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Physical Review A

Stimulated magneto-optical force in the dressed-atom picture

Johannes Söding, Rudolf Grimm

Published Sep 1, 1994• 6 citations
Publisher

Abstract

The simulated magneto-optical force, which in the presence of a longitudinal static magnetic field is exerted on atoms resonant with the high-intensity light field of two counterpropagating, linearly polarized laser beams with an angle of \ensuremath{\sim}45\ifmmode^\circ\else\textdegree\fi{} between their directions of polarization, is described in the dressed-atom picture. This allows an easy calculation of the force on atoms at rest, illustratively explains its nonzero wavelength average, and provides an intuitive understanding of its dependence on the atomic velocity. For a simple atomic model transition (J=0\ensuremath{\leftrightarrows}J'=1) the velocity-dependent force is calculated by considering the motion along the dressed states and using the Landau-Zener model for the nonadiabatic transitions at the avoided level crossings. It is shown that for a certain relation between Larmor and optical Rabi frequency a perfectly diabatic motion takes place, leading to a disappearance of the velocity-tuned (doppleron) resonance structure.

DOI
10.1103/physreva.50.2517

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The simulated magneto-optical force, which in the presence of a longitudinal static magnetic field is exerted on atoms resonant with the high-intensity light field of two counterpropagating, linearly polarized laser beams with an angle of \ensuremath{\sim}45\ifmmode^\circ\else\textdegree\fi{} between their directions of polarization, is described in the dressed-atom picture. This allows an easy calculation of the force on atoms at rest, illustratively explains its nonzero wavelength average, and provides an intuitive understanding of its dependence on the atomic velocity. For a simple atomic model transition (J=0\ensuremath{\leftrightarrows}J'=1) the velocity-dependent force is calculated by considering the motion along the dressed states and using the Landau-Zener model for the nonadiabatic transitions at the avoided level crossings. It is shown that for a certain relation between Larmor and optical Rabi frequency a perfectly diabatic motion takes place, leading to a disappearance of the velocity-tuned (doppleron) resonance structure.
In a one-dimensional model we consider the dependence of the magneto-optical force on the elliptical polarization of laser beams for different types of closed atomic transitions ${J}_{g}\ensuremath{\rightarrow}{J}_{e}$. The linear dependencies on atomic velocity and magnetic field of the magneto-optical force are found analytically. These results establish the possibility (for Jg>0{J}_{g}>0Jg​>0) to capture atoms in a magneto-optical trap even at zero detuning (i.e., at the exact resonance of atoms with laser field) in certain $(ϵ\ensuremath{-}\ensuremath{\theta}\ensuremath{-}\overline{ϵ})$ field configurations as well as in an anomalous blue-detuned region. The nonlinear dependencies of the force on atomic velocity and magnetic field are studied numerically. The capture velocity and the number of trapped atoms are estimated.
The dressed atom approach is used to investigate the evolution of atoms moving in an intense standing wave laser field. When coherences between the dressed states can be neglected, a simple expression is obtained for the radiative force acting on the atoms. The Landau-Zener model, well-known in the theory of slow atomic collisions, is here used to include coherences in an analytic treatment. At high velocities, where the simplest approach breaks down, the results are in good agreement with exact numerical calculations. Applications outside the field of laser cooling are discussed.
We show that the dressed-atom approach provides a quantitative understanding of the main features of radiative dipole forces (mean value, fluctuations, velocity dependence) in the high-intensity limit where perturbative treatments are no longer valid. In an inhomogeneous laser beam, the energies of the dressed states vary in space, and this gives rise to dressed-state-dependent forces. Spontaneous transitions between dressed states lead to a multivalued instantaneous force fluctuating around a mean value. The velocity dependence of the mean force is related to the modification, induced by the atomic motion, of the population balance between the different dressed states. The corresponding modification of the atomic energy is associated with a change of the fluorescence spectrum emitted by the atom. The particular case of atomic motion in a standing wave is investigated, and two regimes are identified in which the mean dipole force averaged over a wavelength exhibits a simple velocity dependence. The large values of this force achievable with reasonable laser powers are pointed out with view to slowing down atoms with dipole
In this letter we present a theoretical study of the coherent diffraction of three-level atoms from a light field with a polarization gradient (counterpropagating crossed linearly polarized beams) and a static magnetic field applied parallel to the laser propagation direction. We show that for a particular ratio of the laser field intensity and the magnetic-field strength, there occurs a resonance between the Larmor precession of the magnetic alignment and the Rabi oscillations. On resonance the atomic wave function is diffracted by an approximately triangular optical potential which leads to a very efficient coherent splitting of the atomic beam. The proposed configuration is particularly interesting in relation to atom interferometry, when efficient coherent beam splitters for atoms are required.
Results of a fairly straightforward experiment on resonant magneto-optical rotation by rubidium-87 atoms revealed strong time-dependence of the polarization plane of light emerging from atomic vapors following a sudden irradiation with a laser beam. The rotation of the plane appears as a not direct consequence of the influence of the magnetic field on atoms. Reported measurements conducted using a vapor cell without any buffer gas or an anti-relaxation wall coating show that transmitted light has initially the same (linear) polarization as the incident one. Rotation of the polarization plane caused by an axial magnetic field develops in time scales similar to the pace of establishing the optical pumping/relaxation equilibrium in the atomic ensemble. The traditional passive Faraday rotation picture providing working description for the resonant magneto-optical effects in steady-state conditions does not explain the observed sequence of evolution of the polarization. The picture has to be augmented with analysis of time dependence in the spatial distribution of relevant quantum states within the atomic ensemble as well as longitudinal and transversal intensity profiles of the light beam. Isolation of external effects caused by the optical pumping and relaxation processes from consequences of internal atomic coherences should uncover more details of mechanisms of the latter in the presence of magnetic field. Plentitude of data available from time-dependent polarization measurements provides strong incentives for further development and tests of comprehensive models of coherent interactions of atomic ensembles with radiation and possibly a base for additional advance in understanding and applications of these phenomena.