Creation of ultracold heteronuclear p-wave Feshbach molecules

TL;DR

This work demonstrates the creation of optically trapped ultracold heteronuclear $p$-wave Feshbach molecules in a $^{23}$Na-$^{87}$Rb mixture by thoroughly characterizing interspecies $p$-wave FRs near $B \approx 284\ \mathrm{G}$ and employing magnetoassociation to form NaRb FMs in both mixed and pure angular-momentum states. Binding energies and resonance parameters are extracted from magnetic-field modulation and loss measurements and are compared with coupled-channel calculations, yielding a consistent determination of the open–closed channel magnetic moment difference $\delta \mu_b$. The authors report pure and mixed $p$-wave NaRb FMs with lifetimes up to tens of milliseconds after residual atoms are removed (e.g., $12(3)\ \mathrm{ms}$ for pure samples and $0.8(1)\ \mathrm{ms}$ in atom–molecule mixtures, with longer lifetimes like $23.5(1)\ \mathrm{ms}$ for a specific state), illustrating the impact of collisional losses and the feasibility of subsequent Raman transfer to the ground state. This work establishes a platform for tunable high-partial-wave interactions in heteronuclear ultracold gases and motivates further studies of low-dimensional loss suppression and nonzero angular-momentum molecular physics.

Abstract

We report the creation of optically trapped ultracold heteronuclear p-wave Feshbach molecules in a mixture of 23Na and 87Rb atoms. With loss spectroscopy and binding energy measurements, we systematically characterize the interspecies p-wave Feshbach resonances near 284 G. Leveraging this understanding, we use magneto-association to form p-wave NaRb Feshbach molecules, producing both pure samples and mixtures of molecules in different angular momentum states. Additionally, we investigate the inelastic loss of these molecules, primarily influenced by atom-molecule and molecule-molecule collisions. Our results represent a significant step toward realizing tunable p-wave interactions in heteronuclear ultracold systems and provide a foundation for exploring non-zero angular momentum molecules.

Figures (6)

• Figure 1: Temperature dependent atom loss spectra near the 284 G $p$-wave FRs. (a) Remaining fractional Na (top) and Rb (bottom) numbers as a function of magnetic field after a 50 ms holding time for a thermal mixture at 2.07 $\mu$K. (b) The same loss measurement for a double BEC sample. For the two peaks of the $m_f = 2$ resonance (left), the holding time is 25 ms, while for the two peaks of the $m_f = 1$ resonance (right), a longer holding time of 120 ms is used. The faster losses observed for the $m_f = 2$ resonance in both (a) and (b) indicate that the coupling strength of this resonance is stronger than that of the $m_f = 1$ resonance. (c) Resonance positions $B_0$ as a function of sample temperature $T$ for the $(m_f = 1, m_l = 1)$ (top) and $(1,0)$ (bottom) peaks. The separation between the two $m_f = 2$ resonances is approximately 40 mG and they overlap at temperatures above 700 nK. The orange lines are linear fits to the slopes.
• Figure 2: Binding energy measurement by magnetic field modulation. (a) Atom loss versus the modulation frequency $\nu$ at 285.039 G for probing the $(1,0)$ resonance. (b) Cloud size versus $\nu$ at 284.884 G for probing the quasi-bound states associated with the $(1,1)$ resonance. (c) The measured binding energy $E_b$ for $(1,1)$ (red circles) and $(1,0)$ (blue circles) resonances. (d), (e) are similar loss and heating measurements for the $m_f = 2$ manifold, respectively. The $E_b$ difference between the two resonances is small but still resolvable. (f) shows the measured $E_b$ for $(2,-1\&0)$ (red circles) and $(2,1)$ (blue circles) resonances. The solid curves in (a), (b), (d), and (e) are fits to Gaussian convoluted with Boltzmann function for extracting $E_b$ (marked by the vertical dashed lines). The solid lines in (c) and (f) are linear fits to determine the magnetic dipole moments of the FMs relative to the atoms (the results are summarized in Table \ref{['tab:p-wave']}).
• Figure 3: First signals of $p$-wave NaRb FMs created via MA. (a) The image in the inset shows the signature of FMs (top small cloud) observed after separating them from residual atoms (bottom cloud) with a magnetic field gradient. The lifetime of the FMs in the presence of residual atoms is only 0.8(1) ms due to fast atom-molecule collisions. (b) After removal of the residual atoms, the lifetime of the pure FMs is extended to 12(3) ms. The FMs, created by sweeping the magnetic field across all resonances, are distributed among $(2,-1\&0)$ and $(2,1)$ states. The red solid curves are exponential fits for extracting the lifetimes.
• Figure 4: Creation of pure $(2, 1)$ FMs. (a) $(2, -1\&0)$ and $(2, 1)$ FMs can be distinguished by the significantly different amount of heating of PD and MD during high-field imaging (see text for details). The red and blue dashed lines represent the positions of the $(2, -1\&0)$ and $(2, 1)$ resonances, respectively. The state of the FMs is determined by the $B$ field endpoint of the MA process. The quench following MA is sufficiently rapid to prevent additional association. (b) The measured lifetime of the pure $(2, 1)$ FMs is 23.5(1) ms and is likely limited by excitation from the trap laser. The endpoint of the MA process is 284.056 G, which lies between the two resonances within region (ii).
• Figure 3 S1: Calculated resonances as a function of relative kinetic energies between two atoms. The solid lines are linear fits, and the slopes are used to derive the inverse of the magnetic moment difference $\delta \mu_b^{\mathrm{th}}$ between the open and closed channels. The resulting $\delta \mu_b^{\mathrm{th}}$ values are summarized in Table 1 of the main text.