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Physical Review A

Scattering of light and atoms in a Fermi-Dirac gas with Bardeen-Cooper-Schrieffer pairing

Janne Ruostekoski

Published Feb 10, 2000• 22 citations
Publisher

Abstract

We theoretically study the optical properties of a Fermi-Dirac gas in the presence of a superfluid state. We calculate the leading quantum-statistical corrections to the standard column density result of the electric susceptibility. We also consider the Bragg diffraction of atoms by means of light-stimulated transitions of photons between two intersecting laser beams. Bardeen-Cooper-Schrieffer pairing between atoms in different internal levels magnifies incoherent scattering processes. The absorption linewidth of a Fermi-Dirac gas is broadened and shifted. Bardeen-Cooper-Schrieffer pairing introduces a collisional local-field shift that may dramatically dominate the Lorentz-Lorenz shift. For the case of the Bragg spectroscopy the static structure function may be significantly increased due to superfluidity in the near-forward scattering.

DOI
10.1103/physreva.61.033605

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We theoretically study the optical properties of a Fermi-Dirac gas in the presence of a superfluid state. We calculate the leading quantum-statistical corrections to the standard column density result of the electric susceptibility. We also consider the Bragg diffraction of atoms by means of light-stimulated transitions of photons between two intersecting laser beams. Bardeen-Cooper-Schrieffer pairing between atoms in different internal levels magnifies incoherent scattering processes. The absorption linewidth of a Fermi-Dirac gas is broadened and shifted. Bardeen-Cooper-Schrieffer pairing introduces a collisional local-field shift that may dramatically dominate the Lorentz-Lorenz shift. For the case of the Bragg spectroscopy the static structure function may be significantly increased due to superfluidity in the near-forward scattering.
We theoretically study the propagation of light in a Fermi-Dirac gas in the presence of a superfluid state. BCS pairing between atoms in different spin levels increases the optical linewidth and line shift of a quantum degenerate Fermi-Dirac gas already at very low densities and introduces a collisional local-field shift that may dramatically dominate the Lorentz-Lorenz shift. These optical properties could possibly signal the presence of the superfluid state and determine the value of the BCS order parameter.
A theoretical treatment of light scattering from a degenerate Fermi gas of trapped ultracold 6Li{}^{6}\mathrm{Li}6Li atoms is presented. We find that the scattered light contains information that directly reflects the quantum pair correlation due to the formation of atomic Cooper pairs resulting from a Bardeen-Cooper-Schrieffer phase transition to a superfluid state. Evidence for pairing should be observable in both the space and time domains.
We present a detailed theoretical study of light scattering off superfluid trapped Fermi gas of atoms at zero temperature. We apply Nambu-Gorkov formalism of superconductivity to calculate the response function of superfluid gas due to stimulated light scattering taking into account the final state interactions. The polarization of light has been shown to play a significant role in response of Cooper-pairs in the presence of a magnetic field. Particularly important is a scheme of polarization-selective light scattering by either spin-component of the Cooper-pairs leading to the single-particle excitations of one spin-component only. These excitations have a threshold of 2Δ2Δ2Δ where ΔΔΔ is the superfluid gap energy. Furthermore, polarization-selective light scattering allows for unequal energy and momentum transfer to the two partner atoms of a Cooper-pair. In the regime of low energy (<<2Δ<< 2Δ<<2Δ) and low momentum (<2Δ/(ℏvF)<2Δ/(\hbar v_F)<2Δ/(ℏvF​), vFv_FvF​ being the Fermi velocity) transfer, a small difference in momentum transfers to the two spin-components may be useful in exciting Bogoliubov-Anderson phonon mode. We present detailed results on the dynamic structure factor (DSF) deduced from the response function making use of generalized fluctuation-dissipation theorem. Model calculations using local density approximation for trapped superfluid Fermi gas shows that when the energy transfer is less than 2Δ02Δ_02Δ0​, where Δ0Δ_0Δ0​ refers to the gap at the trap center, DSF as a function of energy transfer has reduced gradient compared to that of normal Fermi gas.
We study Bragg scattering of laser light by trapped Fermi atoms having two hyperfine spin components in the unitarity-limited strongly interacting regime at zero temperature. We calculate the dynamic structure function of the superfluid trapped Fermi gas in the unitarity limit. Model calculation using local density approximation shows that, the superfluid pairing gap in the unitarity limit is detectable from the measurements of dynamic structure function by Bragg spectroscopy, while in the weak-coupling BCS limit, the gap eludes such spectroscopic detection.
We study stimulated scattering of polarized light in a two-component Fermi gas of atoms at zero temperature. Within the framework of Nambu-Gorkov formalism, we calculate the response function of superfluid gas taking into account the final state interactions. The dynamic structure factor deduced from the response function provides information about the pairing gap and the momentum distributions of atoms. Model calculations using local density approximation indicates that the pairing gap of trapped Fermi gas may be detectable by Bragg spectroscopy due to stimulated scattering.
We show that the thermodynamic properties of an atomic Fermi gas near the unitarity limit for Feshbach scattering is not universal as long as the resonance is narrow on the scale of the Fermi energy. In view of ongoing quantum Monte Carlo simulations, we explore this behavior within a mean-field approach extended to a finite temperature by means of a model potential, which allows for a tuning of the scattering phase shift and its energy dependence. Our results may be relevant for constructing a complete theoretical description of the crossover from a Bose-Einstein condensation (BEC) of composite bosons to a Bardeen-Cooper-Schrieffer (BCS) of Cooper pairs.