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arXiv:cond-mat/9902324 · Physical Review A

Optical response of a superfluid state in dilute atomic Fermi-Dirac gases

Janne Ruostekoski

Published Sep 1, 1999• 35 citations
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Abstract

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.

DOI
10.1103/physreva.60.r1775

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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.
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.
Dilute atomic gases have become a powerful tool for studying many-body quantum mechanics. The best example of this is the achievement of Bose-Einstein condensation in 1995 in a gas of Bose atoms, a discovery which has invoked a confluence of ideas from condensed matter, atomic and nuclear physics. Now a concerted research effort is focused on creating and studying a BCS superfluid in an atomic Fermi gas. In the work presented here we study in detail pairing superfluidity in a Fermi gas of atoms, by self-consistently solving the Bogoliubov-de Gennes equations, both for bulk systems, and for atoms in a harmonic confining potential. A critical part of this work is the derivation of a regularized theory, which is formulated entirely in terms of physically measurable quantities, such that a quantitative comparison between theory and experiment is possible with no adjustable parameters. The resulting equations form a non-linear problem, and the accurate numerical solution of this poses a formidable challenge. A major component of this thesis is the development of efficient computational approaches to overcome these difficulties. Based on the linear response of the gas to a twisting of the order parameter phase, the superfluid density can be defined as a generalized elasticity of the system. Using finite temperature perturbation theory we calculate the superfluid density in an inhomogeneous system. We investigate the structure and thermodynamic properties of a singly quantized vortex line in a gas of superfluid fermionic atoms, making the first quantitative determination the critical rotation frequency for thermodynamic stability of the vortex state, and study the nature of the bound states in the vortex core. These excitations fill the core, making direct imaging of the vortex unlikely. Instead, we propose an experiment to indirectly probe the vortex density of states with laser fields, in a scheme analogous to Scanning Tunneling Microscopy. Furthermore, it is shown that the vortex state causes a shift of the superfluid transition temperature, which can be understood as a finite size effect.
The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the sss-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.
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.