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arXiv:cond-mat/9902172 · Physical Review Letters

Optical Linewidth of a Low Density Fermi-Dirac Gas

Janne Ruostekoski, Juha Javanainen

Published Jun 14, 1999• 59 citations
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Abstract

We study propagation of light in a Fermi-Dirac gas. We analytically obtain the leading density correction to the optical linewidth at zero temperature. This correction is a direct consequence of the quantum statistical correlations of atomic positions that modify the optical interactions between the atoms at small interatomic separations. The gas exhibits a dramatic line narrowing already at very low densities.

DOI
10.1103/physrevlett.82.4741

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With ready access to massive computer clusters we may now study light propagation in a dense cold atomic gas by means of basically exact numerical simulations. We report on a direct comparison between traditional optics, that is, electrodynamics of a polarizable medium, and numerical simulations in an elementary problem of light propagating through a slab of matter. The standard optics fails already at quite low atom densities, and the failure becomes dramatic when the average interatomic separation is reduced to around k(-1), where k is the wave number of resonant light. The difference between the two solutions originates from correlations between the atoms induced by light-mediated dipole-dipole interactions.
We derive the dispersion relation for the propagation of quasiresonant light with frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{L}}$ in an ultracold gas of bosonic atoms in the dilute regime, i.e., for an atomic density ${\mathrm{\ensuremath{\rho}}}_{0}$\ensuremath{\ll}(${\mathrm{\ensuremath{\omega}}}_{\mathit{L}}$/c)3{)}^{3})3. In our calculation, valid up to order 2 in density, two types of corrections to the Lorentz-Lorenz formula for the refractive index appear. The first one is due to the bosonic nature of the atoms and its contribution is related to the two-body correlation function. The second correction originates from multiple scattering of photons within pairs of close atoms, giving rise to the resonant van der Waals interaction. The temperature dependence of the refractive index gives a clear signature of quantum statistical effects, even if the degeneracy threshold for Bose-Einstein condensation is not reached.
Finding a comprehensive and general description of the collective Lamb shift and cooperative broadening in a radiatively interacting system is a long-standing open question. Both energy levels and linewidth of individual atoms are modified by the exchange of real and virtual photons making up the dipole-dipole interaction. We introduce a method to theoretically study weakly-driven, low-excited ensembles of two-level atoms, and obtain an analytic description of the collective Lamb shift and linewidth via a self-consistent formalism including infinite order of correlations which stem from only two-body interactions. We predict the dependency of these quantities, as measurables, on system parameters: the number density of the ensemble, the detuning of an external probe field, and the geometry of the sample.