Formation of Ultracold Molecules by Merging Optical Tweezers

We demonstrate the formation of a single RbCs molecule during the merging of two optical tweezers, one containing a single Rb atom and the other a single Cs atom. Both atoms are initially predominantly in the motional ground states of their respective tweezers. We confirm molecule formation and establish the state of the molecule formed by measuring its binding energy. We find that the probability of molecule formation can be controlled by tuning the confinement of the traps during the merging process, in good agreement with coupled-channel calculations. We show that the conversion efficiency from atoms to molecules using this technique is comparable to magnetoassociation.

Figure 1

(a) Energy levels for the $\mathrm{Rb}+\mathrm{Cs}$ system as a function of separation between two spherically symmetric optical tweezers with confinement length ${\beta }_{\mathrm{rel}}=40\mathrm{nm}$ for relative motion. The red dashed line shows the harmonic trapping experienced by the molecule in the absence of tunneling. An avoided crossing between the molecular and atom-pair states at $\mathrm{\Delta }{z}_{\mathrm{X}}$, expanded in the inset, allows mergoassociation. (b) Cartoon of the interaction energy as a function of interatomic distance when $\mathrm{\Delta }z=\mathrm{\Delta }{z}_{\mathrm{X}}$. (c) The effective matrix element $\mathrm{\Omega }$ between the lowest-energy atom-pair and molecular states as a function of ${\beta }_{\mathrm{rel}}$.

Figure 2

(a) Sequence for molecule formation and detection. (b) The energy of weakly bound RbCs molecules (relative to threshold) as a function of magnetic field, $B_{\mathrm{spec}}$. The points show the measured energies of molecules produced when merging the traps at 205 G (red circles) and below 197 G (blue squares). The purple dashed line indicates the field used for spectroscopy in Fig. 3 from states D and G. Black lines show state energies calculated from the RbCs molecular potential of Ref. [43]. The inset shows the avoided crossing below the resonance near 197 G and highlights the paths for mergoassociation (red arrow) and magnetoassociation (blue arrow) [61].

Figure 3

(a) Spectroscopic identification of molecules formed by mergoassociation (red circles) and magnetoassociation (blue squares) for confinement lengths ${\beta }_{\mathrm{rel}}^{\mathrm{X}}$ at the avoided crossing of (i) 37.7(8), (ii) 47(1), and (iii) 77(2) nm. Light-induced loss is measured as a function of the detuning ${\mathrm{\Delta }}_{\text{thresh}}$ from the transition between the atomic threshold and $({{}^3\mathrm{\Pi }}_1,v^{\prime }=29,J^{\prime }=1)$ at 181 G. (b) The probability of light-induced loss of molecules formed by mergoassociation (red circles) and magnetoassociation (blue squares) as a function of ${\beta }_{\mathrm{rel}}^{\mathrm{X}}$. The theory curves show the calculated Landau-Zener probabilities scaled to match the light-induced loss. The shaded regions indicate the experimental uncertainty in the merging speed.

Figure 4

Microwave spectroscopy of RbCs molecules produced by mergoassociation at $B=4.78\mathrm{G}$. The probability $P_{11}$ of detecting both a Rb and Cs atom at the end of the sequence is shown as a function of the microwave detuning from the transition $(1,1)\to (2,2)$ in atomic Rb for strong (red circles) and weak (blue squares) confinement during merging: ${\beta }_{\mathrm{rel}}^{\mathrm{X}}=39.4(9)$ and 55(1) nm, respectively. When a molecule is formed, we observe the molecular transition $\mathrm{S}\to {\mathrm{S}}^{\prime }$ at detuning 35(2) kHz. The inset shows the energy-level structure of the relevant states with atomic (molecular) states indicated with solid (dashed) lines.