Spin Susceptibility above the Superfluid Onset in Ultracold Fermi Gases

Ultracold atomic Fermi gases can be tuned to interact strongly, which produces a display of spectroscopic signatures above the superfluid transition reminiscent of the pseudogap in cuprates. However, the extent of the analogy can be questioned since many thermodynamic quantities in the low temperature spin-imbalanced normal state can be described successfully using Fermi liquid theory. Here we present spin susceptibility measurements across the interaction strength-temperature phase diagram using a novel radio frequency technique with ultracold ${}^6\mathrm{Li}$ gases. For all significant interaction strengths and at all temperatures we find the spin susceptibility is reduced compared to the equivalent value for a noninteracting Fermi gas. At unitarity, we can use the local density approximation to extract the integrated spin susceptibility for the uniform gas as a function of temperature, which at high temperatures is generally less than theoretically predicted. At low temperatures, our data lie within the range of theoretical predictions, although we can also describe the entire curve using a very simple one-parameter mean field model with monotonically increasing spin susceptibility.

Figure 1

Four closely related experiments with the same atomic cloud preparation but different rf procedures. (a)–(d) The first (second) subscript character on $\mathrm{\Delta }n$ denotes the direction of an adiabatic sweep onto (away from) resonance, where $B$ ($R$) represents blue (red) detuning. We hold the rf for 2 s on resonance between the sweeps. The rf procedure generates a spin difference leading to positive signal in (b) and (c) and negative signal in (a) and (d). (e) 1D profile along the $z$ axis of the trap from summing the net differential signal $(-\mathrm{\Delta }{n}_{BB}+\mathrm{\Delta }{n}_{RR}+\mathrm{\Delta }{n}_{\mathrm{BR}}-\mathrm{\Delta }{n}_{RB})/4$ over the $x$ direction with a $29\mu \mathrm{m}$ wide region centered on the atomic cloud. The data comes from a unitary gas at 210 nK ($T/T_F^t=0.27$).

Figure 2

Differential column density measured at (a) 40.0 mT where interaction is close to zero at 513 nK ($T/T_F^t=0.63$) and (b) 81.4 mT near the unitary point at 210 nK ($T/T_F^t=0.27$). The red dashed lines in (a) and (b) show the noninteracting susceptibility for a gas with the same density profile. In (b), the black solid line is from our mean field model.

Figure 3

Dimensionless integrated susceptibility $\overline{\chi }$. The acronyms “NSF” and “SF” stand, respectively, for experimental data with all nonsuperfluid and with superfluid at the center of the trap; “NI” is the noninteracting Fermi gas result, “MF” is our mean field model with $\alpha =1.61$. “Wla13,” “Ens12,” “Taj14,” and “Pal12” are theoretical results extracted from Refs. [28, 29, 32, 33], respectively, while “FL” is a Fermi liquid model extracted from Ref. [32]. Error bars are derived from the standard deviation of the measurements.

Figure 4

The trap-averaged spin susceptibility normalized to the zero-temperature noninteracting value for weak interactions and across the BEC-BCS crossover. The red dotted line shows the susceptibility of a noninteracting Fermi gas as a function of temperature. Error bars are derived from the standard deviation of many shots (for susceptibility) and from fitting uncertainty (for temperature). Solid curves are calculated using the measured density distribution and our mean field model under the local density approximation, with values of the fit parameter $\alpha$ given by 3.5, 1.5, 1.6, and 0.9 from top to bottom.