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Physical Review A

Cooling and resonance fluorescence of two atoms in a one-dimensional optical molasses

Jingzhong Guo, J. Cooper

Published Apr 1, 1995• 22 citations
Publisher

Abstract

We derive a generalized master equation, which describes the quantized cooling of identical atoms in the laser fields. The effects of the dipole-dipole interaction between the atoms are included explicitly in the master equation. We then calculate the steady-state density matrix of two atoms cooled by a one-dimensional optical molasses. It is shown that when the mean separation between these atoms reduces below the optical wavelength \ensuremath{\lambda}/2\ensuremath{\pi}, cooling will be significantly limited due to the enhanced atom-atom interaction. Based on the quantum regression theorem, we also calculate the resonance fluorescence spectrum emitted by these two atoms, which exhibits features different from those of isolated atoms.

DOI
10.1103/physreva.51.3128

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We derive a generalized master equation, which describes the quantized cooling of identical atoms in the laser fields. The effects of the dipole-dipole interaction between the atoms are included explicitly in the master equation. We then calculate the steady-state density matrix of two atoms cooled by a one-dimensional optical molasses. It is shown that when the mean separation between these atoms reduces below the optical wavelength \ensuremath{\lambda}/2\ensuremath{\pi}, cooling will be significantly limited due to the enhanced atom-atom interaction. Based on the quantum regression theorem, we also calculate the resonance fluorescence spectrum emitted by these two atoms, which exhibits features different from those of isolated atoms.
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 Jg{\mathit{J}}_{\mathit{g}}Jg​=1\ensuremath{\rightarrow}Je{\mathit{J}}_{\mathit{e}}Je​=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.
We study the effects of the resonant dipole interaction between identical atoms undergoing polarization-gradient laser cooling. A generalized master equation, which includes both the atom-field interaction and the dipole-dipole interaction between atoms, is derived. We then apply this equation to the particular case of two identical atoms cooled simultaneously by a one-dimensional cooling field. We show that, as the average center-of-mass separation between the two atoms is reduced to be less than an optical wavelength \ensuremath{\lambda}/2\ensuremath{\pi}, the population of the ground motional state of the atoms begins to decrease sharply, indicating a breakdown of the cooling mechanism due to the enhanced atom-atom interaction.
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 Jg{\mathit{J}}_{\mathit{g}}Jg​=1/2\ensuremath{\rightarrow}Je{\mathit{J}}_{\mathit{e}}Je​=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.
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 analyze the influence of long-range dipole-dipole interactions between atoms with Zeeman substructure on atomic polarization-gradient cooling at low laser power. The system we consider is a cloud of N atoms driven by two counterpropagating linear cross-polarized laser beams (lin\ensuremath{\perp}lin configuration) on a -- transition. In the semiclassical regime we derive analytical results for the change of the cooling force due to collisions and for the diffusion coefficient in the far-field approximation. For the energy regime where the center-of-mass motion is characterized by oscillations in the optical potentials, we estimate the effect of these far-field collisions on the motion-induced sideband structure of the resonance fluorescence spectrum by using a white-noise approximation for the background light field. This gives a qualitative signature of the heating mechanism in such systems.