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arXiv:1002.0257

Cold atom scattering by cavity fields in a two-dimensional geometry

John Martin, Thierry Bastin

Published Feb 1, 2010• 0 citations
arXivHTMLPDF

Abstract

The quantum theory of the cold atom scattering by cavity fields in a two-dimensional geometry is presented. A distinct regime from the usual Raman-Nath, Bragg and Stern-Gerlach regimes is investigated, considering the situation where the cavity light field acts as a repulsive and an attractive two-dimensional potential. General expressions for the scattering lengths (the two-dimensional analogues to the three-dimensional scattering cross-sections) of finding the atoms deexcited or not after their interaction with the cavity are derived. The connection with the classical Rabi limit when the incident atomic kinetic energy is high compared with the atom-field interaction energy is made. In the cold atom regime characterized by much lower incident atomic kinetic energies, the scattering process exhibits very peculiar properties in connection with quasibound states of the atomic motion induced by the attractive potential of the cavity light field.

DOI
10.48550/arxiv.1002.0257

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The quantum theory of the cold atom scattering by cavity fields in a two-dimensional geometry is presented. A distinct regime from the usual Raman-Nath, Bragg and Stern-Gerlach regimes is investigated, considering the situation where the cavity light field acts as a repulsive and an attractive two-dimensional potential. General expressions for the scattering lengths (the two-dimensional analogues to the three-dimensional scattering cross-sections) of finding the atoms deexcited or not after their interaction with the cavity are derived. The connection with the classical Rabi limit when the incident atomic kinetic energy is high compared with the atom-field interaction energy is made. In the cold atom regime characterized by much lower incident atomic kinetic energies, the scattering process exhibits very peculiar properties in connection with quasibound states of the atomic motion induced by the attractive potential of the cavity light field.
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Summary form only given. A new regime in cavity QED is realized in which single atoms interact with the cavity field for very long times (i.e., many Rabi cycles) and in which the atomic kinetic energy is comparable to or smaller than the dipole coupling energy. The mechanical effects of just a few-photon light field should therefore enable single atoms to be trapped in effective potential wells. We consider such a situation in the far detuned dispersive regime of cavity QED, where a single atom is confined in the lower (quantized) bound states of the effective optical potential formed around an antinode of the standing wave cavity field.
In this thesis we investigate the dynamics of cold atoms in optical cavities. We study how the scattering properties of laser driven atoms are modified by the presence of an optical resonator. This investigation can be divided into two parts. First, we study the scaling of the scattering properties with the number of atoms, and we show in particular how Bragg scattering by an atomic lattice is modified by the presence of the resonator. In this case, the atoms are trapped at the antinodes of the cavity mode function by the mechanical potential induced by the resonator. In a second part, we show how this modification of the scattering properties can be used for efficiently cooling single atoms to the ground state of a harmonic trap. In particular, we find that the motion is critically affected by quantum correlations induced by the mechanical coupling with the resonator, which may lead to selective suppression of certain transitions for the appropriate parameters regimes, thereby increasing the cooling efficiency.
We study the amplification of a resonant standing-wave light field due to the interaction with a beam of monovelocity two-level atoms moving in the Raman-Nath regime and in the Bragg regime. The atomic density is low so that, at most, one atom is inside the cavity at a time. This system is very similar to the well-known micromaser but it is operating in the optical region of the field frequencies. Therefore, the situation corresponds to a microlaser. Unlike the micromaser system, the momentum transfer between the atoms and photons in the microlaser essentially effects the center-of-mass motion of the atoms and the evolution of the field.
The diffraction of a coherent, stationary, beam of atoms from a standing wave of light is considered. Particular attention is paid to long interaction times for which the motion of the atoms inside the light field must be taken into account. This is the regime of dynamical diffraction, and is treated within the framework of a set of differential difference equations due to Raman and Nath. The popular Raman-Nath approximation, in which the kinetic energy imparted to the atoms by the light wave is ignored, is no longer valid and the full equations must be solved. When the interaction between the atoms and the light is very weak then few beams are produced. To describe spontaneous emission from the atom one can invoke a complex potential as a model for dissipation. If the atom beam is obliquely incident one finds anomalously high transmission close to the Bragg angles which is the physical manifestation of degeneracies in non-Hermitian matrices. The classical limit is approached when the atom-light interaction is strong, producing many beams. The classical dynamics (geometrical rays) reveal that the farfield intensity pattern is dominated by caustics. These proliferate with increasing interaction distance. Two methods are presented for analytically treating the semiclassical limit of the wave mechanics. The first begins with W.K.B. solutions to the continuised Raman-Nath equations. Mapping onto parabolic cylinder functions removes the spurious divergences of the W.K.B. solutions, giving eigenvectors which are uniformly valid for all scattering angles and may be summed to give the wavefunction. The second method transforms the original W.K.B. eigensum, using the Poisson summation formula, giving a new sum, each term of which has classical significance. This method shows that wave theory decorates the classical caustics with an Airy function intensity profile, as predicted by catastrophe theory.
We study the coherent scattering of weak light from a system of cooled bosonic atoms in a trap. We derive and discuss in detail the scattering equation for such a process that describes multiple scatterings from different atoms. Our theory accounts for atom-atom interactions and determines the density profile of the atomic fields from the self-consistent Bogoliubov-Hartree method. We present two kinds of analytic solutions to the scattering equation using the on-shell approximation and the generalized diffraction theory. We discuss the validity of those approaches, and demonstrate that they both lead to similar results. Our studies indicate that the scattering cross sections exhibit non-Lorentzian shapes with narrow features close to resonance. Coherent scattering occurs mainly in the forward direction, and the angular distribution is limited by the size of the atomic sample in the trap. We present results for various ranges of relevant parameters such as trap size, interaction strength, number of atoms, and temperature, etc. \textcopyright{} 1996 The American Physical Society.