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Journal de Physique II

General theory of frequency modulated selective reflection. Influence of atom surface interactions

M. Ducloy, M. Fichet

Published Dec 1, 1991• 57 citations
Publisher

Abstract

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.

DOI
10.1051/jp2:1991160

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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.
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).
Selective reflection spectroscopy at an interface with a low-density resonant vapor, especially when combined with a frequency modulation technique, is a high-resolution Doppler-free tool for probing atoms interacting with a surface. We analyze different types of relevant surface interaction, emphasizing the spectral consequences of a van der Waals surface attraction associated to a z−3z^{-3}z−3 potential dependence (zzz: distance to the wall). We present detailed results of two series of experiments at a Cs vapor/dielectric window interface on the 6S1/2_{1/2}1/2​-6P3/2_{3/2}3/2​ (λ=852\lambda = 852λ=852 nm) resonance line and on the 6S1/2_{1/2}1/2​-7P second resonance line (λ=455\lambda = 455λ=455 nm and 459 nm). Lineshape analysis at various pressures consistently shows that a van der Waals-type surface attraction has to be considered to interpret strong lineshape distortions and resonance shift. The attractive strengths are found to be equal respectively to ≈2\approx 2≈2 kHz μ\muμm3^33 and ≈20\approx 20≈20 kHz μ\muμm3^33, independently of the considered hyperfine component, within the experimental accuracy. It yields also typical parameters of pressure broadening and shift, which are shown to originate in collisional processes, at densities where the medium is opaque. Theoretical expectations for the VW strength are discussed on the basis of the results of atomic theory. The predicted values are smaller, by a typical factor of 2, than those deduced from the experiments. The validity of the theory, when applied to a dielectric interface, is discussed and seems questionable when the frequency of virtual atomic transitions involved in the van der Waals attraction potential lies in the dielectric window absorption range.
The atomic response to resonant light irradiation near vapor-dielectric interfaces is monitored via high-resolution reflection spectroscopy. One demonstrates that this Doppler-free spectroscopic technique yields a novel probe of atomic dynamics and QED atom-surface long- range interaction. It provides for the first time a spectral evidence of van der Waals attraction, and the method is intrinsically applicable to the observation of surface interaction exerted on excited atoms. Effects related with atomic excitation level, nature of the dielectrics, and atomic collisions are discussed.
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.
Frequency-modulated selective-reflection spectroscopy of the 6S-7P Cs resonance line yields Doppler-free anomalous line shapes that we demonstrate to be fully dominated by the long-range atom-surface interaction potential. The spatial inhomogeneous broadening of the observed line shapes, as well as its dependence on the pressure, the nature of the dielectric window, and the light incidence angle, is fully interpreted with a z(-3) van der Waals attraction model. These experiments clearly prove the feasibility of a spectral analysis of atom-surface interactions.
van der Waals interactions between atoms and dielectric surfaces are reinvestigated. To describe the nonretarded interaction potential between a dispersive dielectric surface and an atom in an arbitrary internal energy state, we derive a general expression in terms of an integral, over real frequency, of the combined atom and surface polarizabilities. It is shown that, for excited atoms, the expression is equivalent to the one obtained by Wylie and Sipe [Phys. Rev. A 32, 2030 (1985)]. We thus demonstrate how to extend this approach to excited atoms interacting with birefringent dielectrics. For isotropic dielectrics, a method of integration in closed form allows us to derive an approximate formula for the van der Waals interaction constant in terms of resonance frequencies and oscillator strengths of both the atom and the dielectric. Frequency-dependent ``dielectric reflection'' coefficients are introduced for virtual atomic dipole couplings either in absorption or in emission. In absorption, the reflection coefficient is always positive and smaller than unity. In emission, it may take arbitrary values, positive or negative (corresponding to van der Waals repulsion). Such a behavior is shown to be related to resonant excitation exchange between the atomic system and the dielectric medium, when an atomic transition frequency gets in resonance with a dielectric absorption band. Numerical calculations performed for the cesium-sapphire system are shown to be in good agreement with data obtained by selective-reflection spectroscopy. Finally, experimental tests of the birefringent character of the sapphire response are discussed.