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arXiv:cond-mat/0405510

Bragg scattering of light in a strongly interacting trapped Fermi gas of atoms

Bimalendu Deb

Published May 21, 2004• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.cond-mat/0405510

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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.
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We propose a Bragg spectroscopy experiment to measure the onset of superfluid pairing in ultracold trapped Fermi gases. In particular, we study two-component Fermi gases in the weak coupling BCS and Bose Einstein condensation limits as well as in the strong coupling unitarity limit. The low-temperature Bragg spectrum exhibits a gap directly related to the pair-breaking energy. Furthermore, the Bragg spectrum has a large maximum just below the critical temperature when the gas is superfluid in the BCS limit. In the unitarity regime, we show how the pseudogap in the normal phase leads to a significant suppression of the low-frequency Bragg spectrum.
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.
Theoretical predictions for the dynamic structure factor of a harmonically trapped Fermi superfluid near the Bose-Einstein condensate--Bardeen-Cooper-Schrieffer (BEC-BCS) crossover are compared with recent Bragg spectroscopy measurements at large transferred momenta. The calculations are based on a random-phase (or time-dependent Hartree-Fock-Gorkov) approximation generalized to the strongly interacting regime. Excellent agreement with experimental spectra at low temperatures is obtained, with no free parameters. Theoretical predictions for zero-temperature static structure factor are also found to agree well with the experimental results and independent theoretical calculations based on the exact Tan relations. The temperature dependence of the structure factors at unitarity is predicted.
We present a high-precision determination of the universal contact parameter in a strongly interacting Fermi gas. In a trapped gas at unitarity, we find the contact to be 3.06±0.08 at a temperature of 0.08 of the Fermi temperature in a harmonic trap. The contact governs the high-momentum (short-range) properties of these systems, and this low-temperature measurement provides a new benchmark for the zero-temperature homogeneous contact. The experimental measurement utilizes Bragg spectroscopy to obtain the dynamic and static structure factors of ultracold Fermi gases at high momentum in the unitarity and molecular Bose-Einstein condensate regimes. We have also performed quantum Monte Carlo calculations of the static properties, extending from the weakly coupled BCS regime to the strongly coupled Bose-Einstein condensate case, that show agreement with experiment at the level of a few percent.
This article provides an overview of recent developments and emerging topics in the study of two-component Fermi gases using Bragg spectroscopy. Bragg scattering is achieved by exposing a gas to two intersecting laser beams with a slight frequency difference and measuring the momentum transferred to the atoms. By varying the Bragg laser detuning, it is possible to measure either the density or spin response functions which characterize the basic excitations present in the gas. Specifically, one can measure properties such as the dynamic and static structure factors, Tan’s universal contact parameter and observe signatures for the onset of pair condensation locally within a gas.