Heteronuclear Long-Range Rydberg Molecules

We present the formation of homonuclear ${\mathrm{Cs}}_2$, ${\mathrm{K}}_2$, and heteronuclear CsK long-range Rydberg molecules in a dual-species magneto-optical trap for ${}^{39}\mathrm{K}$ and ${}^{133}\mathrm{Cs}$ by one-photon UV photoassociation. The different ground-state-density dependence of homo- and heteronuclear photoassociation rates and the detection of stable molecular ions resulting from autoionization provide an unambiguous assignment. We perform bound-bound millimeter-wave spectroscopy of long-range Rydberg molecules to access molecular states not accessible by one-photon photoassociation. Calculations based on the most recent theoretical model and atomic parameters do not reproduce the full set of data from homo- and heteronuclear long-range Rydberg molecules consistently. This shows that photoassociation and millimeter-wave spectroscopy of heteronuclear long-range Rydberg molecules provide a benchmark for the development of theoretical models.

Figure 1

Upper panel, ${{\mathrm{Cs}}_2}^{+}$ and lower panel, ${\mathrm{CsK}}^{+}$ ion signals as a function of the photoassociation laser detuning from the $\mathrm{Cs}(22{}^2{\mathrm{P}}_{3/2})\leftarrow \text{Cs}\mathbf{(}6{{}^2\mathrm{S}}_{1/2}(F=3)\mathbf{)}$ transition recorded after $25\mu \mathrm{s}$ of photoassociation. The Cs density was varied (legend in upper panel, values in cubic centimeters) and the K density was $2.5(3)\times {10}^{10}{\mathrm{cm}}^{-3}$. Inset: full (open) circles are the scaled integrals of the ${\mathrm{CsK}}^{+}$ (${{\mathrm{Cs}}_2}^{+}$) signal. Dashed lines represent linear and quadratic fits.

Figure 2

Photoassociation spectra of Cs (K) atoms prepared in the $F=3$ ($F=1$) ground state. Upper row: Cs PFI (left), ${{\mathrm{Cs}}_2}^{+}$ (middle), and ${\mathrm{CsK}}^{+}$ (right) autoionization signal recorded below the $\mathrm{Cs}(31{{}^2\mathrm{P}}_{3/2})\leftarrow \text{Cs}[6{{}^2\mathrm{S}}_{1/2}(F=3)]$ transition. Resonances assigned to the $v=0$ level in the outermost well of the ${{}^3\mathrm{\Sigma }}^{+}$ (${{}^{1,3}\mathrm{\Sigma }}^{+}$) states are marked by full (dotted) blue (${\mathrm{Cs}}_2$) and green ($\overline{\mathrm{Cs}}\mathrm{K}$) lines. Bottom row: K PFI (left), ${\mathrm{CsK}}^{+}$ (middle), and ${{\mathrm{K}}_2}^{+}$ (right) autoionization signal below the $\mathrm{K}(29{{}^2\mathrm{P}}_{3/2})\leftarrow \mathrm{K}[4{{}^2\mathrm{S}}_{1/2}(F=1)]$ transition. Resonances assigned to the $v=0$ level in the outermost well of the ${{}^3\mathrm{\Sigma }}^{+}$ (${{}^{1,3}\mathrm{\Sigma }}^{+}$) states are marked by full (dotted) magenta (${\mathrm{K}}_2$) and red ($\overline{\mathrm{K}}\mathrm{Cs}$) lines. The gray dotted lines in the upper (lower) panels show the respective signals recorded in single-species Cs (K) MOTs. The signals have been averaged over 20 repetitions and a running average of 5, corresponding to a resolution of 1.2 MHz.

Figure 3

Millimeter-wave spectrum of the transition from a $\mathrm{Cs}(37{{}^2\mathrm{P}}_{3/2})\mathrm{K}(4{{}^2\mathrm{S}}_{1/2})\mathbf{(}{{}^3\mathrm{\Sigma }}^{+}(v=0)\mathbf{)}$ LRM to $\mathrm{Cs}(37{{}^2\mathrm{S}}_{1/2})\mathrm{K}(4{{}^2\mathrm{S}}_{1/2})$ LRMs (K in $F=2$). Upper panel, $\mathrm{Cs}(37{\mathrm{S}}_{1/2})$ PFI, and lower panel, ${\mathrm{CsK}}^{+}$ signal as a function of the millimeter-wave detuning from the transition $\mathrm{Cs}(37{{}^2\mathrm{S}}_{1/2})\mathrm{K}(4{{}^2\mathrm{S}}_{1/2})\leftarrow {{}^3\mathrm{\Sigma }}^{+}(v=0)$. The resonance assigned to the $v=0$ level in the outermost well of the ${{}^3\mathrm{\Sigma }}^{+}$ (${{}^{1,3}\mathrm{\Sigma }}^{+}$) state is marked by a full (dotted) red line. The gray bar masks a signal from two-photon excitation of atomic Rydberg states caused by overlapping UV and millimeter-wave pulses. The signals have been averaged as in Fig. 2 (resolution 1.0 MHz).

Figure 4

${{}^3\mathrm{\Sigma }}^{+}$ ($\mathrm{\Omega }=1/2$) interaction potentials correlating to the indicated molecular asymptotes. The minima of the outermost potential well $D_e$ are marked by dashed gray lines. The energy $D_0$ of the vibrational ground states and the respective probability densities are indicated by filled curves.