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Journal of Physics B Atomic Molecular and Optical Physics

Rectification of the gradient force acting on a three-level atom in a bichromatic standing light wave

A. I. Sidorov, Rudolf Grimm, Vladilen S Letokhov

Published Sep 14, 1991• 15 citations
Publisher

Abstract

This paper presents the results of studies into the spatial behaviour of the gradient force acting on a three-level Lambda -atom in a two-frequency standing light wave. The effect of spatially inhomogeneous optical pumping and light-induced level shifts results in the wavelength-averaged force becoming other than zero. The magnitude of the rectified force is comparable with that of the gradient force in a single-frequency standing light wave.

DOI
10.1088/0953-4075/24/17/010

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This paper presents the results of studies into the spatial behaviour of the gradient force acting on a three-level Lambda -atom in a two-frequency standing light wave. The effect of spatially inhomogeneous optical pumping and light-induced level shifts results in the wavelength-averaged force becoming other than zero. The magnitude of the rectified force is comparable with that of the gradient force in a single-frequency standing light wave.
On the previous work of acquiring an unidirectional dipole force over macro-quantitative optical wavelengths by imposing two standing waves of two different frequencies on an atom in the reference[1],the fluctuation of the rectified dipole-force is derived and calculated by means of quantum aggressive theory.The results show that DI from the interaction between atomic dipole's zero-point fluctuation and the gradient of the light field amplitude has great magnitude being the dominant factor of the fluctuation and varies as the space extremely similar with the rectified dipole force;DS from the interaction between the atomic dipole and zero-point vacuum's vibration is so small that it can be neglected.The heating effect of the atom from the fluctuations is harmful for the atom's trapping by means of dipole force.
Rectified dipole forces1 offer the possibility of providing deep potential wells for neutral atoms. In the intense standing wave, a two-level atom can experience a large dipole force due to the large intensity gradient. However, this force changes sign on the optical wavelength scale, preventing the formation of deep potential wells. If a second, nearly commensurate, standing wave is added, its ac Stark shift causes the effective detuning of the first field to vary on the optical wavelength scale. The resulting change in sign of the detuning can counteract the change in sign of the intensity gradient, causing the force to maintain its sign over many wavelengths (i.e., the force becomes rectified), thereby forming a deep potential well. This rectified force is periodic with the beat wavelength between the two laser fields. In a three-level atom the same basic mechanism applies, but with the advantage that the two frequencies of the bichromatic standing wave can now be tuned dose to resonance with the two transitions of the atom.
In this paper we present a new calculation of the force on a stationary three-level atom in a bichromatic standing-wave light field (see Fig. 1). Contrary to other theoretical treatments,1 which ignore optical pumping into the trapped state, we find that a stationary atom experiences no force when there is no difference frequency detuning (i.e., when Δ = 0). However, when there is a nonzero differential detuning (Δ ≠ 0) there can be force components that vary in both the wavelength of the optical fields and their beat wavelength. This stimulated force can be much larger than the maximum spontaneous force associated with this system. To obtain a simple physical interpretation of this force, the problem is treated in a basis that is formed from symmetric |+〉 and antisymmetric |−〉 linear combinations of the atomic ground states2 (see Fig. 1).
A new three-dimensional scheme for rectifying a gradient force is proposed and analyzed. The scheme is based on the use of a strong, partially coherent optical field involving a component with a fluctuating phase. It is shown that the rectification of a gradient force acting on atoms with a nondegenerate ground state is a second-order effect with respect to field strength in this scheme, whereas an analogous effect is third-order in coherent bichromatic fields. Conditions for three-dimensional confinement of atoms are obtained by using the velocity dependence of the rectified radiative force. For a large class of atoms, such as even-even isotopes of ytterbium and alkaline-earth elements, these conditions can be implemented at a relatively high effective temperature (of the particle ensemble) of about 10 K. This finding can be used to widen substantially the range of energies of atoms amenable to effective three-dimensional optical manipulation.