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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Strong Gaussian standing wave: an efficient tool for laser cooling of atomic beams

Pavel Zemánek, Christopher J. Foot

Published Jan 1, 1998• 3 citations
Publisher

Abstract

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.

DOI
10.1117/12.301361

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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.

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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.
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.
Recent advances in experimental laser cooling have shown the possibility of stopping an atomic beam using the light pressure force of a counter-propagating laser wave. As an application to laser cooling, it is proposed to build a single frequency cesium laser that has a narrow linewidth. Laser cooling techniques are used to cool an atomic beam of cesium to an average velocity of 5 m/s, corresponding to a temperature of 0.2°K. Expressions of the basic forces that a laser wave exerts on atoms are derived according to a semi-classical approach. The experimental problems and methods of avoiding these problems are treated in detail. A computer Monte-Carlo simulation is used to discuss the feasibility of building the proposed laser. This simulation was done for an ensemble of 10,000 atoms of cesium, and it included the effects of the gravitational force and the related experimental variables. The possibility of building single frequency lasers that use a cooled medium of noble gases, and many other applications of laser cooling are briefly discussed at the end of this work.
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.
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.