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Physical Review A

Selective reflection from a vapor of three-level atoms

Gerard Nienhuis, F. Schuller

Published Aug 1, 1994• 17 citations
Publisher

Abstract

We study internal selective reflection from a dielectric-vapor interface, where three levels of the vapor atoms in a \ensuremath{\Lambda} configuration are connected by two light frequencies. The reflectivity contains then both a sub-Doppler structure due to spatial dispersion in the boundary layer and the dark resonance arising from coherent population trapping. We derive analytical expressions for the reflectivity of either one of the two light beams. The contributions from atoms approaching or leaving the interface are strongly different, whereas they are identical for the case of two-state atoms.

DOI
10.1103/physreva.50.1586

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We study internal selective reflection from a dielectric-vapor interface, where three levels of the vapor atoms in a \ensuremath{\Lambda} configuration are connected by two light frequencies. The reflectivity contains then both a sub-Doppler structure due to spatial dispersion in the boundary layer and the dark resonance arising from coherent population trapping. We derive analytical expressions for the reflectivity of either one of the two light beams. The contributions from atoms approaching or leaving the interface are strongly different, whereas they are identical for the case of two-state atoms.
We evaluate the emission into a dielectric induced by the dipole polarization of an atomic vapor, in the case where two light beams are incident on the dielectric-vapor interface. These beams are a weak signal beam and a pump beam. Effects of spatial dispersion, arising from deexcitation of the vapor particles at collisions with the interface, are accounted for. The reflected radiation contains sub-Doppler structures arising from combinations of the effects of velocity-dependent transient behavior and the nonlinear response of the vapor. We express the modification of the signal-field reflection due to the pump field in terms of an effective susceptibility of the signal field. This susceptibility explicitly depends on the incidence angles and the frequencies of both beams. We present explicit simplified expressions for this effective susceptibility, valid in special cases. We also give some numerical results.
We calculate the reflection coefficient for a light beam incident on the interface between a dielectric and a resonant atomic vapor to first order in the dipole polarization in the vapor. The angle of incidence and the polarization direction are chosen arbitrarily, and saturation is fully accounted for. The atoms are supposed to get deexcited at collisions with the surface. The resulting transient behavior of atoms leaving the surface is responsible for a nonlocal response. This spatial dispersion near the surface is known to produce a natural-linewidth-limited resonance in the vapor reflection coefficient at normal incidence. Our analysis shows that this sub-Doppler structure is broadened by the residual Doppler effect for non-normal incidence. This structure disappears at the critical angle for total internal reflection, where one predicts a conventional Voigt-type dispersion response, based on the complex-refractive-index approach. We also calculate the saturation broadening of the atomic response for large intensities. Beyond the critical angle, the spectral response suddenly shifts from dispersion to absorption line shapes. In the case of total internal reflection, the spatial dispersion leads to an additional Lorentzian broadening, which results from an effective imaginary Doppler shift at passage through the evanescent wave (transit-time broadening).
The conditions of observation of direct two-photon-induced dispersion in three-level reflection spectroscopy at a vapor-dielectric interface are discussed. One shows how pump frequency modulation allows one to discriminate the two-photon singular contribution associated with atoms moving quasiparallel to the dielectric interface, and therefore single out off-resonant Doppler-free two-photon dispersion in selective reflection. A nonperturbative theoretical approach to two-photon reflection is shown to predict a dynamic Stark shift of the two-photon resonance, which has been experimentally observed on the 6S-6P-8S transition of cesium. \textcopyright{} 1996 The American Physical Society.
We study the cascade three-level selective-reflection spectroscopy for normal incidence at a dielectric--atomic-vapor interface in a pump-probe scheme. Taking into account the effects of spatial dispersion arising from deexcitation by collisions with the interface and the transient response of atoms leaving the surface, we evaluate the modification of the probe-field reflection induced by the presence of the pump field in terms of a nonlocal nonlinear susceptibility. The dependence of this susceptibility on the probe frequency for various given pump frequencies is calculated. Sub-Doppler structures in the selective reflection spectrum are obtained and analyzed. Potential applications to the study of the interaction of highly excited atomic states with the surface are indicated.
The conditions of observation of direct two-photon-induced dispersion in three-level reflection spectroscopy at a vapor-dielectric interface are discussed. One shows how pump frequency modulation allows one to discriminate the two-photon singular contribution associated with atoms moving quasiparallel to the dielectric interface, and therefore single out off-resonant Doppler-free two-photon dispersion in selective reflection. A nonperturbative theoretical approach to two-photon reflection is shown to predict a dynamic Stark shift of the two-photon resonance, which has been experimentally observed on the 6S-6P-8S transition of cesium. @S1050-2947~96!06009-X#
We calculate the modulation of the reflection coefficient for a frequency-modulated (FM) light beam incident on the interface between a dielectric and an atomic vapor. The vapor is described as a gas of resonant, Doppler-broadened, two-level systems, with transition frequency and linewidth arbitrarily depending on the atom-dielectric distance. The atoms are supposed to get deexcited at collisions with the surface. The transient atomic response is calculated to first order in the incident field, for both incoming and desorbed atoms. The reflection coefficient, evaluated to first order in the vapor dipole polarization, leads to a formal expression of the reflectivity modulation, valid for arbitrary atom-surface interaction potentials. One first discusses the reflection signal in absence of wall interactions, for arbitrary modulation frequencies. At large frequencies, it allows one to monitor both vapor absorption and dispersion. Second, the formal theory is applied to the case of a Van der Waals-London surface attraction exerted on the atomic vapor. Both normal and oblique beam incidences are considered. One shows how the vapor dispersion signal is red-shifted and strongly distorted by the appearance of vapor-surface long-range interactions, and how it can be used to monitor these interactions. At non-normal incidences, the lineshapes get Doppler-broadened.