Forming a Single Molecule by Magnetoassociation in an Optical Tweezer

We demonstrate the formation of a single NaCs molecule in an optical tweezer by magnetoassociation through an $s$-wave Feshbach resonance at 864.11(5) G. Starting from single atoms cooled to their motional ground states, we achieve conversion efficiencies of 47(1)%, and measure a molecular lifetime of 4.7(7) ms. By construction, the single molecules are predominantly [77(5)%] in the center-of-mass motional ground state of the tweezer. Furthermore, we produce a single $p$-wave molecule near 807 G by first preparing one of the atoms with one quantum of motional excitation. Our creation of a single weakly bound molecule in a designated internal state in the motional ground state of an optical tweezer is a crucial step towards coherent control of single molecules in optical tweezer arrays.

Figure 1

Magnetoassociation at the $s$-wave resonance. (a) Schematic of magnetic field ramp and trap merge and separation sequence as a function of time. Solid (dashed) line indicates one-way molecule conversion (conversion back to atoms for molecule survival detection). Time spent for magnetoassociation is varied for different experiments; see text for details. (b) Determination of the $s$-wave resonance location. The magnetic field is ramped linearly from 866.5 G to the various magnetic fields at $1\mathrm{G}/\mathrm{ms}$. Lower panel: survival probabilities of Na (orange squares) and Cs (blue circles) when both species are loaded. The solid lines are fits to an error function, from which we extract the left and right asymptote values and resonance location. Vertical dashed line indicates resonance location determined from the fit. Upper panel: same experimental run with initial one-body loading. Horizontal dotted lines are the mean values for each species.

Figure 2

Molecule formation and dissociation efficiencies. (a) Purple circles indicate $\mathrm{Na}+\mathrm{Cs}$ joint survival probability after magnetoassociation. The magnetic field is ramped linearly from 866 to 863.9 G at different rates. Green squares indicate $\mathrm{Na}+\mathrm{Cs}$ joint survival probability with an additional reverse magnetic field ramp at the same rate after molecule formation. The solid lines are best-fit curves and the gray shaded areas indicate the errors on the fit. See text for fit details. (b) Lifetime of Feshbach molecule held at $B-B_{\mathrm{res}}=-0.3\mathrm{G}$ and trap intensity $81\mathrm{kW}/{\mathrm{cm}}^2$. Solid line is best fit to an exponential decay.

Figure 3

Characterization of $s$-wave Feshbach molecule lifetime. (a) Dependence on trap intensity. The trap is adiabatically ramped to and held at different intensities after magnetoassociation at $B-B_{\mathrm{res}}=-0.3\mathrm{G}$. The line is a best fit to inverse scaling. (b) Dependence on magnetic field. The field is ramped to different values during magnetoassociation while the trap intensity is fixed at $81\mathrm{kW}/{\mathrm{cm}}^2$. The solid line is the mean value. (c) The negative binding energy $-E_b$ (dashed line, left axis) and closed-channel fraction $Z$ (solid line, right axis) from coupled-channel bound-state calculations as a function of magnetic field. See text for details.

Figure 4

$p$-wave FR spectroscopy by FR-enhanced photoassociation. The atoms are held at a fixed magnetic field in an intense tweezer. Blue (orange) line shows spectrum with (without) motional excitation of Na. Shaded areas indicate error bars. The arrow indicates the resonance used for magnetoassociation in the inset. Inset: $p$-wave Feshbach molecule formation. The magnetic field is ramped linearly from 807.6 G to the various magnetic fields at $0.02\mathrm{G}/\mathrm{ms}$. Same color scheme as main figure. Blue (orange) curve is fit to error function (mean value across the range).