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arXiv:1308.5487 · Physical Review Letters

Local Observation of Pair Condensation in a Fermi Gas at Unitarity

Marcus Lingham, Kristian Fenech, Sascha Hoinka, Chris J. Vale

Published Mar 13, 2014• 26 citations
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Abstract

We present measurements of the local (homogeneous) density-density response function of a Fermi gas at unitarity using spatially resolved Bragg spectroscopy. By analyzing the Bragg response across one axis of the cloud, we extract the response function for a uniform gas which shows a clear signature of the Bose-Einstein condensation of pairs of fermions when the local temperature drops below the superfluid transition temperature. The method we use for local measurement generalizes a scheme for obtaining the local pressure in a harmonically trapped cloud from the line density and can be adapted to provide any homogeneous parameter satisfying the local density approximation.

DOI
10.1103/physrevlett.112.100404

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We present measurements of the local (homogeneous) density-density response function of a Fermi gas at unitarity using spatially resolved Bragg spectroscopy. By analyzing the Bragg response across one axis of the cloud, we extract the response function for a uniform gas which shows a clear signature of the Bose-Einstein condensation of pairs of fermions when the local temperature drops below the superfluid transition temperature. The method we use for local measurement generalizes a scheme for obtaining the local pressure in a harmonically trapped cloud from the line density and can be adapted to provide any homogeneous parameter satisfying the local density approximation.
We present an experimental study of the high-energy excitation spectra of unitary Fermi gases. Using focused beam Bragg spectroscopy, we locally probe atoms in the central region of a harmonically trapped cloud where the density is nearly uniform, enabling measurements of the dynamic structure factor for a range of temperatures both below and above the superfluid transition. Applying sum rules to the measured Bragg spectra, we resolve the characteristic behavior of the universal contact parameter, C, across the superfluid transition. We also employ a recent theoretical result for the kinetic (second-moment) sum rule to obtain the internal energy of gases at unitarity.
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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 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 investigate pseudogap phenomena in the unitarity limit of a trapped superfluid Fermi gas. Including effect of strong pairing fluctuations within a T -matrix approximation, as well as effects of a harmonic trap within the local density approximation (LDA), we calculate the local superfluid density of states below the superfluid phase transition temperature T c . We show that the spatial region where single-particle excitations are dominated by the pseudogap may still exist even below T c , due to inhomogeneous pairing fluctuations caused by the trap potential. From the temperature dependence of the pseudogapped density of states, we identify the pseudogap regime of the unitarity Fermi gas with respect to the temperature and spatial position. We also show that the combined T -matrix theory with the LDA can quantitatively explain the local pressure which was recently observed in the unitarity limit of a 6 Li Fermi gas.
Using a multiple-image reconstruction method applied to a harmonically trapped Bose gas, we determine the equation of state of uniform matter across the critical transition point, within the local density approximation. Our experimental results provide the canonical description of pressure as a function of the specific volume, emphasizing the dramatic deviations from the ideal Bose gas behavior caused by interactions. They also provide clear evidence for the nonmonotonic behavior with temperature of the chemical potential, which is a consequence of superfluidity and Bose-Einstein condensation. The measured thermodynamic quantities are compared to mean-field predictions available for the interacting Bose gas. The limits of applicability of the local density approximation near the critical point are also discussed, focusing on the behavior of the isothermal compressibility.