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Journal of Experimental and Theoretical Physics Letters

Influence of the spatial rotation of a polarization plane on the radiative friction force in light fields with polarization gradients

A. V. Bezverbnyĭ

Published Aug 1, 2001• 0 citations
Publisher

Abstract

Simple atomic models (1/2→1/2 and 1/2→3/2 transitions) were taken as an example to consider, in the sub-Doppler cooling approximation, influence of the spatial rotation of a polarization plane on the radiative friction force at arbitrary field configurations of dimensionality D <1. Spatial gradients of the angles determining this rotation additionally contribute to the friction force. This contribution is comparable in magnitude with other forces if the detuning δ is on the order of the radiative relaxation constant γ. For the j → j +1 transitions, the contribution promotes sub-Doppler cooling at δ<0, whereas for the j → j transitions (half-integer j ) it induces anisotropic heating and cooling processes.

DOI
10.1134/1.1410218

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Simple atomic models (1/2→1/2 and 1/2→3/2 transitions) were taken as an example to consider, in the sub-Doppler cooling approximation, influence of the spatial rotation of a polarization plane on the radiative friction force at arbitrary field configurations of dimensionality D <1. Spatial gradients of the angles determining this rotation additionally contribute to the friction force. This contribution is comparable in magnitude with other forces if the detuning δ is on the order of the radiative relaxation constant γ. For the j → j +1 transitions, the contribution promotes sub-Doppler cooling at δ<0, whereas for the j → j transitions (half-integer j ) it induces anisotropic heating and cooling processes.
The authors discuss the radiation force in a one-dimensional sigma + - sigma - laser standing wave, for transitions J to J+ Delta J, for any J. and Delta J=+or-1.0. in the limit of low saturation of the atomic transition. The interaction between the radiation field and the atom produces a motion-induced orientation of the atomic ground state which grows rapidly with J. The radiative force on the atom is sensitive to this orientation. For J to J+1 the dissipative part of the total force is much larger than the reactive part, at low velocities, while for the other cases the two contributions are roughly equal and opposite. By using a simple method of calculation, the authors gain much physical insight into the mechanism of induced orientation, and give quantitative results for the size of the radiation force, including both the low-velocity friction coefficient and the velocity capture range.
The light force on slow atoms in a light field with arbitrary polarization distribution is explicitly evaluated in the case of an atomic transition J yields J with half-integer J values. The expression of the force is based on an exact analytical expression for the steady-state density matrix of the atoms. The force is naturally separated in contributions resulting from gradients of the field intensity, the polarization ellipticity, and the phase. In addition to a conservative part this force also contains a vortex component. In areas of spatial localization, where the total force vanishes, the atomic motion is governed by a potential, which in general is not harmonic for J greater than 1/2. Simple model of the formation of a one- or two-dimensional spatial atomic grating in a specific light field configuration illustrates the results.
The motion of slow atoms with degenerate energy levels in a resonant, nonuniformly polarized laser field is described by the Fokker-Planck equation for the atomic distribution function in phase space in terms of the semiclassical approach. Field gradient expansions are used for the spatially nonuniform coefficients of the equation. For closed atomic transitions J g =J→J e =J+1 (J g and J e are the total angular momenta of the ground and excited states, respectively), new analytical results are presented for the light pressure force and the friction and diffusion coefficients in momentum space. These results allow the kinetic effects (laser cooling, localization in optical potential wells, etc.) in a field of arbitrary one-, two-, or three-dimensional configuration to be investigated. In several cases, the new contributions to the friction coefficient are interpreted qualitatively.
We calculate the light forces on atoms with a ground state of angular momentum F > 0 for the case that the fields are enclosed in an optical ring resonator. At the example of polarization gradient cooling using counterpropagating σ + –σ − fields coupled to a F → F + 1 transition we obtain explicit analytical expressions for the dipole-and radiation pressure forces. The additional cavity-mediated terms enhance the friction forces and yield substantial cooling even for very large atom–field detunings, where spontaneous emission is negligible. This should allow for lower final temperatures and higher densities than in free space. The new cooling force is related to stimulated Raman transitions between different ground-state sublevels, which leads to phase locking of the two polarization modes in the cavity. This provides non-destructive, detailed real-time information on the atomic motion from monitoring the output fields.
We present two cooling mechanisms that lead to temperatures well below the Doppler limit. These mechanisms are based on laser polarization gradients and work at low laser power when the optical-pumping time between different ground-state sublevels becomes long. There is then a large time lag between the internal atomic response and the atomic motion, which leads to a large cooling force. In the simple case of one-dimensional molasses, we identify two types of polarization gradient that occur when the two counterpropagating waves have either orthogonal linear polarizations or orthogonal circular polarizations. In the first case, the light shifts of the ground-state Zeeman sublevels are spatially modulated, and optical pumping among them leads to dipole forces and to a Sisyphus effect analogous to the one that occurs in stimulated molasses. In the second case (σ+−σ− configuration), the cooling mechanism is radically different. Even at very low velocity, atomic motion produces a population difference among ground-state sublevels, which gives rise to unbalanced radiation pressures. From semiclassical optical Bloch equations, we derive for the two cases quantitative expressions for friction coefficients and velocity capture ranges. The friction coefficients are shown in both cases to be independent of the laser power, which produces an equilibrium temperature proportional to the laser power. The lowest achievable temperatures then approach the one-photon recoil energy. We briefly outline a full quantum treatment of such a limit.
For atomic media with resonant Doppler-broadened transitions of J=0 to J'=1 or J=1 to J'=0 type and taking into account the relaxation due to depolarizing collisions a theory of nonlinear magneto-optic polarization phenomena is developed. The theory is valid in the case of both arbitrary resonance linearly-polarized radiation intensity and arbitrary external magnetic field spatial orientation. The Faraday and Voigt geometries are analysed in detail, and in the case of the Faraday geometry the effect is considered of a noncompensated magnetic field transverse component on the shape of a dependence relating the radiation polarization plane rotation angle to a magnetic field longitudinal component. In the case of the Voigt geometry an essential effect is found of the angle between the radiation initial polarization and transverse magnetic field vectors on the character of the dependence relating the radiation polarization plane rotation angle to the transverse magnetic field magnitude.