Precision Measurements of Collective Oscillations in the BEC-BCS Crossover

We report on precision measurements of the frequency of the radial compression mode in a strongly interacting, optically trapped Fermi gas of ${}^6\mathrm{Li}$ atoms. Our results allow for a test of theoretical predictions for the equation of state in the BEC-BCS crossover. We confirm recent quantum Monte Carlo results and rule out simple mean-field BCS theory. Our results show the long-sought beyond-mean-field effects in the strongly interacting Bose-Einstein condensation (BEC) regime.

Figure 1

Radial sloshing observed at a trap power of 540 mW and $B=735\mathrm{G}$ ($1/k_{F}a=1.55$). The two-dimensional center-of-mass motion is represented in a coordinate system ($x^{\prime }$, $y^{\prime }$) rotated by 45° with respect to the principal axes of the trap. The beat signal between the two sloshing eigenmodes demonstrates the ellipticity of the trap with the two eigenfrequencies ${\omega }_x/2\pi =570\mathrm{Hz}$ and ${\omega }_y/2\pi =608\mathrm{Hz}$ (ellipticity $ϵ=0.066$).

Figure 2

Radial compression oscillation observed for the same conditions as the sloshing mode data in Fig. 1. The radial width is determined by averaging the horizontal and vertical Thomas-Fermi radii after expansion. Here we obtain ${\omega }_c/2\pi =1185\mathrm{Hz}$.

Figure 3

Normalized compression mode frequency $f_c$ versus interaction parameter $1/k_{F}a$. The experimental data include the small corrections for trap ellipticity and anharmonicity and can thus be directly compared to theory in the limit of an elongated harmonic trap with cylindrical symmetry. The open and closed circles refer to the measurements listed in Table  for ${\omega }_{\perp }/2\pi \approx 290\mathrm{Hz}$ and 590 Hz, respectively. The error bars indicate the typical scatter of the data points. The filled triangle shows a zero-temperature extrapolation of the measurements displayed in Fig. 4. The theory curves refer to mean-field BCS theory (lower curve) and QMC calculations (upper curve) and correspond to the data presented in Ref. 19. The horizontal dashed lines indicate the values for the BEC limit ($f_c=2$) and the unitarity limit ($f_c=\sqrt{10/3}=1.826$).

Figure 4

Normalized compression mode frequency $f_c$ versus damping rate for $1/k_{F}a=0.94$ ($U_0=7.3\mu \mathrm{K}$). The error bars represent $1\sigma$ fit uncertainties. The dashed lines indicate the zero-temperature values predicted by QMC calculations (upper line) and mean-field BCS theory (lower line).