Observation of broad $p$-wave Feshbach resonances in ultracold ${}^{85}\mathrm{Rb}-{}^{87}\mathrm{Rb}$ mixtures

We observe Feshbach resonances in ultracold mixtures of ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ atoms in the ${}^{85}\mathrm{Rb}|2,+2\rangle +{}^{87}\mathrm{Rb}|1,+1\rangle$ and ${}^{85}\mathrm{Rb}|2,-2\rangle +{}^{87}\mathrm{Rb}|1,-1\rangle$ scattering channels. The positions and properties of the resonances are predicted and characterized using the semianalytic multichannel quantum-defect theory by Gao. Of particular interest, a number of broad entrance-channel-dominated $p-\mathrm{wave}$ resonances are identified, implicating exciting opportunities for studying a variety of $p-\mathrm{wave}$ interaction–dominated physics.

Figure 1

The essence of MQDT based on the analytic solutions to the Schrödinger equation with a $-1/R^6$ potential [32]. The real molecular potentials are replaced by a single pure $-\frac{C_6}{R^6}+\frac{{\hslash }^2}{2\mu }\frac{l(l+1)}{R^2}$ potential (extended from the real long-range potential) cut off by a sharp infinite repulsive wall (dashed line) at $R_W$, which accounts for the multichannel effect from short ranges. The effective “quantum defect” $R_W\left(\epsilon \right)$ depends sensitively on the scattering energy $\epsilon$ for a “narrow” FR.

Figure 2

The essential elements of our experimental setup. ${}^{87}\mathrm{Rb}$ and ${}^{85}\mathrm{Rb}$ atoms are loaded into a magneto-optical trap (MOT) from a common Zeeman slower. A 1064-nm optical dipole trap is used to confine the atoms for FR loss spectroscopy. A single bichromatic imaging beam overlapping with one of the MOT beams is used to probe the atom numbers of both species in sequence.

Figure 3

Feshbach spectrum for the ${}^{85}\mathrm{Rb}|2,-2\rangle +{}^{87}\mathrm{Rb}|1,-1\rangle$ channel. Top panel: The remaining fraction of ${}^{85}\mathrm{Rb}$ atoms normalized to the off-resonant values after 400–1000 ms interaction with ${}^{87}\mathrm{Rb}$ at $\sim 2\mu \mathrm{K}$ is shown as a function of magnetic field. Every data point is averaged over five runs. Error bars denoting typical standard deviations are shown at specific magnetic fields for illustrative purposes. We fit the data using a multipeak Gaussian profile to get the eye-guiding line (red solid line). Bottom panel: The $s-\mathrm{wave}$ (blue solid line) and $p-\mathrm{wave}$ (red dashed line) RGSL, ${\tilde{a}}_l\left(B\right)/{\overline{a}}_l$, computed using the semianalytic MQDT.

Figure 4

The same as in Fig. 3 but for the ${}^{85}\mathrm{Rb}|2,+2\rangle +{}^{87}\mathrm{Rb}|1,+1\rangle$ channel after 600-ms interaction time.

Figure 5

Temperature dependence of the broadest $p-\mathrm{wave}$ resonance observed in the ${}^{85}\mathrm{Rb}|2,+2\rangle +{}^{87}\mathrm{Rb}|1,+1\rangle$ channel ($J$ in Fig. 4). The loss feature narrows, and its left edge becomes steeper as the temperature of the mixture is lowered from $\sim 2\mu \mathrm{K}$ (red diamonds) to $\sim 400\mathrm{nK}$ (black circles). The solid lines represents the fits to the data using an asymmetric double sigmoid function to account for the asymmetric line shapes.

Figure 6

A clear doublet splitting emerges for the 823-G $p-\mathrm{wave}$ FR in Fig. 4 at a temperature of $\sim 260\mathrm{nK}$.