Production of optically trapped ${}^{87}\mathrm{RbCs}$ Feshbach molecules

We report the production of ${}^{87}\mathrm{RbCs}$ Feshbach molecules in a crossed-beam dipole trap. A mixture of ${}^{87}\mathrm{Rb}$ and ${}^{133}\mathrm{Cs}$ is cooled close to quantum degeneracy before an interspecies Feshbach resonance at 197 G is used to associate up to $\sim 5000$ molecules with a temperature of $\sim 300$ nK. The molecules are confined in the dipole trap with a lifetime of 0.21(1) s, long enough for future experiments exploring optical transfer to the absolute ground state. We have measured the magnetic moment of the Feshbach molecules in a magnetic bias field range between 181 and 185 G to demonstrate the ability to control the character of the molecular state. In addition, we have performed Feshbach spectroscopy in a field range from 0 to 1200 G and located three previously unobserved resonances at high magnetic fields.

Figure 1

(a) The intraspecies scattering length of ${}^{133}\mathrm{Cs}$ in the $(f,m_f)=(3,+3)$ state (black) and ${}^{87}\mathrm{Rb}$ in the $(1,+1)$ state (gray), calculated using the $s$, $d$, and $g$ basis functions for ${}^{133}\mathrm{Cs}$ and $s$ and $d$ basis functions for ${}^{87}\mathrm{Rb}$ versus magnetic field. (b) Upper panel: the interspecies scattering length between ${}^{87}\mathrm{Rb}$ and ${}^{133}\mathrm{Cs}$ in the same spin states as in (a), calculated using the $s$ and $d$ basis functions, versus magnetic field. The gray shaded area marks the range relevant to the magnetoassociation discussed in Sec. 3 and shown in Fig. 3. Lower panel: the calculated weakly bound molecular states arising from $L=0$ ($s$ states). The bound-state energies are plotted relative to the energy of the lowest hyperfine state of ${}^{87}\mathrm{Rb}$ +${}^{133}\mathrm{Cs}$, that is, the $(1,+1)+(3,+3)$ hyperfine level. All the bound states shown are for $M_{\mathrm{tot}}=4$, corresponding to $s$-wave scattering in the lowest channel.

Figure 2

Interspecies Feshbach resonances measured at (a) 790.2(2) G and (b) 1115.2(2) G. The ${}^{133}\mathrm{Cs}$ atom number shows a minimum and a maximum for each resonance. The minima define the resonance positions, while experimental widths are determined by the difference between the positions of the minima and maxima. Lorentzian fits to specific ranges of the results determine the positions. Gray shaded regions indicate the uncertainty in each position. Error bars show the standard deviations for multiple control shots at specific magnetic fields.

Figure 3

The magnetoassociation sequence. The interspecies Fesh-bach resonances at (a) 181.55(5) G and (b) 197.10(3) G detected through loss in the ${}^{133}\mathrm{Cs}$ atom number as described in Sec. 2. (c) Upper panel: the interspecies scattering length between ${}^{87}\mathrm{Rb}$ and ${}^{133}\mathrm{Cs}$ in the relevant magnetic field range. The gray shaded areas mark the field ranges shown in (a) and (b). Lower panel: the weakly bound molecular states relevant to the magnetoassociation sequence calculated using the $s$ and $d$ basis functions as discussed in the text. Also shown are the magnetic moments for each bound state. Molecules are produced at the Feshbach resonance at 197.10(3) G and then transferred into the $|-2(1,3)d(0,3)\rangle$ state at 181 G following the path shown by the solid black line.

Figure 4

The experimental sequence for the creation, Stern-Gerlach separation, and detection of Feshbach molecules. An ultracold atomic mixture is initially created by evaporation in the dipole trap at a bias field of 22 G. Subsequently, the timing sequences shown for the bias field, magnetic field gradient, and laser power in each beam of the crossed dipole trap are applied. The horizontal dotted line indicates the position of the Feshbach resonance at 197.10(3) G used for magnetoassociation. The dashed lines show the changes to routine implemented to trap the atoms in the dipole trap. The hold time $\tau$ in the dipole trap is varied to measure the lifetime of the molecules.

Figure 5

Optimizing the production of Feshbach molecules by changing the composition of the initial ultracold atomic mixture. (a) Atom number and (b) peak phase-space density for ${}^{87}\mathrm{Rb}$ (closed squares) and ${}^{133}\mathrm{Cs}$ (open squares) at the end of a fixed evaporation sequence as a function of the number of ${}^{133}\mathrm{Cs}$ atoms loaded into the magneto-optical trap. (c) The corresponding number of molecules produced by magnetoassociation normalized to the peak number ($\sim 3000$ molecules in this case). The inset shows the geometric mean of the ${}^{87}\mathrm{Rb}$ and ${}^{133}\mathrm{Cs}$ peak phase-space densities. A strong correlation between the molecule conversion efficiency and the mean phase-space density is observed.

Figure 6

Lifetime of ${}^{87}\mathrm{RbCs}$ molecules in the $|-2(1,3)d(0,3)\rangle$ state at 181 G held in the optical dipole trap. A magnetic field gradient of 44 G/cm is applied to levitate the molecules and the power in each beam of the dipole trap is 100 mW. Under these conditions, there is no trapping potential for the atoms. The solid line shows an exponential fit to the results, which yields a lifetime of 0.21(1) s.

Figure 7

Magnetic moment of the ${}^{87}\mathrm{RbCs}$ molecules as a function of the magnetic bias field. The experimental points are determined by finding the magnetic field gradient at which the molecules are levitated. Note the measurements are restricted to magnetic moments in the high-field-seeking region due to the current coil geometry in the experiment. The solid line is the theoretical prediction for the molecular states following the magnetoassociation path shown in Fig. 3.