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arXiv:quant-ph/0104022 · Physical Review A

Slow light propagation in trapped atomic quantum gases

Özgür Esat Müstecaplıoğlu, Li You

Published May 30, 2001• 6 citations
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Abstract

We study semiclassical slow light propagation in trapped two-level atomic quantum gases. The temperature-dependent behaviors of both group velocity and transmissions are compared for low-temperature Bose, Fermi, and Boltzman gases within the local-density approximation for their spatial density profile.
DOI
10.1103/physreva.64.013604

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We study interactions of light with a sample of two-level atoms, with full inclusion of angular momentum degeneracy, at temperatures and densities such that the quantum statistics of the atoms may have an effect. Coupled propagation equations are given for light and matter fields, and plausible general simplifications are enumerated. In particular, the motion of the atoms during the excited-state lifetime may often be ignored. The propagation equations of light and matter fields are decoupled within the assumption that the detuning of the driving light from atomic resonance is large, and the spectrum of scattered light is studied for ideal Bose and Fermi gases. In addition to the expected image of the velocity distribution, the spectra contain qualitatively distinct features that depend on the statistics of the atoms. This is because for bosons (fermions), those scattering events in which an atom recoils to an already occupied state are enhanced (inhibited).
Summary form only given. The recent observation of slow light propagation by Harris and Hau (1999) motivates the study of nonlinear optical processes under conditions where slow group velocity, or equivalently large nonlinearity, is the dominant feature of the problem. By combining electromagnetically induced transparency (EIT) and cold atom technology, a sharp resonance is created with a transmission linewidth much less than the natural linewidth of the atoms. A pulse of light propagating in this medium has a phase velocity of c and a group velocity that can be less than 10/sup -7/ c. As a light pulse of sufficiently wide bandwidth enters a cold-atom, EIT medium, the pulse shape, electric field strength, and power density remain nominally unchanged. Concurrently, because the group velocity is decreased, the stored energy per volume must increase. This increase occurs by spatial compression of the travelling pulse. A pulse measuring 300 m in free space compresses to 30 /spl mu/m within the cold-atom medium.
For the known, experimentally realized conditions, the detailed analysis of the field-induced transparency and formation of exceptionally low group velocity of probe light is performed. The secondary fields being due to the atomic polarization induced by the two propagating light pulses - coupling (or dressing) and probe ones, resonant to the adjoining transitions in a three-level scheme, are explicitly taken into account. Partly linear (relative to the probe pulse field) and completely non-linear regimes are considered. Particularly, the outputting coupled wave is shown to be slightly amplified, when the probe light pulse “disappears” inside the medium.
We calculate the shift, due to interatomic interactions, of an optical transition in an atomic Fermi gas trapped in an optical lattice, as in recent experiments of Campbell et al. [Science 324, 360 (2009)]. Using a pseudospin formalism to describe the density matrix of atoms, we derive a Bloch equation which incorporates both spatial inhomogeneity of the probe laser field and interatomic interactions. Expressions are given for the frequency shift as a function of pulse duration, detuning of the probe laser, and the spatial dependence of the electric field of the probe beam. In the low temperature semiclassical regime, we find that the magnitude of the shift is proportional to the temperature.