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Physical Review A

Dipole interactions in a resonant quantum coherent gas

Richard T. Hammond

Published Apr 1, 1993• 1 citation
Publisher

Abstract

The susceptibility of a quantum coherent gas is derived near resonance and the effect of dipole-dipole interactions are assessed for a three-level system using mean-field theory. It is shown that the gas exhibits an ultralarge index effect with no absorption with the dipole effects included, but that for large N (number of atoms per unit volume) the dipole interactions have a marked effect. These results imply that the dipole interactions of a coherent gas near resonance do not destroy the ultralarge absorption-free index effect.

DOI
10.1103/physreva.47.3360

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The susceptibility of a quantum coherent gas is derived near resonance and the effect of dipole-dipole interactions are assessed for a three-level system using mean-field theory. It is shown that the gas exhibits an ultralarge index effect with no absorption with the dipole effects included, but that for large N (number of atoms per unit volume) the dipole interactions have a marked effect. These results imply that the dipole interactions of a coherent gas near resonance do not destroy the ultralarge absorption-free index effect.
We present a mean field analysis of the effects of molecular rotation on the excitation spectrum and stability of ultracold dipolar gases. For an unpolarized homogeneous gas interacting with a pure dipole-dipole interaction, we find that for the rotational state L = 1 the dipole-dipole interaction causes a splitting of the translation-rotation energy levels into a single M = 0 and a doubly degenerate M = ±1 excitation. For all other rotational states, the dipole-dipole interaction does not lead to coupling of translations and rotations and therefore has no effect on the rotational degeneracy of the excitations. The addition of arbitrarily small electric fields is found to introduce instabilities similar to those known to arise in the fully polarized dipolar gas. As in the case of a fully polarized gas, addition of a large enough short range repulsive potential is seen to stabilize the system, with the critical value of the repulsive interaction required for stabilization being larger when rotations are included.
We study the effect of near dipole-dipole interactions on the electric susceptibility of a coherently prepared three-level $\ensuremath{\Lambda}$ system. We discuss the influence of atomic nonlinearities on the recently predicted enhancement of the absorptionless index of refraction and inversionless gain due to local field effects [J.P. Dowling and C.M. Bowden, Phys. Rev. Lett. 70 1421 1993] and predict a density dependent, or piezophotonic, switching between absorption and amplification.
A theory is developed for the resonant dielectric susceptibility of a high density gas which consists of two level atoms interacting through the dipole–dipole potential. A many body collision model, which includes the binary as well as the shielding effects, is investigated. The linear response of the dielectric is given by a generalized transport equation. Self-consistent coupled equations are derived for the various collision operators, using the propagator techniques. In the two limiting cases, the results of the binary collision model and those of the shielded interaction model, respectively, are recovered. The equations are simplified by neglecting the nonresonant contributions. Finally, a solution is obtained in the resonance broadening approximation. The resulting expression for the dielectric susceptibility includes the two body collision as well as the many body shielding effects. In particular, it includes the important collective excitation transfer effects. The proposed many body collision model should be appropriate for the resonant, linear response of high density gases.
The local-field effects are considered which are feasible in a dense ensemble of resonant atoms modeled by multilevel quantum systems. Our approach is based on the generalized two-level system [V.S. Butylkin, A.E. Kaplan, and Yu.G. Khronopulo, Zh. \'Eksp. Teor. Fiz. 59, 921 (1970)]. Making use of this model, we take account of the nonresonant polarization and Stark shift of the absorption line due to the difference in linear polarizabilities of atoms in ground and excited states. With near dipole-dipole interaction and quadratic Stark effect included simultaneously, new features of the hysteresis behavior of the population difference as a function of the external-field intensity are predicted.