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Optics Letters

Method for increasing the velocity acceptance of stimulated laser cooling

Ralph G. DeVoe

Published Oct 15, 1991• 6 citations
Publisher

Abstract

A new method is proposed for laser cooling atoms with Doppler shifts an order of magnitude larger than the homogeneous linewidth of the atomic transition. Two traveling waves cross at an oblique angle and form long-wavelength standing waves. The resulting broadband stimulated cooling forces are predicted to stop 0.1% of the flux of a 500-K atomic sodium beam in a distance of 300 microm and a time of a few microseconds. This is more than 100 times faster than current methods.

DOI
10.1364/ol.16.001605

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Physical Review A•Jul 1, 1992•1 citation
A new method is proposed for laser cooling atoms with Doppler shifts an order of magnitude larger than the homogeneous linewidth of the atomic transition. Two traveling waves cross at an oblique angle and form long-wavelength standing waves. The resulting broadband stimulated cooling forces are predicted to stop 0.1% of the flux of a 500-K atomic sodium beam in a distance of 300 microm and a time of a few microseconds. This is more than 100 times faster than current methods.
A new method is proposed for laser cooling atoms with Doppler shifts an order of magnitude larger than the homogeneous linewidth of the atomic transition. Two traveling waves cross at a small angle and form standing waves whose wavelength is much longer than that of either traveling wave. This allows one to extend the region in which the laser cooling force is proportional to velocity. The resulting broadband stimulated cooling forces are predicted to stop 0.1% of the flux of a 500-K atomic sodium beam in a distance of 300 μm and a time of a few microseconds. This is more than 100 times faster than current methods. Numerical integration and the method of Gordon and Ashkin have been used to calculate the cooling forces which result when two traveling waves cross at an angle 2a. The stimulated cooling forces are reduced in intensity by sin2a but are proportional to velocity over an interval which is larger by 1/sin a. This allows one to stop a substantial fraction of an atomic beam without chirping the laser or Zeeman tuning the atoms.
An atom moving in a strong standing wave radiation field may be translationally cooled by the induced or dipole force.1 The dipole force is proportional to I1/2, where I is the laser intensity, whereas the Doppler (usual) cooling force saturates with increasing I. Since laser sources can provide intensities which are much greater than the saturation intensities of many atomic transitions, cooling via the dipole force can be much more efficient than Doppler cooling. The dipole force has been used to cool the transverse2,3 and the longitudinal4 velocities of atoms in an atomic beam.
A theoretical analysis is given for one-dimensional laser cooling below the Doppler limit of J=1/2 ground-state atoms. The laser field consists of a pair of counterpropagating, linearly polarized, low-power beams, whose polarization directions differ by an angle \ensuremath{\theta} (0\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}\ensuremath{\pi}/2). For \ensuremath{\theta}\ensuremath{\ll}1, the effective optical-pumping time is shown to increase strongly near the nodes of the standing wave, and the cooling force can be much larger than that for \ensuremath{\theta}=\ensuremath{\pi}/2. Moreover, for \ensuremath{\theta}\ensuremath{\ll}1, it can be shown that the stimulated part of the atomic diffusion is reduced considerably as compared with that for \ensuremath{\theta}=\ensuremath{\pi}/2. As a consequence it is possible to achieve an equilibrium atomic distribution that, for \ensuremath{\theta}\ensuremath{\ll}1, is characterized by a mean kinetic energy that is lower than that predicted to occur for \ensuremath{\theta}=\ensuremath{\pi}/2. The equilibrium velocity distribution is not necessarily Maxwellian, and thus the temperature of the atomic ensemble may not be well defined. The achievable kinetic energy is so small that the cooled atoms may be trapped in the vicinity of the laser-field nodes.
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#.
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 investigate the force on a two-level atom interacting with intense monochromatic laser fields which are combinations of standing and traveling waves. We present a continued-fraction solution to the optical Bloch equations. Using this solution to calculate the force on an atom, we have examined the slowing and cooling of a thermal Na atomic beam. We find that the addition of a traveling wave to an intense standing wave can significantly improve the slowing rate and simultaneously decrease the final velocity of the cooled beam.