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Physical Review A

Effects of resonant dipole interaction between atoms on laser cooling: The case of two identical atoms

Jingzhong Guo

Published Oct 1, 1994• 10 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.50.r2830

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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 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 resolved sideband laser cooling of a one-dimensional optical lattice with one atom per site, and in particular the effect of the dipole interaction between radiating atoms. For simplicity, we consider the case where only a single cooling laser is applied. We derive a master equation and solve it in the limit of a deep lattice and weak laser driving. We find that the dipole interaction significantly changes the final temperature of the particles, increasing it for some phonon wave vectors and decreasing it for others. The total phonon energy over all modes is typically higher than in the noninteracting case but can be made lower by the right choice of parameters.
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.
We present a calculation of one-dimensional sub-Doppler cooling of neutral atoms, in which the atomic center-of-mass motion is quantized. The cooling field consists of a pair of counterpropagating, linearly polarized laser beams, with their polarizaton vectors at an angle \ensuremath{\theta} with respect to each other. The steady-state atomic density matrix is analyzed as a function of \ensuremath{\theta}. It is shown that, depending on the internal atomic level scheme, the equilibrium population of the quantized ground state of atomic center-of-mass motion can either increase or decrease significantly when \ensuremath{\theta} is reduced from \ensuremath{\pi}/2. These effects are interpreted based on the spatial localization of atoms in the light-induced potential wells.
A cold atomic gas with an inverted population on a transition coupled to a field mode of an optical resonator constitutes a generic model of a laser. For quasi-continuous operation, external pumping, trapping and cooling of the atoms is required to confine them in order to achieve enough gain inside the resonator. As inverted atoms are high-field seekers in blue detuned light fields, tuning the cavity mode to the blue side of the atomic gain transition allows for combining lasing with stimulated cavity cooling and dipole trapping of the atoms at the antinodes of the laser field. We study such a configuration using a semiclassical description of particle motion along the cavity axis. In extension of earlier work we include free space atomic and cavity decay as well as atomic dipole-dipole interactions and their corresponding forces. We show that for a proper choice of parameters even in the bad cavity limit the atoms can create a sufficiently strong field inside the resonator such that they are trapped and cooled via the superradiant lasing action with less than one photon on average inside the cavity.
The theory of an atom dipole trap composed of a focused, far red-detuned, trapping laser beam, and a pair of red-detuned, counterpropagating, cooling beams is developed for the simplest realistic multilevel dipole interaction scheme based on a model of a (3+5)-level atom. The description of atomic motion in the trap is based on the quantum kinetic equations for the atomic density matrix and the reduced quasiclassical kinetic equation for atomic distribution function. It is shown that when the detuning of the trapping field is much larger than the detuning of the cooling field, and with low saturation, the one-photon absorption (emission) processes responsible for the trapping potential can be well separated from the two-photon processes responsible for sub-Doppler cooling atoms in the trap. Two conditions are derived that are necessary and sufficient for stable atomic trapping. The conditions show that stable atomic trapping in the optical dipole trap can be achieved when the trapping field has no effect on the two-photon cooling process and when the cooling field does not change the structure of the trapping potential but changes only the numerical value of the trapping potential well. It is concluded that the separation of the trapping and cooling processes in a pure optical dipole trap allows one to cool trapped atoms down to a minimum temperature close to the recoil temperature, keeping simultaneously a deep potential well.