Critical Temperature and Condensate Fraction of a Fermion Pair Condensate

We report on measurements of the critical temperature and the temperature dependence of the condensate fraction for a fermion pair condensate of ${}^6\mathrm{Li}$ atoms. Bragg spectroscopy is employed to determine the critical temperature and the condensate fraction after a fast magnetic field ramp to the molecular side of the Feshbach resonance. Our measurements reveal evidence of level off of the critical temperature and limiting behavior of condensate fraction near the unitarity limit.

Figure 1

Time sequence of the experiment. After evaporative cooling at various magnetic field $B_{\mathrm{evap}}$, the optical trap is tuned off at $t=0$. At the same time, the magnetic field is rapidly turned off to convert fermion pairs to tightly bound molecules. The Bragg pulse is applied at $t=500\mu \mathrm{s}$. After a 3-ms free fall, we ramped up the magnetic field across the Feshbach resonance to dissociate the molecules. Then, the magnetic field is again switched off to cross the Feshbach resonance nonadiabatically before taking absorption images [30].

Figure 2

Bragg diffraction spectroscopy. Molecules slightly below $T_c$ without (a) and with (b) the zero momentum component that is diffracted by the Bragg pulse. The curves represent the radially integrated density profiles, and the insets show the two-dimensional images. (c) The number of diffracted molecules at the Bragg resonance. $T_c$ is identified with the point (indicated by the arrow) at which the slope changes. (d) The Bragg spectrum of strongly interacting molecules at 780 G. The condensate fraction and temperature are deduced from this spectrum (see text).

Figure 3

Temperature dependence of the condensate fraction. The condensate fraction is plotted against $T/T_{\mathrm{F}}$, where $T_{\mathrm{F}}$ is the Fermi temperature of a harmonically trapped system. Dotted lines show guides to the eye. The solid curve shows the condensate fraction of noninteracting bosons in a harmonic trap. The vertical error bars involve statistical and systematic errors, the latter arising from possible inelastic collisions during TOF after projection [34]. The inset shows the condensate fraction at 760 G obtained from the Bragg spectroscopy (filled squares) and from fitting the profile after projection with a Thomas-Fermi distribution for the condensate and a Gaussian distribution for the thermal component (open squares). The two sets of data agree within experimental accuracy.

Figure 4

$T_c/T_{\mathrm{F}}$ versus dimensionless interaction parameter $(k_{\mathrm{F}}a{)}^{-1}$. Filled circles show $T_c$ determined by the BE distribution, and open circles show $T_c$ determined by the MB distribution. The solid curve shows the theoretical prediction of weakly interacting bosons in a harmonic trap [32], where we assume that the molecular scattering length is given by 0.6 times the atomic scattering length [23].