Conversion of an Atomic Fermi Gas to a Long-Lived Molecular Bose Gas

We have converted an ultracold Fermi gas of ${}^6\mathrm{L}\mathrm{i}$ atoms into an ultracold gas of ${}^6\mathrm{L}\mathrm{i}_2$ molecules by adiabatic passage through a Feshbach resonance. Approximately $1.5\times {10}^5$ molecules in the least-bound, $v=38$, vibrational level of the $X^1{\Sigma }_g^{+}$ singlet state are produced with an efficiency of 50%. The molecules remain confined in an optical trap for times of up to 1 s before we dissociate them by a reverse adiabatic sweep.

Figure 1

Coupled-channels calculation of the narrow Feshbach resonance between the two lowest Zeeman sublevels of ${}^6\mathrm{L}\mathrm{i}$. The scattering length is shown in units of the Bohr radius. The predicted location of the resonance is at a slightly higher field than observed (Figs. 2, 4).

Figure 2

Lifetime of an incoherent mixture of the two lowest Zeeman sublevels as a function of the static field strength. The field is calibrated to 0.05 G by the frequency of the resonance transition between the two sublevels. The lifetime here is defined as the time at which the total atom number has fallen to $1/e$ of its initial value. There are no detectable atoms at 543.25 G following the 1 s triangle wave which creates the incoherent mixture, but by monitoring the decay of atom signal following a short $\pi /2$ pulse instead, the lifetime is found to be less than 200 ms. The background lifetime of 13 s, shown by the light horizontal line, is mainly due to off-resonant scattering induced by the trap lasers.

Figure 3

Dependence of atom loss on inverse sweep rate. The field is ramped linearly from high to low field. The solid circles represent the average of 6–10 measurements and the error bars are the standard deviations of these measurements. The solid line is an exponential fit, giving a decay constant of $1.3\mathrm{m}\mathrm{s}/\mathrm{G}$.

Figure 4

Dependence of atom loss on final field. The field is ramped down from 549 G to various final fields. The inverse sweep rate, ${\dot{B}}^{-1}$, is greater than $12\mathrm{m}\mathrm{s}/\mathrm{G}$ for all of the data. The data points and error bars correspond to multiple averages, as in Fig. 3. The solid line is a fit to an empirical function (given in the text).

Figure 5

Measurement of the molecular lifetime. The field is ramped downward through the Feshbach resonance and back to the starting field. The time $\tau$ is defined as the interval between traversing the field $B_o$ on the downward sweep and again on the upward sweep. The inverse sweep rate is $3.5\mathrm{m}\mathrm{s}/\mathrm{G}$ and the starting field is 549 G. The field is ramped down to a final field, whose value depends on $\tau$, and immediately ramped back to the starting field. For the data point at 40 ms the final field is 538 G, while for $\tau =248\mathrm{m}\mathrm{s}$, the final field is 508 G, and so on. For the three points with the largest $\tau$, the field is ramped down to 369 G and held there for the required time before being brought back. Although we did not perform a systematic study of lifetime as a function of field, the molecular lifetime was observed to be field independent for the range of final fields used here. The data points and error bars are the averages and standard deviations, respectively, of 8 to 16 measurements.