In terms of the laser parameters, U 0 is given by 16 U 0 = | | 2 4 2 + 2 . 1 Here is the linewidth of the transition, is the laser de- *Present address: School of Physics, University of Melbourne, Parkville Vic 3052, Australia PHYSICAL REVIEW A FEBRUARY 1997 VOLUME 55, NUMBER 2 55 1331