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Physical Review Letters

Quantized motion of cold cesium atoms in two- and three-dimensional optical potentials

G. Grynberg, Brahim Lounis, Philippe Verkerk, J.-Y. Courtois, Ch Salomon

Published Apr 12, 1993• 332 citations
Publisher

Abstract

Quantization of atomic motion is observed in two- and three-dimensional cesium optical molasses by stimulated Raman spectroscopy. A new geometry is used with the minimum number of laser beams, so that the topography of the optical potential is not sensitive to phase drifts of the molasses beams. The deepest potential wells are located on a hexagonal lattice in two dimensions and on a body-centered-cubic lattice in three dimensions. They correspond to purely circularly polarized light, allowing a Lamb-Dicke narrowing of the transitions between vibrational levels to occur.

DOI
10.1103/physrevlett.70.2249

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Quantization of atomic motion is observed in two- and three-dimensional cesium optical molasses by stimulated Raman spectroscopy. A new geometry is used with the minimum number of laser beams, so that the topography of the optical potential is not sensitive to phase drifts of the molasses beams. The deepest potential wells are located on a hexagonal lattice in two dimensions and on a body-centered-cubic lattice in three dimensions. They correspond to purely circularly polarized light, allowing a Lamb-Dicke narrowing of the transitions between vibrational levels to occur.
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In a one-dimensional polarization-gradient cooling scheme, with two counter-propagating laser beams having mutually orthogonal linear polarization, a linear array of potential wells for cold atoms are formed. These optical potential wells are created by the spatially varying light shift of the atomic ground state. Transitions between quantized vibrational states in such wells have been observed by stimulated1 and spontaneous2 Raman spectroscopy. Recently, this was extended to three dimensions using both four beams3 and six beams.4 In this work, we intersect four travelling-wave laser beams, all polarized in the same plane, as indicated in Fig. 1. This produces a threedimensional body-centered cubic lattice of potential wells for cesium atoms. The laser wavelength is tuned 25 linewidths below the 62S1/2(F = 4) → 62P3/2(F = 5) transition at 852 nm; and the resultant lattice constants (distances between wells of the same character) are λ / 2 perpendicular to the plane of polarization, and λ × 2 in the plane of polarization.
We have measured the spectrum of fluorescence from 85Rb in 1-D optical molasses. The spectrum consists of a central peak and one set of sidebands characteristic of quantized atomic motion. In a 1-D molasses consisting of two counterpropagating, linear, and orthogonally polarized laser beams, optical potential wells are spaced λ/4 apart where the polarization is circular. Polarization gradient cooling reduces the temperature to a point where the atoms are trapped in these wells. The atomic motion is approximated by a quantum mechanical harmonic oscillator. We interpret the central peak as transitions beginning and ending in the same bound level and the sidebands as Raman transitions changing the vibrational quantum number by ±1. The observed level spacing in the well is proportional to the square root of the light shift. The relative strength of the blue and red sideband is given by a Boltzman factor, allowing us to determine the temperature. As expected, the temperature increases linearly with the light shift.
The spatial distribution of cesium atoms in a 1D optical molasses are probed by measuring the absorption (or amplification) of a weak laser beam. Very narrow stimulated Raman and Rayleigh resonances are observed. The position of the Raman resonance gives access to the oscillation frequency of the atoms in the wavelength-scale optical potential. From the width of the Raman lines (~35 kHz), we deduce the damping time of this oscillation, which exhibits a dramatic lengthening due to the spatial confinement of atoms to a fraction of optical wavelength (Lamb–Dicke effect). Furthermore, the narrow stimulated Rayleigh signals (8 kHz) give experimental evidence for a large scale spatial order of the atomic gas presenting some analogy with an antiferromagnetic medium.
We present an experimental investigation of a three-dimensional (3D) optical lattice where the light polarization is linear at the bottom of the potential wells instead of being circular as in previous studies. In the present situation, optical pumping induces frequent transitions between differently light-shifted Zeeman sublevels (jumping regime). However, narrow vibrational lines are still observed as a result from a motional narrowing-like phenomenon taking place in this lattice. The atomic kinetic temperature is investigated and shown to be lower than in a standard 3D lin ⊥ lin optical lattice.
We have observed the quantized motion of atoms trapped in wavelength‐sized optical potential wells. Using high‐resolution spectroscopy of the resonance fluorescence of laser‐cooled Rb atoms, we have identified spontaneous Raman transitions between bound vibrational levels. From the fluorescence spectrum, we can measure the spacing of the vibrational levels, population distributions and temperatures, and determine that the atoms are localized to λ/15. These measurements are in excellent quantitative agreement with recent quantum Monte Carlo calculations.