$C{}^1{\mathrm{\Sigma }}^{+}, A{}^1{\mathrm{\Sigma }}^{+}$, and $b{}^3{\mathrm{\Pi }}_{0^{+}}$ states of LiRb

We present the first spectroscopic studies of the $C{}^1{\mathrm{\Sigma }}^{+}$ electronic state and the $A{}^1{\mathrm{\Sigma }}^{+}$–$b{}^3{\mathrm{\Pi }}_{0^{+}}$ complex in ${}^7\mathrm{Li}-{}^{85}\mathrm{Rb}$. Using resonantly enhanced, two-photon ionization, we observed $v=7$, 9, 12, 13, and 26–45 of the $C{}^1{\mathrm{\Sigma }}^{+}$ state. We augment the REMPI data with a form of depletion spectra in regions of dense spectral lines. The $A{}^1{\mathrm{\Sigma }}^{+}$–$b{}^3{\mathrm{\Pi }}_{0^{+}}$ complex was observed with depletion spectroscopy, depleting to vibrational levels $v=0\to 29$ of the $A{}^1{\mathrm{\Sigma }}^{+}$ state and $v=8\to 18$ of the $b{}^3{\mathrm{\Pi }}_{0^{+}}$ state. For all three series, we determine the term energy and vibrational constants. Finally, we outline several possible future projects based on the data presented here.

Figure 1

Energy level diagram for the LiRb molecule showing relevant PECs from Ref. [18]. Vertical lines show various optical transitions, including (a) photoassociation of molecules below the Rb $D_1$ asymptote; (b) spontaneous decay of excited-state molecules leading to a wide range of $X{}^1{\mathrm{\Sigma }}^{+}$ vibrational levels, drawn for $v^{\prime \prime }=2$; (c) REMPI to ionize LiRb molecules, labeled ${\nu }_c$ in other figures; and (d) excitation to deplete the REMPI signal. The dashed black line represents the 2(1)-4(1) PA resonance, while the dashed blue line represents the depletion state.

Figure 2

RE2PI spectra from $v^{\prime \prime }=42$ and 43 to the $C{}^1{\mathrm{\Sigma }}^{+}$ electronic state. Solid green lines and numbers label transitions $C{}^1{\mathrm{\Sigma }}^{+}{v}^{\prime }\leftarrow v^{\prime \prime }=43$; dashed black lines and numbers label transitions $C{}^1{\mathrm{\Sigma }}^{+}{v}^{\prime }\leftarrow v^{\prime \prime }=42$.

Figure 3

Depletion spectroscopy of RE2PI data on transitions from $v^{\prime \prime }=42$ and 43 to the $C{}^1{\mathrm{\Sigma }}^{+}$ and $D{}^1\mathrm{\Pi }$ electronic states. For these data, the solid blue trace represents the original data from Fig. 2; the dashed red trace, the RE2PI data retaken in the presence of a depletion laser driving the $B{}^1\mathrm{\Pi } v^{\prime }=20\leftarrow v^{\prime \prime }=43$ transition. Reduction of a peak height in the presence of the depletion laser indicates that the initial state is $v^{\prime \prime }=43$. Assignments of these lines are labeled as follows: solid green lines, $C{}^1{\mathrm{\Sigma }}^{+}\leftarrow v^{\prime \prime }=43$; dashed black lines, $C{}^1{\mathrm{\Sigma }}^{+}\leftarrow v^{\prime \prime }=42$; dotted black lines, $D{}^1\mathrm{\Pi }\leftarrow v^{\prime \prime }=42$; and dot-dashed green lines, $D{}^1\mathrm{\Pi }\leftarrow v^{\prime \prime }=43$.

Figure 4

Comparison of theoretical vibrational spacings (blue circles) to our measurements (red triangles) for (a) $A{}^1{\mathrm{\Sigma }}^{+}$ and (b) $b{}^3{\mathrm{\Pi }}_{0^{+}}$. Dashed black vertical lines connect data sets to guide the eye. The dashed red line is the fit using Eq. (1) and the molecular constants listed in Table 3. Large deviations in experiment vs theory are driven by perturbations. The unevenness of the theoretical predictions in the $v^{\prime }=0$–4 region for $A{}^1{\mathrm{\Sigma }}^{+}$ and the $v^{\prime }=7$–12 region for $b{}^3{\mathrm{\Pi }}_{0^{+}}$ is an artifact caused by imperfect conversion from adiabatic to diabatic PECs. Finally, we note that (b) suggests that our extracted constants, ${\omega }_e$ and $x_e$, for the $b{}^3{\mathrm{\Pi }}_{0^{+}}$ state are too large. Our data for this state are limited, and it appears that if both were smaller, the fit would better match the theory (blue circles).

Figure 5

Calculated ${\mathrm{V}}_{\mathrm{int}}=A_{\mathrm{Rb}}{\left|\langle {\mathrm{\Psi }}_{b{}^3\mathrm{\Pi }}|{\mathrm{\Psi }}_{A{}^1{\mathrm{\Sigma }}^{+}}\rangle \right|}^2$/2, divided by the state energy difference, for $A{}^1{\mathrm{\Sigma }}^{+}$ (a) $v^{\prime }=2$, (b) $v^{\prime }=5$, (c) $v^{\prime }=8$, and (d) $v^{\prime }=11$ interacting with the vibrational levels of the $b{}^3{\mathrm{\Pi }}_{0^{+}}$ state. PECs are from Ref. [18], and we calculated the vibrational wave functions and FCFs using level8.0 [22]. $A_{\mathrm{Rb}}=250{\mathrm{cm}}^{-1}$ is the atomic rubidium spin-orbit constant.

Figure 6

Calculated STIRAP strengths from $v^{\prime \prime }=43$ to $v^{\prime \prime }=0$ through $C{}^1{\mathrm{\Sigma }}^{+}, v^{\prime }$ as a function of the vibrational level $v^{\prime }$. We estimate the STIRAP strength as $I_{\mathrm{rel}}=\sqrt{{\mathrm{FCF}}_{\mathrm{down}}{\mathrm{FCF}}_{\mathrm{up}}}$ [25] in the absence of any information on the transition dipole moments. The wider, green-shaded region represents the states accessible with commercially available green diode lasers, while the enclosed, red-shaded region represents the states accessible with 730-nm diode lasers (the green laser also covers this range). From this $C{}^1{\mathrm{\Sigma }}^{+}, v^{\prime }=22$ stands out as the best available intermediate state using these lasers, while being the third-best intermediate state overall.