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Physical Review A

Two-photon Doppler-free spectroscopy of trapped atoms

Claudio Lenz Cesar, Daniel Kleppner

Published Jun 1, 1999• 23 citations
Publisher

Abstract

We describe the systematics of two-photon Doppler-free excitation of atoms confined in a cylindrical harmonic trap, at densities far from the regime of quantum degeneracy. The line shape is explained in terms of momentum transfer between the light beam and the trapped atoms. This formalism extends the semiclassical analysis of time-of-flight broadening. The results, which are general, were motivated by the development of two-photon Doppler-free spectroscopy of trapped atomic hydrogen.

DOI
10.1103/physreva.59.4564

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We describe the systematics of two-photon Doppler-free excitation of atoms confined in a cylindrical harmonic trap, at densities far from the regime of quantum degeneracy. The line shape is explained in terms of momentum transfer between the light beam and the trapped atoms. This formalism extends the semiclassical analysis of time-of-flight broadening. The results, which are general, were motivated by the development of two-photon Doppler-free spectroscopy of trapped atomic hydrogen.
Non-stationary two-photon absorption coherent spectroscopy free of Doppler broadening in an atomic gas has been considered in detail. Correct account has been taken of the level degeneracy and depolarizing collisions. This two-photon Doppler-free spectroscopy has been developed for determining the relaxation rates of the atomic multipole moments in gas. A criterion to test the adopted model of the depolarizing collisions has been developed. A possible method for the identification of the atomic transitions in the angular momentum has been formulated. A technique of precisely determining the separation between the energy levels of the two-photon transition has been proposed. The conditions under which the Stokes wave is conjugated with respect to the probe pulse in amplitude, phase and polarization have been determined for the atomic gas in the presence of depolarizing collisions.
We report observation of the 1S-2S two-photon transition in hydrogen confined in a magnetic trap at submillikelvin temperatures. The excitation spectrum can display a sharp central feature arising from periodic motion of the trapped atoms. The metastable 2S atoms remain trapped, and have a lifetime close to the natural lifetime of 122 ms. These developments open the way to achieving the transition's natural linewidth. We have also demonstrated that the temperature of the gas can be determined from the line shape, providing an important tool for the study of cold trapped hydrogen. The resolution in these experiments appears to be limited by laser stability, currently 3 kHz.
A detailed analysis is made of transient coherent Doppler-free spectroscopy of two-photon absorption in an atomic gas. The hyperfine structure of the levels and elastic depolarizing collisions are allowed for. The analysis is used to develop a method for the determination of the time constant of relaxation of the multipole moments of atoms when such relaxation is due to radiative decay and collisions with a buffer gas. A way of determining the separation between the hyperfine structure components is demonstrated. It is shown that under conditions of excitation of the atoms the hyperfine structure of the levels can give rise to quantum beats of the density of a conjugate wave.
A theory of the influence of binary collisions on the line shapes associated with Doppler-free spectroscopy is presented. The specific calculation is for two-photon absorption through a real or virtual intermediate state, but the extension of the results to alternative level schemes is included. Collisions are treated quite generally at first, but, ultimately, a simple but reasonable collision model is adopted to properly account for both the "phase-interrupting" and "velocity-changing" aspects of collisions. It is shown that collisional processes can be used to distinguish between the "two-quantum" and "stepwise" contributions to the two-photon excitation rate. Moreover, it is demonstrated that systematic experimental line-shape investigations, in addition to providing tests of current collision theories, can lead to values for collision broadening and shift parameters, excitation transfer rates, magnetic substate relaxation rates, velocity-changing collision rates, and collision kernels. Consequently, Doppler-free spectroscopy can provide a new and important probe of collision effects in atomic and molecular systems.
Summary form only given. Utilizing cold and trapped atoms for precision spectroscopy of weak atomic transitions has two important advantages: the suppression of Doppler and time-of-flight broadenings and a combination of long interaction times, weak perturbations and tight confinement, which can be obtained using dark optical traps. We present a new and extremely sensitive method for measuring weak transitions with cold atoms in a dark optical trap, using electron shelving spectroscopy. Our scheme is based on a /spl Lambda/ system. Atoms with two ground states (for example, two hyperfine levels) are stored in the trap in a level that is coupled to the upper (excited) state, by an extremely weak transition. Atoms that undergo the weak transition may be shelved by a spontaneous Raman transition on the second ground level, which is uncoupled to the excited level by the measured photons. Finally, the detection scheme benefits from the multiply excited fluorescence of a strong closed transition from the uncoupled ground-state, that utilizes quantum amplification due to the electron shelving technique. We realized this scheme on a 5S/sub 1/2//spl rarr/5D/sub 5/2/ two-photon transition in cold and optically trapped /sup 85/Rb atoms.