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Europhysics Letters (EPL)

Sub-kHz Rayleigh Resonance in a Cubic Atomic Crystal

Andreas Hemmerich, Claus Zimmermann, Theodor W. Hänsch

Published Apr 10, 1993• 76 citations
Publisher

Abstract

We have observed quantized motion of rubidium atoms spatially confined by dipole forces inside microscopic light traps. A cubic lattice of such traps is formed by three mutually orthogonal standing waves. We compare 2D and 3D confinement in the same experiment by observing the absorption of a weak probe laser beam. In both cases we observe Raman transitions between vibrational levels and a central Rayleigh resonance. When we switch to 3D confinement the line width of this Rayleigh resonance dramatically decreases to values below 1 kHz.

DOI
10.1209/0295-5075/22/2/003

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We have observed quantized motion of rubidium atoms spatially confined by dipole forces inside microscopic light traps. A cubic lattice of such traps is formed by three mutually orthogonal standing waves. We compare 2D and 3D confinement in the same experiment by observing the absorption of a weak probe laser beam. In both cases we observe Raman transitions between vibrational levels and a central Rayleigh resonance. When we switch to 3D confinement the line width of this Rayleigh resonance dramatically decreases to values below 1 kHz.
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We have investigated the spectral broadening in the near-resonance fluorescence spectrum of a single rubidium atom trapped in a three-dimensional (3D) optical lattice in a strong Lamb-Dicke regime. Besides the strong Rayleigh peak, the spectrum exhibited weak Stokes and anti-Stokes Raman sidebands. The line width of the Rayleigh peak for low potential depths was well explained by matter-wave tunneling between the first-two lowest vibrational states of 3D anisotropic harmonic potentials of adjacent local minima of the optical lattice.
We study a novel property of light scattering by Rb atoms confined in a far off-resonance optical dipole force trap. The trapping laser wavelength varies from 780 nm to 860 nm and its intensity is about 1 MW/cm{sup 2}. Spontaneous Raman scattering of photons from the trapping laser can change the ground-state hyperfine quantum number F of the atoms. We observe the relaxation time by measuring the population of the F=3 level after optically pumping the atoms into the F=2 level. Spontaneous photon scatter rates as low as 10{sup 3} s{sup -1} have been observed, corresponding to recoil heating rates below 1 mK/s. For detuning from resonance {Delta} greater than the excited-state fine-structure splitting the total scatter rate, including Rayleigh scattering, decreases as {Delta}{sup 2} while the spontaneous Raman scatter rate decreases as {Delta}{sup 4}. This is due to interference between the Raman scattering amplitudes from the two excited-state fine-structure levels in the Kramers-Heisenberg formula. Because Rayleigh scattering dominates, the atoms` F and M{sub F} quantum numbers are preserved even after many scattering events. This makes far off-resonance optical traps ideal for studies of state-selective collisions and collective phenomena.
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
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.