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Physical Review Letters

Dynamics and spatial order of cold cesium atoms in a periodic optical potential

Philippe Verkerk, Brahim Lounis, Ch Salomon, Claude N. Cohen-Tannoudji, J.-Y. Courtois, G. Grynberg

Published Jun 29, 1992• 289 citations
Publisher

Abstract

The spatial distribution and the dynamics of Cs atoms in a 1D optical molasses are probed by measuring the absorption (or amplification) spectrum of a weak laser beam. Narrow (35--50 kHz) Raman lines give access for the first time to the frequency and to the damping of the atom's oscillation in the potential wells associated with light shifts. A narrower (8 kHz) Rayleigh resonance demonstrates the existence of a large-scale spatial order of the atoms, presenting some analogy with an antiferromagnetic medium.

DOI
10.1103/physrevlett.68.3861

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The spatial distribution and the dynamics of Cs atoms in a 1D optical molasses are probed by measuring the absorption (or amplification) spectrum of a weak laser beam. Narrow (35--50 kHz) Raman lines give access for the first time to the frequency and to the damping of the atom's oscillation in the potential wells associated with light shifts. A narrower (8 kHz) Rayleigh resonance demonstrates the existence of a large-scale spatial order of the atoms, presenting some analogy with an antiferromagnetic medium.
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.
In two recent experiments Verkerk et al. and our group have observed quantization of the center-of-mass motion of laser cooled atoms in sub-wavelength sized potential wells formed by the light field of a 1-dimensional optical molasses. Our 1-dimensional optical molasses consists of a pair of counterpropagating laser beams of orthogonal, linear polarization, creating a series of potential wells separated by {lambda}/4. Polarization gradient laser cooling reduces the thermal energy of the atoms until they are trapped in well resolved vibrational levels near the bottom of the wells. Transitions between these vibrational levels are seen in a high resolution spectrum of fluorescence, where they give rise to a Rayleigh peak centered at the laser frequency, and well resolved Raman sidebands shifted by a frequency {plus_minus}{omega}, typically on the order of 100 kHz. We find quantitative agreement between the measured level separation h{omega} and the results of a calculation of the bandstructure in the periodic optical potential. Based on the observed ratio of the strength of the blue to the red sideband we determine the temperature of the atoms, and find agreement with theoretical predictions. Based on the level spacing and temperature we find the atoms to be localized to {approx}/15, withmore » up to 50-60% of the population of the trapped atoms in the vibrational ground state. We observe intriguing differences between fluorescence radiated by localized atoms, and the fluorescence radiated by non-localized atoms in a 1-dimensional optical molasses composed of a pair of counterpropagating laser beams of opposite circular polarization. The prospect of observing quantum motion and spatial order in 2 and 3 dimensions, and the consequences for the spectrum of fluorescence, will be discussed.« less
We present a detailed theoretical investigation of the transmission spectrum of a probe beam interacting with atoms in a one-dimensional optical molasses obtained with linearly cross-polarized counterpropagating pump beams. The study is performed for a Jg{\mathit{J}}_{\mathit{g}}Jg​=1/2\ensuremath{\rightarrow}Je{\mathit{J}}_{\mathit{e}}Je​=3/2 atomic transition in the limit where the Hamiltonian part of the atom-field coupling is predominant over the relaxation part. We analyze the stimulated Raman transitions occurring between different vibrational levels of the atoms in the periodic potential created by the light shifts, and we show a dramatic lengthening of the damping time of coherences between such levels due to the Lamb-Dicke effect. Very narrow Rayleigh resonances with a shape sensitive to the probe polarization appear for a probe frequency close to the pump frequency. We interpret these resonances in terms of scattering of the pump waves on density and magnetization gratings, and show that they provide important information about the dynamics and localization of atoms at the bottom of the potential wells. Such information should also be accessed by phase-conjugation experiments. Finally, indications on the treatment of other atomic transitions are given.
In this paper we report on the first purely ``pump-probe'' nonlinear laser spectroscopy results in a slow atomic beam. We have observed Raman, Rayleigh, and recoil-induced resonances (RIR) in a continuous beam of slow and cold cesium atoms extracted from a two-dimensional (2D) magneto-optical-trap (MOT) with the moving molasses technique. The RIR enabled us to measure the velocity distribution, therefore the average speed (0.6--4 m/s) and temperature (50--500 \ensuremath{\mu}K) of the atomic beam. Compared to time of flight, this technique has the advantage of being local, more sensitive in the low-velocity regime (v<1m/s),(v<1 \mathrm{m}/\mathrm{s}),(v<1m/s), and it gives access to transverse velocities and temperatures. Moreover, it may be extended to measure atomic velocities in the 2D MOT source of the atomic beam.
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.