Determination of the Superfluid Gap in Atomic Fermi Gases by Quasiparticle Spectroscopy

We present majority and minority radio frequency spectra of strongly interacting imbalanced Fermi gases of ${}^6\mathrm{Li}$. We observed a smooth evolution in the nature of pairing correlations from pairing in the superfluid region to polaron binding in the highly polarized normal region. The imbalance induces quasiparticles in the superfluid region even at very low temperature. This leads to a local bimodal spectral response, which allowed us to determine the superfluid gap $\Delta$ and the Hartree energy $U$.

Figure 1

Tomographically reconstructed rf spectra for various regions of the atomic sample at unitarity. (a) Balanced superfluid, (b) polarized superfluid, (c) moderately polarized transition region, and (d) highly polarized normal region. The panel on the left shows a phase-contrast image of the atomic cloud before rf excitation. The positions of the spectra (a) to (d) are marked in the phase-contrast image and by the arrows in Fig. 2. Red: Majority spectrum, blue: Minority spectrum. Local polarizations ${\sigma }_{\mathrm{loc}}$ and local temperature $T/T_F$, respectively: (a) $-0.04(2)$, 0.05(1); (b) 0.03(1), 0.06(1); (c) 0.19(1), 0.06(2); (d) 0.64(4), 0.10(2). The negative value in (a) implies that the local polarization as inferred from phase-contrast imaging underestimates ${\sigma }_{\mathrm{loc}}$ by up to 0.05.

Figure 2

Spatially resolved rf spectra of an imbalanced Fermi gas at unitarity. (a) The right half shows the majority spectra as a function of position in the trap expressed in terms of the majority Fermi radius $R_{\uparrow }$, the left half displays the minority spectra. The superfluid to normal transition region is marked by the gray vertical lines. The local polarization ${\sigma }_{\mathrm{loc}}$ is given by the short-dashed red line. The error bars are the standard deviation of the mean value. The arrows indicate the position of the four spectra shown in Fig. 1. The image is a bilinear interpolation of 2500 data points, each plotted data point in the image is the average of three measured data points. The spatial resolution of the image is $0.045·R_{\uparrow }$.

Figure 3

Creation and spectroscopy of quasiparticles. (a) Population imbalance thermally generates quasiparticles even at low temperatures comparable to $\Delta -{\mu }_{\uparrow }$. ${\mu }_{\uparrow }$ is the chemical potential of the majority component. (b) The rf spectrum consists of a quasiparticle peak at negative frequencies and the pair dissociation spectrum at positive frequencies (dotted line). On resonance, the Hartree contribution $U$ acts as an effective attraction and hence shifts the entire spectrum into the positive direction.

Figure 4

(a) Normalized peak positions of pairing peaks and quasiparticle peak at unitarity as a function of position in the trap. The SF-N boundary (cusp in column density difference [19]) is marked by the dashed vertical lines. The arrow indicates the limit of low quasiparticle population relevant for (b). Majority: blue open squares (pairing peak) and solid black circles (quasiparticle peak). Minority: solid red triangles. (b) Pairing peak and quasiparticle peak positions as a function of the local interaction strength $1/k_{F}a$ in the limit of small local imbalance [see arrow in (a)]. Pairing peak: solid circles; quasiparticles peaks: open circles.