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Physical Review Letters

Localization of atoms in a three-dimensional standing wave

Christoph Ira Westbrook, Richard N. Watts, Carol E. Tanner, S. L. Rolston, William D. Phillips, Paul D. Lett, P. L. Gould

Published Jul 2, 1990• 159 citations
Publisher

Abstract

We have used a heterodyne technique to observe the spectrum of resonance fluorescence from sodium atoms in optical molasses. The spectra show a very narrow feature which we attribute to Dicke narrowing of the fluorescence from atoms localized to less than an optical wavelength in three-dimensional standing-wave potential wells.
DOI
10.1103/physrevlett.65.33

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Early experiments on ultracold optical molasses relied on time-of-flight and other ballistic techniques to measure the temperature of atoms released from the molasses.1,2 At the extremely low temperatures observed, the size of the molasses, the effects of gravity, the probe that detected the falling atoms, and the way in which the laser beams forming the molasses were turned off produced a large systematic uncertainty in the temperature determination. Here, we report a direct measurement of the Doppler width of the fluorescence spectrum of Na atoms still viscously confined in the molasses. We determined this spectrum using an optical heterodyne technique and we believe this to be the first time an atomic fluorescence spectrum has been heterodyned. The temperature deduced from the Doppler width is in good agreement with that determined using improved time-of-flight techniques. The heterodyne technique has the added advantage of providing spatially resolved temperature measurements. In addition to the nominally 600-kHz wide Doppler peak, we see a much narrower (60-kHz wide) peak which we tentatively ascribe to Dicke narrowing due to confinement by optical forces.
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 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.
Two- and three-dimensional atom localization in a two-level atom–field system via resonance fluorescence is suggested. For the two-dimensional localization, the atom interacts with two orthogonal standing-wave fields, whereas for the three-dimensional atom localization, the atom interacts with three orthogonal standing-wave fields. The effect of the detuning and phase shifts associated with the corresponding standing-wave fields is investigated. A precision enhancement in position measurement of the single atom can be noticed via the control of the detuning and phase shifts.