Extensive high-resolution photoassociation spectra and perturbation analysis of the $2\left(0^{-}\right)$ long-range state of ultracold RbCs molecules

We report high-resolution photoassociation (PA) spectra of RbCs in the $2\left(0^{-}\right)$ long-range state. Transitions to more than 50 vibrational levels were recorded with the largest binding energy being 507.5 ${\mathrm{cm}}^{-1}$. By fitting the experimental transition frequencies to the improved LeRoy-Bernstein formula, the $C_6$ coefficient for the potential energy curve of the $2\left(0^{-}\right)$ state was determined to be $-1509\pm 97$ a.u.. Perturbation-induced energy level shift and state mixing of the long-range $2\left(0^{-}\right)$ and 3(1) states have been analyzed using an effective Hamiltonian that may be applied to mixing between other excited states of RbCs, as well as other heteronuclear diatomic molecules. Experimentally observed PA transitions to the $\nu =190$ vibrational level of the $2\left(0^{-}\right)$ state and a vibrational perturbing level in the 3(1) state have been fit using the effective Hamiltonian, which provides the accurate value of the perturbation coefficient ${\beta }_0$. The experimentally determined rovibronic structure and the deperturbation analysis provide critical information for the search of new schemes for efficient production of ultracold RbCs molecules in the ground state.

Figure 1

PA scheme for production of ultracold RbCs molecules. (a) A pair of ${}^{85}\mathrm{Rb}$ and Cs atoms are excited (red solid arrow) to the $2\left(0^{-}\right)$ state. The formed RbCs molecule then decays spontaneously to its ground state (red dash arrow). (b) Long-range PECs labeled using Hund's case (c) notations. The $2\left(0^{-}\right)$ (red line) and 3(1) (green line) states are mixed with each other.

Figure 2

A typical PA spectrum with $\nu =156$ in the $2\left(0^{-}\right)$ state. The $x$ axis indicates the excitation frequency relative to the ${}^{85}\mathrm{Rb}\left(5S_{1/2}\right)+\mathrm{Cs}\left(6P_{1/2}\right)$ asymptote at 11178.4172 ${\mathrm{cm}}^{-1}$, i.e., the binding energy of excited RbCs molecules. Dips in the fluorescence spectra of Rb and Cs atoms are due to formation of RbCs molecules by PA.

Figure 3

(a) Binding energy ${(D-E_{\nu })}^{1/3}$ as a function of the vibrational quantum number $\nu$ in the long-range $2\left(0^{-}\right)$ state. Experimentally determined values (blue circles) are compared with fits using the LRB (green dashed line) and improved LRB (red solid line) models. $X$ axis intercepts of the fit lines are fit values for ${\nu }_D$. Inset shows residuals of the fits. (b) Rotational constant $B_{\nu }$ as a function of the vibrational quantum number $\nu$.

Figure 4

(a) Trap loss signal of the $2\left(0^{-}\right)$ state. The calculated energy eigenvalues with and without perturbation are denoted by red solid and blue dashed lines, respectively. (b) Trap loss signal of the 3(1) state. Only Rb trap loss signals are shown for clarity. PA transitions of Cs have identical transition frequencies and similar intensities as Rb.

Figure 5

Mixing of the $2\left(0^{-}\right)$ and 3(1) states for rotational quantum numbers $J=0,1,2,3$.

Figure 6

(a) REMPI spectrum with PA transition to the unassigned perturbing vibrational level of the 3(1) state. (b) REMPI spectrum with PA transition to the $\nu =190$ level of the $2\left(0^{-}\right)$ state.