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Physical Review A

Laser cooling, friction, and diffusion in a three-level cascade system

Wilbert Rooijakkers, W. Hogervorst, W. Vassen

Published Oct 1, 1997• 19 citations
Publisher

Abstract

A model is presented to calculate optical forces, friction, and diffusion for three-level atoms in a ladder configuration. This model is then applied to the ${2}^{3}{S}_{1}{\ensuremath{-}2}^{3}{P}_{2}{\ensuremath{-}3}^{3}{D}_{3}$ cascade in metastable helium. It is demonstrated that metastable helium atoms can be decelerated within a much shorter distance using cascade excitation by overlapping traveling waves. The equilibrium temperature representing the final width of the velocity distribution is calculated as a function of laser detuning and intensity. This equilibrium temperature is also calculated for the situation of overlapping standing waves (one-dimension), and is found to be well above the Doppler limit for two-level ${2}^{3}{S}_{1}{\ensuremath{-}2}^{3}{P}_{2}$ excitation. Numerical results are compared with existing experimental data.

DOI
10.1103/physreva.56.3083

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A theoretical study is carried out for the laser cooling of a moving three-level atom in a ladder configuration, driven by a bichromatic laser fields with a broad-band squeezed vacuum. The friction, diffusion coefficients and the equilibrium temperature are calculated numerically and shown graphically as a function of two-photon detunings for various cases of the squeezed vacuum. It is shown that the relative phases between the two coherent fields and the squeezed vacuum field play an important role in the cooling process. For a suitable choice of parameters, the atomic cooling temperature may be reduced to below that in the case of a vacuum, even down to two orders below the Doppler temperature limit. The efficiency of this cooling scheme is also analyzed.
Radiation pressure on metastable helium atoms can be increased by an order of magnitude using the combined action of two lasers exciting the 1s2s3S11s2s^{3}S_{1}1s2s3S1​- 1s2p3P21s2p^{3}P_{2}1s2p3P2​- 1s3d3D31s3d^{3}D_{3}1s3d3D3​ cascade. This increase has been measured as a function of laser intensities and is explained in a model based on the optical Bloch equations, the coherences playing a crucial role. Possible applications for deceleration are discussed.
A laser cooling scheme for atoms with an effective three-level \ensuremath{\Lambda} configuration is presented. The cooling force is obtained by using two standing light waves, each interacting only with one of the two atomic transitions and both detuned red with respect to the transition. For a given laser power, the force exceeds the largest force on a two-level atom by a factor of 2 or more and the atomic velocity capture range is at the same time significantly increased. The spatially averaged force as well as the spatially averaged momentum diffusion coefficient, as a function of the atomic velocity, is calculated. The semiclassical steady-state momentum distributions are presented for some specific cases and an experimental realization of the cooling scheme is proposed for the case of metastable helium.
Radiation pressure and laser cooling of a moving three-level ladder-type atom in bichromatic travelling fields are considered. The dependence of the force on parameters such as detunings, Rabi frequencies and spontaneous decay rates is calculated numerically and shown graphically and analytical expressions for the force are obtained for some special parameter values. It is shown that the radiation pressure shows Doppler-shifted resonance peaks resulting respectively from one-photon and two-photon transitions. Using the present scheme, Doppler cooling of sodium exploiting the 3 2 S 1/2 –3 2 P 3/2 –3 2 D 5/2 cascade transitions is investigated. It is found that temperatures lower than the Doppler limit can be achieved.
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.