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Journal of the Optical Society of America B

Dressed-atom approach to atomic motion in laser light: the dipole force revisited

Jean Dalibard, Claude N. Cohen-Tannoudji

Published Nov 1, 1985• 528 citations
Publisher

Abstract

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forces (mean value, fluctuations, velocity dependence) in the high-intensity limit where perturbative treatments are no longer valid.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

DOI
10.1364/josab.2.001707

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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forces (mean value, fluctuations, velocity dependence) in the high-intensity limit where perturbative treatments are no longer valid.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
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.
The effect of the dipole force and its fluctuation on the motion of Li atoms in an intense, one-dimensional, near-resonant standing light wave has been investigated, both theoretically and experimentally. The duration of the interaction of the atoms with the standing wave was varied from several tens of spontaneous emission lifetimes to several hundred. For a standing wave frequency blue-detuned from resonance, diffusive heating can dominate the time-averaged dissipative dipole force so that there is no steady-state momentum distribution. However, for sufficiently large blue detunings the rate of diffusion is so slow that the resulting distribution approaches a quasi-steady state. For red detunings the diffusion is balanced with the force and a true steady-state is achieved. A Monte Carlo method based on the density matrix equations in the dressed-state representation is applied to simulate the atomic motion. The dynamics of atom channeling is studied. One of the important applications of this investigation is adiabatic laser cooling of atoms. Lithium atoms channeled in the nodes of an intense standing wave radiation field are cooled to near the recoil limit, a single photon's momentum hbark\\hbar{k}hbark, by adiabatically reducing the radiation intensity. The final momentum distribution has a narrow component with a root mean squared momentum of 2 hbark\\hbar{k}hbark in one-dimension. The data are compared with the results obtained by the Monte Carlo method. This process may be useful for cooling and increasing the phase-space density of atoms confined in a magnetic trap.
This work discusses the effect of a high-intensity standing wave laser field on the motion of neutral atoms moving with a relatively high velocity. The analysis involves a detailed calculation of the force acting on the atoms and the calculation of the diffusion tensor associated with the fluctuations of the quantum force operator. The high-intensity laser field limit corresponds to a Rabi frequency much greater than the natural rate of the atom. The general results are valid for any atomic velocity. Results are then specialized to the case of slow and fast atoms where the Doppler shift of the laser frequency due to the atomic motion is either smaller or larger than the natural decay rate of the atom. The results obtained for the force and diffusion tensor are applied to a particular ideal experiment that studies the evolution of a fast atomic beam crossing a high-intensity laser beam. The theories developed previously, for a similar laser configuration, discuss only the low atomic velocities case and not the more realistic case of fast atoms. Here, an approximate solution of the equation for the distribution is obtained. Starting from the approximate distribution function, the deflection angle and dispersion angle for themore » atomic beam with respect to the free motion are calculated.« less
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.
The dressed atom approach provides a tool to investigate the dynamics of an atom-laser system by fully retaining the quantum nature of the coherent mode. In its standard derivation, the internal atom-laser evolution is described within the rotating-wave approximation, which determines a doublet structure of the spectrum and the peculiar fluorescence triplet in the steady state. However, the rotating wave approximation may fail to apply to atomic systems subject to femtosecond light pulses, light-matter systems in the strong-coupling regime or sustaining permanent dipole moments. This work aims to demonstrate how the general features of the steady-state radiative cascade are affected by the interaction of the dressed atom with propagating radiation modes. Rather than focusing on a specific model, we analyze how these features depend on the parameters characterizing the dressed eigenstates in arbitrary atom-laser dynamics, given that a set of general hypotheses is satisfied. Our findings clarify the general conditions in which a description of the radiative cascade in terms of transition between dressed states is self-consistent. We provide a guideline to determine the properties of photon emission for any atom-laser interaction model, which can be particularly relevant when the model should be tailored to enhance a specific line. We apply the general results to the case in which a permanent dipole moment is a source of low-energy emission, whose frequency is of the order of the Rabi coupling.
We have investigated the effect of the dipole force and its fluctuation on the motion of Li atoms in an intense, one-dimensional, near-resonant standing light wave. The duration of the interaction of the atoms with the standing wave was varied from several tens of spontaneous-emission lifetimes to several hundreds. For a standing-wave frequency blue detuned from resonance, diffusive heating can dominate the time-averaged dissipative dipole force so that there is no steady-state momentum distribution. However, for sufficiently large blue detunings, the rate of diffusion is so slow that the resulting distribution approaches a quasisteady state. For red detunings, the diffusion is balanced with the force and a true steady state is achieved. We apply a Monte Carlo method based on the density-matrix equations in the dressed-state representation to simulate the atomic motion. The dynamics of atom channeling is discussed.