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Bulletin of the American Physical Society

Quantum motion of laser trapped atoms

Poul Jessen

Published May 1, 1993• 0 citations

Abstract

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

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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 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.

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.

We study theoretically the spectrum of resonance fluorescence and laser-cooling dynamics corresponding to quantized atomic motion in one-dimensional optical molasses. We consider an atom with a

{\mathit{J}}_{\mathit{g}}

=1\ensuremath{\rightarrow}

{\mathit{J}}_{\mathit{e}}

=2 transition interacting with two counterpropagating laser beams. The laser light is assumed to be linearly polarized with an angle \ensuremath{\theta} between the polarization vectors. We discuss the spectrum of resonance fluorescence, the spectroscopy of band structure in the optical potentials, and the population of the vibrational quantum levels as a function of the angle between the polarization vectors.

Ultralow temperatures produced with polarization-gradient cooling now allow atoms to be trapped in shallow optical potential wells. We present evidence for the quantized motion of atoms in a 1-D optical molasses with the observation of spontaneous Raman transitions between vibrational levels in these wells, observed in fluorescence. In addition, we discuss the features of a far off resonance trap (FORT) -- a single focus dipole force trap so far off resonance to be an essentially ground-state trap.

We study theoretically the spectrum of resonance fluoresence from one-dimensional molasses consisting of two-level atoms with Zeeman substructure. The center-of-mass motion of the atom is treated fully quantum mechanically. The spectrum shows sidebands due to transitions between vibrational levels in optical potentials generated by the laser light. Detailed results are presented for the

{\mathit{J}}_{\mathit{g}}

=1/2\ensuremath{\rightarrow}

{\mathit{J}}_{\mathit{e}}

=3/2 atomic transition in a laser configuration with two counterpropagating waves with orthogonal polarizations. We have solved the corresponding quantum master equation and calculated the relevant autocorrelation function of the atomic dipole using (i) a direct numerical solution of the master equation, (ii) a wave-function simulation of the master equation and correlation function employing periodic time-dependent Bloch wave functions, and (iii) a semiclassical bipotential calculation for the spectrum including a simple quantum correction.

We observe transitions of laser-cooled Rb between vibrational levels in subwavelength-sized optical potential wells, using high-resolution spectroscopy of resonance fluorescence. We measure the spacing of the levels and the population distribution, and find the atoms to be localized to 1/15 of the optical wavelength. We find up to 60% of the population of trapped atoms in the vibrational ground state. The dependence of the spectrum on the parameters of the optical field provides detailed information about the dynamics of laser-cooled atoms.