Production Efficiency of Ultracold Feshbach Molecules in Bosonic and Fermionic Systems

We investigate the production efficiency of ultracold molecules in bosonic ${}^{85}\mathrm{Rb}$ and fermionic ${}^{40}\mathrm{K}$ when the magnetic field is swept across a Feshbach resonance. For adiabatic sweeps of the magnetic field, our novel model shows that the conversion efficiency of both species is solely determined by the phase space density of the atomic cloud, in contrast with a number of theoretical predictions. In the nonadiabatic regime our measurements of the ${}^{85}\mathrm{Rb}$ molecule conversion efficiency follow a Landau-Zener model.

Figure 1

(a) Molecular conversion in ${}^{85}\mathrm{Rb}$ as a function of the inverse magnetic field sweep rate. The initial conditions of the atomic cloud were $N=87000$, $T=40.6\mathrm{nK}$, and $n=1.3\times {10}^{11}{\mathrm{cm}}^{-3}$. The solid line is a fit to Eq. (1). (b) Initial mean density of the atomic cloud ($n$) divided by $1/e$ sweep rate (${\dot{B}}_{1/e}$) and plotted against mean density. The dashed line shows the best fit of Eq. (2) to the data. For the four low density points, the vertical error bars are dominated by the uncertainty in fitting ${\dot{B}}_{1/e}$. At higher densities, the cloud experienced significant heating during the ramps across the resonance; hence the density of the final point has significant uncertainty. This heating limited the maximum density used.

Figure 2

Molecule conversion efficiency in ${}^{85}\mathrm{Rb}$ as a function of peak phase space density (circles). The solid line shows a simulation based on our conversion theory, fitted to the data with a single pairing parameter ${\gamma }_b=0.44(3)$ [Eq. (3)]. The dashed lines indicate the uncertainty in ${\gamma }_b$. Inset: molecule conversion efficiency in ${}^{40}\mathrm{K}$ as a function of peak phase space density (for full data range, see Fig. 3). The best-fit simulation based on our conversion theory is shown as a solid line, with the uncertainty indicated by dotted lines.

Figure 3

Molecule conversion efficiency in ${}^{40}\mathrm{K}$ as a function of $T/T_F$. (Note that $T/T_F$ uniquely determines the phase space density of a fermionic cloud.) The initial clouds have mean densities for each spin state ranging from $1\times {10}^{12}$ to $2\times {10}^{13}{\mathrm{cm}}^{-3}$ and 52(2)% of the atoms are in the $m_f=-7/2$ state. The data are fitted with the same conversion model as for ${}^{85}\mathrm{Rb}$. The best-fit curve has a pairing parameter of 0.38(4). The dotted lines indicate the uncertainty on this result. Note that conversion efficiencies far greater than 50% are measured.