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−3 potential dependence (
z: distance to the wall). We present detailed results of two series of experiments at a Cs vapor/dielectric window interface on the 6S
1/2-6P
3/2 (
λ=852 nm) resonance line and on the 6S
1/2-7P second resonance line (
λ=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 kHz
μm
3 and
≈20 kHz
μm
3, 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.
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.
Up to now, Doppler-free nonlinear spectroscopy has been applied to atoms inside a gas medium (volume spectroscopy). We have extended these methods to atoms in the vicinity of a surface. The basic principle consists of monitoring reflectivity changes produced when a laser beam, incident on a glass–vapor interface, is brought into resonance with an atomic transition. For Doppler-free spectroscopy, two counterpropagating beams are used to operate velocity selection. If these two beams are under normal incidence in the glass—velocity selection perpendicular to the surface—one observes saturated dispersion (selective reflection sensitive to the real index). For incidence angles in the glass (prism) larger than the critical angle (total internal reflection), a standing evanescent wave is produced in the gas (velocity selection along the surface), and saturated absorption is detected. Experimental demonstration was performed on the Na resonance line; high sensitivity (10−4 relative reflectivity change) and spectral resolution as good as 20 MHz were obtained. The main limitation to better resolution comes from the short atomic transit time in the evanescent wave (typical extension ~λ). Relevant applications of these techniques should also concern the diagnostics of optically thick media, as analysis of interaction between gas-phase atoms and the surface, notably atom–wall collisions, and modification of the spontaneous emission characteristics.
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.