Photoassociative formation of ultracold RbCs molecules in the $\left(2\right){}^3\Pi$ state

We have investigated photoassociative formation of RbCs molecules in the ${\left(2\right)}^3\Pi$ excited state correlated to $v=8$, $\left(5\right)0^{+}$ vibrational level in detail. The metastable ground-state RbCs molecules formed by spontaneous decay are ionized by pulsed dye laser through resonance-enhanced two-photon ionization. A rate equation of the photoionization process is introduced to explain the dependence of RbCs${}^{+}$ molecular ion intensity on the ionization laser intensity. The saturation effect of molecular ion intensity appears as the photoassociation laser intensity increases. The rotational constant and centrifugal distortion constant are derived to be 0.01304 cm${}^{-1}$ and 0.000015 cm${}^{-1}$ from the photoassociation spectrum with a high sensitivity, respectively. The measured electric dipole moment of the observed $\left(2\right){}^3\Pi$ state RbCs molecules is 4.7(6) D by Stark effect in static electric field.

Figure 1

Formation and ionization scheme of RbCs molecules in the $\left(2\right){}^3\Pi$ state. A pair of ${}^{85}$Rb and ${}^{133}$Cs atoms during collision is excited to a deeply bound level (a), which is the $\left(2\right){}^3\Pi$ state correlated to the Rb($5P_{1/2}$) + Cs($6S_{1/2}$) atomic asymptote under a photoassociative photon. The metastable $a{}^3{\Sigma }^{+}$ state molecules are formed by spontaneous decay (b) and are ionized by resonance-enhanced two-photon ionization [(c) and (d)] through the $\left(3\right){}^3\Pi$ intermediate state correlated to the Rb($5S_{1/2}$) + Cs($5D_{3/2,5/2}$) atomic asymptote. It is also likely that some of the excited-state molecules decay to the lowest level of the $X{}^1{\Sigma }^{+}$ ground state due to spin-orbit coupling between the $\left(2\right){}^1\Pi$ and $\left(2\right){}^3\Pi$ states (e). The potential energy curves of RbCs molecules are based on the data in Refs. [36, 37] and labeled with Hund case (a).

Figure 2

Experimental time sequence and typical time-of-flight mass spectrums. (a) Experimental time sequence (not to scale) in our experiment. An accelerating electric field is used to accelerate the ions ionized by the dye laser. Static electric field on the grid is used to measure the electric dipole moment of RbCs molecules by the dc Stark effect. (b) and (c) Ion signals detected by MCP in the absence and the presence of the PA laser. When the PA laser is focused on the Rb-Cs dark SPOTs, not only does the RbCs${}^{+}$ molecular ion appear, but also the other ions are enhanced. The red dashed lines indicate the value of $-8$ mV on the vertical axis for comparison between (b) and (c).

Figure 3

Photoassociative spectrum of RbCs molecules in the $\left(2\right){}^3\Pi$ state and theoretical fit for the corresponding rotational constant and centrifugal distortion constant. (a) Rotational structures of photoassociative RbCs molecules in the $\left(2\right){}^3\Pi$ state. The five peaks correspond to $J=0$, 1, 2, 3, and 4 rotational levels of excited-state RbCs molecules at short range. (b) Dependence of the energy interval $\Delta E$ on the rotational number $J$ for the $\left(2\right){}^3\Pi$-state RbCs molecules. The red dots represent experimental data, and the error bars are the standard deviations derived from five different measurements. The blue dashed line and green solid line are fitted to Eq. (4) without and with centrifugal distortion constant $D_v$ for the same experimental data. The square of coefficients of correlation $R^2$ in the two fit processes are 0.99914 and 0.99999, respectively.

Figure 4

RbCs${}^{+}$ molecular ion intensity for $J=0$, 1, and 2 rotational levels as a function of ionization laser intensity (a) and PA laser intensity (b). The different lines in (a) are fitted to experimental data by Eq. (6). The lines show that a saturation effect appears when the pulsed ionization laser intensity is large enough. The curves in (b) represent the fits to the saturation model by Bohn and Julience, described in Eq. (8). The saturation intensities for $J=0$, 1, and 2 are about 84, 102, and 93 W/cm${}^2$, respectively.

Figure 5

Stark effect of $\left(2\right){}^3\Pi$ state RbCs molecules. Stark shifts of RbCs molecules for rotational number (a) $J=0$, 1 and (b) $J=2$ are shown vs dc electric fields from 0 to 350 V/cm. The error bars correspond to standard deviations in mean value, averaged over five repeated experimental measurements while keeping other parameters constant. All curves are fitted to a quadratic Stark effect, denoted by Eq. (9).