Short-range photoassociation of LiRb

We have observed short-range photoassociation of ${}^7\mathrm{Li}{}^{85}\mathrm{Rb}$ to the two lowest vibrational states of the $d{}^3\mathrm{\Pi }$ potential. We have also observed several $a^3{\mathrm{\Sigma }}^{+}$ vibrational levels with generation rates between $\sim {10}^2$ and $\sim {10}^3$ molecules per second, resulting from the spontaneous decay of these $d{}^3\mathrm{\Pi }$ molecules. We observe an alternation of the peak heights in the rotational photoassociation spectrum that depends on the parity of the excited molecular state. Franck-Condon overlap calculations predict that photoassociation to higher vibrational levels of the $d{}^3\mathrm{\Pi }$ potential, in particular, the sixth vibrational level, should populate the lowest vibrational level of the $a{}^3{\mathrm{\Sigma }}^{+}$ state at a rate as high as ${10}^4$ molecules per second. This work also motivates an experimental search for short-range photoassociation to other bound molecular states, such as $c{}^3{\mathrm{\Sigma }}^{+}$ or $b{}^3\mathrm{\Pi }$, as prospects for preparing ground-state molecules.

Figure 1

Energy level diagram for the LiRb molecule showing the relevant PECs from Ref. [36]. Vertical lines show transitions, including (a) the photoassociation, with frequency ${\nu }_a$; (b) the spontaneous decay of $d{}^3\mathrm{\Pi }$ molecules leading to $a{}^3{\mathrm{\Sigma }}^{+}$ molecules; and (c) the first step of REMPI ionization of $a{}^3{\mathrm{\Sigma }}^{+}$ molecules, at frequency ${\nu }_c$, through $f{}^3\mathrm{\Pi }$ (whose PEC is not shown, for clarity). The dashed horizontal black line represents our PA states. Inset: Spin-orbit components of the $d{}^3\mathrm{\Pi }$ state and also the nearby $D{}^1\mathrm{\Pi }$ state.

Figure 2

PA spectrum of the $d{}^3\mathrm{\Pi },v=0$ state. We observe PA to molecules with $J=0$ to 3 and have labeled PA to molecules with positive and negative parity as dashed red lines and solid green lines, respectively. This parity alternates based on the $J$ quantum number in the $\mathrm{\Omega }=0^{\pm }$ states. These assignments are consistent with those determined by depletion spectroscopy to the same states [32]. Our assignments indicate that free-to-bound PA transitions to molecular states with negative parity are significantly stronger than their positive-parity counterparts, sometimes by almost an order of magnitude. For these scans, the REMPI laser was tuned to the transition from $a^3{\mathrm{\Sigma }}^{+},v^{\prime \prime }=7$ to $f^3{\mathrm{\Pi }}_0,v^{\prime }=4$ at $17 654.8 {\mathrm{cm}}^{-1}$. Inset: High-resolution PA scan to the $\mathrm{\Omega }=0^{+},J=1$ state with a fit based on Eq. (1). $\mathrm{\Delta }$ is the detuning from the fitted peak center. An asterisk denotes a hyperfine echo from the MOT population in Li $F=1$ or Rb $F=3$ atoms.

Figure 3

Parities for the partial waves of the scattering state and final $d{}^3{\mathrm{\Pi }}_{\mathrm{\Omega }}$ states, adapted and modified from Ref. [38]. Solid green and dashed red arrows correspond, respectively, to the alternating strong- and weak-dipole-allowed PA transitions to the $d{}^3{\mathrm{\Pi }}_0$ state shown in Fig. 2. The parity of every state or wave is shown as a circled plus or minus sign. Transitions to $\mathrm{\Omega }=1$ or 2 states and the small energy splitting of the $J$ states are not shown, for clarity. Note that we can resolve the energy splitting between different parities for $\mathrm{\Omega }=0^{\pm }$ states but not for $\mathrm{\Omega }=1$ or 2 states. $J^{\prime \prime \prime }$ refers here to the total angular momentum of the scattering state along the $a{}^3{\mathrm{\Sigma }}^{+}$ potential for scattering through different partial waves.

Figure 4

Sample REMPI spectrum. Solid blue, dotted red, and dashed black lines, respectively, are our assignments for progressions from $a{}^3{\mathrm{\Sigma }}^{+},v^{\prime \prime }=2,$ some combination of $v^{\prime \prime }=$ 4 or 7, and $v^{\prime \prime }=6$ to vibrational levels $v^{\prime }=3$–8 of the $f{}^3{\mathrm{\Pi }}_0$ state. Each data point is the average of 100 REMPI pulses and is smoothed by averaging over nearest neighbors. (Although not labeled here, we have assignments for more than 90% of the observed REMPI resonances.)

Figure 5

Predicted generation rates, $R$, of the $a{}^3{\mathrm{\Sigma }}^{+},v^{\prime \prime }=0$ state using PA to different vibrational levels $v$ of the $d{}^3\mathrm{\Pi }$ states. To generate this plot, we assumed experimental conditions similar to those we used in the present work except, of course, for the frequency of the PA laser. Inset: Sketch of PECs, bound wave functions of interest, and the scattering wave function at $500 \mu K$. Note the high generation rate of $v^{\prime \prime }=0$ predicted from PA using the $d{}^3\mathrm{\Pi },v=6$ state.