Condensation of Pairs of Fermionic Atoms near a Feshbach Resonance

We have observed Bose-Einstein condensation of pairs of fermionic atoms in an ultracold ${}^6\mathrm{Li}$ gas at magnetic fields above a Feshbach resonance, where no stable ${}^6\mathrm{Li}_2$ molecules would exist in vacuum. We accurately determined the position of the resonance to be $822\pm 3\mathrm{G}$. Molecular Bose-Einstein condensates were detected after a fast magnetic field ramp, which transferred pairs of atoms at close distances into bound molecules. Condensate fractions as high as 80% were obtained. The large condensate fractions are interpreted in terms of preexisting molecules which are quasistable even above the two-body Feshbach resonance due to the presence of the degenerate Fermi gas.

Figure 1

Determination of the Feshbach resonance position. Shown is the onset of molecule dissociation when the magnetic field was slowly raised and then ramped down to zero field with a variable rate: Using a switch-off of the power supply at an initial rate of $30\mathrm{G}/\mu \mathrm{s}$ (crosses), a linear ramp to zero field of $100\mathrm{G}/\mathrm{ms}$ (circles), a linear ramp for 16 ms at $12.5\mathrm{G}/\mathrm{ms}$, followed by switch off (triangles). The identical threshold for the two lowest ramp rates determines the resonance position to be $822\pm 3\mathrm{G}$, marked by an arrow.

Figure 2

Emergence of a Bose-Einstein condensate of atom pairs as the temperature was lowered. Shown are column densities (after 6 ms of time of flight) of the fermion mixture after a rapid transfer ramp from 900 G for three different initial temperatures $T/T_F\approx 0.2$, 0.1 and 0.05, together with their axially integrated radial density profiles. The dashed line is a Gaussian fit to the thermal component. Condensate fractions are 0.0, 0.1, and 0.6. Each cloud consists of about $2\times {10}^6$ molecules. The field of view is $3\times 3\mathrm{mm}$.

Figure 3

Condensate fraction after the rapid transfer vs initial magnetic field, for different hold times at that field in the shallow trap ($P=25\mathrm{mW}$). Crosses: 2 ms hold time, after 500 ms ramp to 1000 G and 4 ms ramp to the desired field; squares and circles: 100 ms and 10 s hold time, after 500 ms ramp from 770 G. The reduction of the condensate fraction for long hold times far on the left side of the resonance is probably due to the rapidly increasing inelastic losses for the more tightly bound molecules [20, 23]. The lower condensate fraction at high field for long hold times is probably an effect of lower density since the number of atoms had decayed by a factor of 4 without change in temperature.

Figure 4

Condensate fraction for different temperatures as a function of magnetic field. The temperature of the molecular cloud was varied by stopping the evaporative cooling earlier and applying parametric heating before ramping to the final magnetic field. Temperatures are parametrized by the molecular condensate fraction $N_0/N$ at 820 G (open circles: 0.8; filled circles: 0.58; open squares: 0.51; filled squares: 0.34; “$+$”: 0.21; triangles: 0.08; “$\times$”: $<0.01$). The lowest temperature was realized in the shallow trap ($P=25\mathrm{mW}$); the higher temperatures required a deeper trap ($P=150\mathrm{mW}$).

Figure 5

Temperature and magnetic field ranges over which pair condensation was observed (using the same data as in Fig. 4). The right axis shows the range in $T/T_F$ (measured at 1025 G) which was covered. For high degeneracies, fitting $T/T_F$ was less reliable and we regard the condensate fraction as a superior “thermometer.” Note that for an isentropic crossover from a BEC to a Fermi sea, $T/T_F$ is approximately linearly related to the condensate fraction on the BEC side [24]. For our maximum densities the region where $k_F|a|\ge 1$ extends from about 710 G onward.