Ultralong-Range Rydberg Bimolecules

We predict that ultralong-range Rydberg bimolecules form in collisions between polar molecules in cold and ultracold settings. The interaction of $\mathrm{\Lambda }$-doublet nitric oxide (NO) with long-lived Rydberg $\mathrm{NO}(nf,ng)$ molecules forms ultralong-range Rydberg bimolecules with GHz energies and kilo-Debye permanent electric dipole moments. The Hamiltonian includes both the anisotropic charge-molecular dipole interaction and the electron-NO scattering. The rotational constant for the Rydberg bimolecules is in the MHz range, allowing for microwave spectroscopy of rotational transitions in Rydberg bimolecules. Considerable orientation of NO dipole can be achieved. The Rydberg molecules described here hold promise for studies of a special class of long-range bimolecular interactions.

Figure 1

${{}^3\mathrm{\Sigma }}^{+}$ Born-Oppenheimer potential energy curves near the $\mathrm{NO}(40g)\text{−}\mathrm{NO}(\mathrm{X}{{}^2\mathrm{\Pi }}_{1/2})$ thresholds. The molecular $\mathrm{\Lambda }$-doublet splitting are identified by $|+⟩$ and $|-⟩$ labels. The wave functions of long-lived Rydberg bimolecular states are shown at the energy level. The magnitude and direction of orientation of the NO molecular dipole for each electronic well are also shown. All the interactions in the Hamiltonian (2) are included in obtaining these potential curves.

Figure 2

BO potential energy curves of the $\mathrm{NO}(n=15,l\ge 3)\text{−}\mathrm{NO}(\mathrm{X}{{}^2\mathrm{\Pi }}_{1/2})$ ultralong-range Rydberg bimolecule including (a) the charge-dipole only and (b) all the interactions in the Hamiltonian (2). Details of the curves including all interactions near the (c) $\mathrm{NO}(15g)\text{−}\mathrm{NO}(\mathrm{X}{{}^2\mathrm{\Pi }}_{1/2})$ and (d) $\mathrm{NO}(15f)\text{−}\mathrm{NO}(\mathrm{X}{{}^2\mathrm{\Pi }}_{1/2})$ dissociation thresholds; the vibrational wave functions are shown at the energy level. The bound states near the avoided crossing in (c) are quantum reflected states [55].

Figure 3

(a) BO potential energy curves of the $\mathrm{NO}(n=40,l\ge 3)\text{−}\mathrm{NO}(\mathrm{X}{{}^2\mathrm{\Pi }}_{1/2})$ Rydberg bimolecule including all the interactions in the Hamiltonian (2). Details of the curves near the (b) $\mathrm{NO}(40f)\text{−}\mathrm{NO}(\mathrm{X}{{}^2\mathrm{\Pi }}_{1/2},|-⟩)$ and (c) $\mathrm{NO}(40f)\text{−}\mathrm{NO}(\mathrm{X}{{}^2\mathrm{\Pi }}_{1/2},|+⟩)$ dissociation thresholds; the vibrational wave functions are shown at the energy level. For illustration, we highlight the magenta curve in (a), which is completely blueshifted and supports a number of bound vibrational levels in the different wells. In (b), the degree of orientation of the NO dipole in the two outer wells is, respectively, 0.33 and $-0.40$, i. e., the NO dipole is pointing away from the ${\mathrm{NO}}^{+}$ core and toward the core, respectively. Whereas in (c), the degree of orientation in the two bound states is, respectively, 0.43 and 0.32.