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Journal of Physics B Atomic and Molecular Physics

Internal and translational atomic states in a laser-deflected beam

Benno H. W. Hendriks, Gerard Nienhuis

Published Jul 14, 1987• 2 citations
Publisher

Abstract

The authors study the effect of level degeneracy and of the polarisation of the driving field on the correlated evolution of the translational states and of the number of fluorescent photons for atoms in a monochromatic radiation field. The evolution equations are formally solved for the case of deflection of an atomic beam by a laser beam. They give explicit solutions for the distribution of deflection angles in several special cases.

DOI
10.1088/0022-3700/20/13/014

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The authors study the effect of level degeneracy and of the polarisation of the driving field on the correlated evolution of the translational states and of the number of fluorescent photons for atoms in a monochromatic radiation field. The evolution equations are formally solved for the case of deflection of an atomic beam by a laser beam. They give explicit solutions for the distribution of deflection angles in several special cases.
The exchange of momentum between atoms and photons in a deflection experiment is usually described by different formalisms depending on whether the interaction time T is shown or long compared with the radiative lifetime tau R . The authors present a new approach to this problem leading to a single theoretical expression valid in both limits and therefore allowing the transition between them to be studied. They interpret in this way the resonant Kapitza-Dirac effect and the optical Stern and Gerlach effect appearing in the short-time limit (T<< tau R ) as well as the deflection profiles usually deduced from a Fokker-Planck equation in the long-time limit (T>> tau R ). The transition between these two regimes is interpreted in terms of momentum transfer due to absorption and stimulated emission of laser photons, convoluted by the distribution of recoil due to spontaneously emitted photons.
We have performed experimental and theoretical studies of the deflection of a sodium atomic beam by a laser tuned to the 3 2{\mathrm{}}^{2}2S1/2{S}_{1/2}S1/2​,F=2--3 2{\mathrm{}}^{2}2P3/2{P}_{3/2}P3/2​,F=3 transition. The intensity profile of the deflected beam was measured at different laser power levels and for different laser polarizations. Calculations using a constant force derived from a two-level atom yield deflections which are too large. The results of more realistic simulation calculations agree very well with the measured deflection. Those calculations incorporate the atomic-beam spatial and velocity distributions as well as the laser frequency distribution and polarization state. Optical pumping, loss of atoms to the nonresonant F=1 ground state, and Doppler shifting of the atoms out of resonance are all considered, as also are the statistics and angular distributions of the spontaneous photons.
We investigate to which extent the quantum nature of light modifies laser-induced atomic beam deflection in a plane standing wave. Our model considers a single two-level atom interacting with a single quantized standing wave mode of the electromagnetic field. We neglect spontaneous emission into other field modes, an approximation valid for short enough times. We find that there is an essential qualitative difference between the cases of a coherent field and a thermal field. For a coherent field, the atomic momentum distribution after interaction has two symmetric peaks on the wings and resembles the semiclassical result of Arimondo et al. [Phys. Rev. A 24, 898 (1981)]. For a thermal field, this distribution has its maximum at p = 0. It is characterized by a constant contribution at p = 0, some sharp interference features, and near-Gaussian wings. The only feature common to both cases is that in the Raman-Nath regime of scattering, the range on transverse momenta grows linearly with time at a rate proportional to 〈 n 〉 , where 〈 n 〉 is the mean number of photons in the field.
The theory of the collisional and radiative relaxation of an atom perturbed by foreign-gas atoms in the presence of an intense monochromatic laser beam is developed. The spatial degeneracy of the levels and the reorientation effects of the collisions are included. The impact approximation is not made, but the Doppler effect is neglected. The spectrum of the fluorescent and scattered light is obtained from an eigenvalue problem in Liouville space using the dressed-atom approach and rotationally irreducible tensors. Minimal symmetry-adapted bases in Liouville space are constructed for linear, circular and elliptical incident polarisation. The method is illustrated for S 0 -P 1 transitions.
The present paper considers a model of a single-mode laser based on two-level atoms having translational degrees of freedom. Correlation of the field and the atomic motion due to the recoil effect is taken into account. The self-consistent theory describing dynamic properties of the system is performed on the basis of semiclassical approximation. It is shown that due to the weak friction of resonant atoms in the buffer gas, their translational motion is strongly coupled with the radiation field. The field intensity and the momentum of atoms in the stationary state are calculated. The stationary momentum distribution is obtained and is shown to be far from an equilibrium distribution in the case of weak friction.
An experiment is analyzed in which an atomic beam in a collinear, counterstreaming laser beam is deflected by an inhomogeneous dc electric field. The force acting on the translational motion of the atom is found. This describes a modification of the deflection due to the laser. The atom tends to decouple itself from the laser, but a method is suggested for a continuous recoupling. This can result in a large difference in the scattering between atoms coupled to the laser and atoms uncoupled. The applicability to isotope separation is pointed out.