Formation of bosonic $^{23}$Na$^{41}$K Feshbach molecules

TL;DR

This work addresses the creation of ultracold bosonic $^{23}$Na$^{41}$K Feshbach molecules and paves the way for ground-state dipolar Bose gases. The authors implement radio-frequency association on a broad interspecies Feshbach resonance near $B_0=73.6$ G to produce over $10^4$ molecules from a mixed atomic gas, and map the molecular binding energy versus $B$, revealing a resonance width of $\Delta=5.1$ G. They also develop an extended rate-equation model that, with parameters tied to the association dynamics, quantitatively reproduces observed lifetimes, finding $1/e$ lifetimes up to $2.1$ ms in the presence of background Na and $6.9$ ms after Na removal. These results establish a robust platform for transferring to the rovibrational ground state via STIRAP and enable exploration of novel many-body phenomena in strongly dipolar Bose gases, including multilayer and extended Bose-Hubbard physics, with both bosonic and fermionic NaK isotopologues.

Abstract

Ultracold Feshbach molecules are a crucial intermediate step for the creation of quantum degenerate gases of strongly dipolar molecules. After coherent transfer to the rovibrational ground state, these dimers can realize stable dipolar gases with strong, tunable long-range interactions. Here, we report the creation of bosonic $^{23}$Na$^{41}$K Feshbach molecules by radio-frequency (RF) association. An RF pulse applied on the molecular side of an interspecies Feshbach resonance at 73.6(1)~G associates up to $1.1(1)\times10^4$ molecules from a thermal mixture of $^{23}$Na and $^{41}$K atoms. Measurements of the binding energy reveal a broad resonance width of 5.1(2)~G, facilitating robust control over interspecies interactions. The molecule lifetime in the presence of background atoms exceeds 2~ms, extending to 7~ms after removal of $^{23}$Na. These results constitute a key step toward the production of ultracold $^{23}$Na$^{41}$K ground state molecules for the exploration of novel many-body phenomena in strongly dipolar Bose gases.

Figures (6)

• Figure 1: Formation of bosonic $^{23}$Na$^{41}$K Feshbach molecules. (a) Schematic illustration of RF association from free atoms to weakly bound Feshbach molecules. (b) Arrival spectroscopy of Feshbach molecules at $B{=}72.3$ G. Gray circles show the number of $^{41}$K $\vert$1,1$\rangle$ atoms; the dashed line marks the atomic spin-flip transition at 35.686(1) MHz. Blue circles show the associated molecule number; the dash-dotted line indicates the fitted molecular resonance at 35.791(1) MHz. The inset shows an absorption image of molecules taken in trap on the $^{41}$K imaging transition. (c) Number of associated molecules versus RF frequency at $B{=}72.4$ G for mixture temperatures of 0.26(10) $\mu$K, 0.43(21) $\mu$K, and 0.73(6) $\mu$K. Fits to the asymmetric free-to-bound lineshape yield temperatures of 0.27(3) $\mu$K, 0.46(6) $\mu$K, and 0.84(12) $\mu$K, respectively. Error bars denote the standard error of the mean.
• Figure 2: Molecular binding energy versus magnetic field. Blue circles and white squares denote measurements from arrival spectroscopy and atom-loss spectroscopy, respectively. The solid line is a fit to the asymptotic binding energy model weighted by the errors. The lower right inset shows the arrival spectrum at $B$ = 72.3 G, yielding $E_{b}$/$h$ = 105(1) kHz. The upper left inset shows representative atom-loss spectra for Na (gray squares) and K (white squares), giving $E_{b}$/$h$ = 448(1) kHz. Error bars denote the standard error of the mean.
• Figure 3: Characterization of molecule association. (a) Number of molecules as a function of temperature. The gray-shaded area indicates the temperature range below the critical temperature of $^{41}$K. The temperatures are extracted from the thermal wings of the $^{41}$K clouds. (b) Molecule number versus RF pulse duration. The maximum number is reached near $\sim$3.4 ms, after which the loss becomes dominant over the molecule association. (c) Number of molecules created at various mixture ratios. To ensure an adequate dynamic range for these measurements, the typical temperature is kept at $\sim$0.5 $\mu$K. The solid lines represent numerical solutions of the rate equations fitted to the experimental data. The dashed lines are $\pm1\sigma$ confidence intervals, and the error bars denote the standard error of the mean.
• Figure 4: Lifetime measurement of $^{23}$Na$^{41}$K Feshbach molecules. (a) Gray circles show the number of molecules as a function of hold time with $^{23}$Na prepared in the $\vert1,1\rangle$ state. Blue squares show the number of molecules with $^{23}$Na removed. The solid lines are simulations obtained from the rate-equation model using the extracted loss coefficients. (b) Molecular lifetime with $^{23}$Na atoms transferred to the $\vert1,0\rangle$ state. Error bars in (a) and (b) represent the standard error of the mean. (c) Measured molecular lifetimes as a function of magnetic field. The error bars of the lifetimes represent 95$\%$ confidence intervals.
• Figure 5: Schematic diagram of the experimental sequence. $B_\mathrm{prep}$ denotes the magnetic field where the mixture is initially prepared before the ramp. $B_\mathrm{Int}$ is the intermediate magnetic field for the LZ sweep of $^{41}$K atoms. $B$ represents the magnetic field at which molecules are RF associated, set below the Feshbach resonance position $B_\mathrm{0}$ = 73.6(1) G. The diagram is not to scale.