Local Observation of Pair Condensation in a Fermi Gas at Unitarity

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Local Observation of Pair Condensation in a Fermi Gas at Unitarity

M. G. Lingham, K. Fenech, S. Hoinka, and C. J. Vale

Phys. Rev. Lett. 112, 100404 – Published 13 March 2014

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.

Received 18 November 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.100404

Authors & Affiliations

M. G. Lingham, K. Fenech, S. Hoinka, and C. J. Vale^*

Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne, Victoria 3122, Australia

^*To whom all correspondence should be addressed. cvale@swin.edu.au

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Vol. 112, Iss. 10 — 14 March 2014

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Images

Figure 1
(a) Experimental arrangement for measuring the Bragg response. Two laser beams with wave vectors ${\vec{k}}_{1}$ and ${\vec{k}}_{2}$ , intersecting at an angle of $2 θ = 84 °$ , produce a moving interference pattern that illuminates a trapped atom cloud. The long axis of the cloud is aligned along $z$ , and Bragg scattering imparts momentum along $x$ . (b),(c) Averaged optical density images ${OD}_{x, z}^{(ω)}$ of an atom cloud following (b) a relatively strong Bragg kick at a frequency of $ω = ω_{r} / 2$ and (c) no Bragg kick at $ω = 0$ . These images appear nearly identical due to the short ( $300 μ s$ ) time of flight; however, subtracting them (d) shows that atoms have been displaced from left to right. Another difference image is shown in (e) for two images obtained at Bragg frequencies of $ω_{r}$ and 0. The two difference images are themselves subtly different; (d) the atom displacement for $ω_{r} / 2$ is concentrated close to the center of the cloud, while (e) displacement for $ω_{r}$ is more diffuse, with greater response from the wings of the cloud. The viewing area of all images in (b)–(e) is $340 \times 510 μ m$ .
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Figure 2
Local (homogeneous) Bragg spectra of a unitary Fermi gas measured below (blue and green lines and circles) and above (orange and red lines and circles) the superfluid transition temperature $T_{c} = 0.167 T_{F}$ [7]. Local values of $T / T_{F}$ and $k / k_{F}$ contributing to each measurement are given in the text. Solid lines are a guide to the eye. Spectra below $T_{c}$ are dominated by a sharp feature at $ω_{r} / 2$ corresponding to pair scattering, while the spectra above $T_{c}$ show a rounder response peaked just below $ω_{r}$ corresponding to the continuum of single-particle excitations. Inset: Bulk response of a trapped unitary Fermi gas at a temperature of $T = 0.08 T_{F}^{B}$ (from Ref. [19]) which shows a weaker pairing signature at $ω_{r} / 2$ , as well as a broader peak centered near $ω_{r}$ , due to the averaging over a range of relative temperatures and wave vectors in an inhomogeneous trapped cloud.
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Figure 3
(a) False color image of the local (homogeneous) response $χ_{(k, ω_{r} / 2)}^{''}$ of a unitary Fermi gas as a function of the relative temperature $T / T_{F}$ and wave vector $k / k_{F}$ . The image was constructed by measuring the local response for a range of clouds prepared at different initial temperatures and binned according to temperature and wave vector. Dashed white lines show the temperatures and wave vectors spanned by individual (averaged) clouds. A rapid increase in the response is observed for temperatures $T / T_{F} < 0.2$ , due to the appearance of the pair condensate. (b) Local response versus relative temperature for wave vectors in the range $4.5 < k / k_{F} < 5.5$ , using data indicated by the grey shaded region in (a). This smaller range of momenta shows the sudden increase in the response below $T_{c} = 0.167 T_{F}$ [7] [solid brown lines in (a) and (b)]. Also shown (dashed black line) is the calculated response for an ideal gas at $ω_{r} / 2$ for $k = 5 k_{F}$ which shows the opposite temperature dependence to the data. Dash-dotted blue lines are straight line fits to the data over the temperature ranges $0.11 < T / T_{F} < 0.17$ and $0.2 < T / T_{F} < 0.6$ used to estimate the critical temperature.
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