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Optics Letters

Two-photon optical Ramsey spectroscopy of freely falling atoms

Raymond G. Beausoleil, Theodor W. Hänsch

Published Nov 1, 1985• 14 citations
Publisher

Abstract

Using a simple semiclassical model, we explore ultrahigh-resolution optical two-photon spectroscopy of cold neutral atoms falling freely in a fountain. Considering atoms that interact with the same standing-wave laser field twice on their parabolic trajectories, and averaging over a Maxwellian velocity distribution, we predict a nearly Lorentzian line shape with just the natural linewidth. First-order Doppler shifts cancel even if the counterpropagating beams are slightly misaligned, and sub-Hertz resolution appears feasible with a fountain of modest dimensions.

DOI
10.1364/ol.10.000547

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International Laser Science Conference•Jan 1, 1986•0 citations
Using a simple semiclassical model, we explore ultrahigh-resolution optical two-photon spectroscopy of cold neutral atoms falling freely in a fountain. Considering atoms that interact with the same standing-wave laser field twice on their parabolic trajectories, and averaging over a Maxwellian velocity distribution, we predict a nearly Lorentzian line shape with just the natural linewidth. First-order Doppler shifts cancel even if the counterpropagating beams are slightly misaligned, and sub-Hertz resolution appears feasible with a fountain of modest dimensions.
We present a semiclassical analysis of ultrahigh-resolution two-photon optical Ramsey spectroscopy of cold neutral atoms falling freely in a fountain. Considering atoms which interact with the same standing-wave laser field twice on their parabolic trajectories and averaging over a broad atomic velocity distribution, we predict a nearly Lorentzian line shape whose width is just the natural linewidth. We have investigated a number of systematic corrections to the atomic resonance frequency, including first-order and second-order Doppler shifts, gravitational red shifts, and ac Stark shifts. First-order Doppler shifts due to vertical motion cancel even if the counterpropagating beams are slightly misaligned, and resolutions below 1 Hz appear feasible with a fountain of modest dimensions.
The two-photon spectrum of sodium atoms, excited by two counterpropagating evanescent waves, is investigated both experimentally and theoretically. Sub-Doppler linewidths are observed, which are quantitatively reproduced by a rigorous theoretical approach that takes into account optical pumping and transit time broadening due to the translational motion of the arriving and departing atoms through the evanescent-wave fields. The velocity distribution of the atoms desorbing from the surface is found to obey a cosine law, which has a significant influence on the observed line shapes.
We demonstrate coherent Doppler-free three-photon excitation of the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ optical clock transition and the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ intercombination transition in free-space thermal clouds of 88Sr^{88}\mathrm{Sr}88Sr atoms. By appropriate orientation of the wave vectors of three lasers incident on the atoms, the first-order Doppler shift can be eliminated for all velocity classes. Three-photon excitation of the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ transition enables high-contrast Ramsey spectroscopy with interrogation times comparable to the $21\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{s}$ natural lifetime using a single near-resonant laser source. Three-photon spectroscopy on the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ clock transition, using only laser frequencies nearly resonant with the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ transitions, enables a reduction in Doppler broadening by two orders of magnitude and a corresponding $\ensuremath{\sim}470\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}$ linewidth without a confining potential.
A collection of stationary or nearly stationary atoms would be an ideal sample on which to perform high-resolution spectroscopy. Spectral width, shifts, and distortions that are due to second-order-Doppler and transit-time effects, which now limit high-resolution Doppler-free spectroscopies, would be virtually eliminated. Such low-energy atoms would also be useful for loading into the shallow optical1,2 or magnetic3,4 traps that have been proposed. By irradiating an atomic beam with a near-resonant counter- propagating laser, we have produced such a sample of atoms. The average velocity of the atoms is nearly zero, and the spread in velocities is equivalent to that of a gas at a temperature of about 1 K.
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.