Electronic structure of ultralong-range Rydberg penta-atomic molecules with two polar diatomic molecules

We explore the electronic structure of ultralong-range penta-atomic Rydberg molecules from a merger of a Rydberg atom and two ground-state heteronuclear diatomic molecules. Our focus is on the interaction of $\mathrm{Rb}(23s$) and $\mathrm{Rb}(n=20$, $l\ge 3$) Rydberg states with ground and rotationally excited KRb diatomic polar molecules. For symmetric and asymmetric configurations of the penta-atomic Rydberg molecule, we investigate the metamorphosis of the Born-Oppenheimer potential curves, essential for the binding of the molecule, with varying distance from the Rydberg core and analyze the alignment and orientation of the polar diatomic molecules.

Figure 1

A sketch (not to scale) of the Rydberg PentaMol formed by a Rydberg atom and two diatomic polar molecules in the (a) symmetric and (b) asymmetric configurations. The first and second diatomic molecules, as referred to throughout the text, are identified in these sketches with 1 and 2, respectively.

Figure 2

Symmetric configuration of the Rydberg PentaMol: adiabatic electronic potential curves evolving from the degenerate manifold $\mathrm{Rb}(n=20$, $l\ge 3$) and the Rydberg state $\mathrm{Rb}(23s$) for total magnetic quantum number $M_J=0$. Calculations have been performed, including in the coupled basis of the diatomic molecule (6) rotational excitations up to (a) $N_i=4$, (b) $N_i=5$, and (c) $N_i=6$, $i=1,2$.

Figure 3

Symmetric configuration of the Rydberg PentaMol: Adiabatic electronic potential curves evolving from the Rydberg manifold $\mathrm{Rb}(n=20$, $l\ge 3$) with total magnetic quantum number (a) $M_J=0$ and (b) $M_J=1$.

Figure 4

Rydberg TriMol: Adiabatic electronic potential curves evolving from the Rydberg manifold $\mathrm{Rb}(n=20$, $l\ge 3$) with total magnetic quantum number (a) $M_J=0$ and (b) $M_J=1$.

Figure 5

Rydberg PentaMol: Orientation of the first (thin lines) and second (thick lines) diatomic molecule for the two lowest-lying adiabatic potentials evolving from the Rydberg manifold $\mathrm{Rb}(n=20$, $l\ge 3$) for total magnetic quantum number (a) $M_J=0$ and (b) $M_J=1$. The alignment of these two diatomic molecules is identical and is presented for the two lowest-lying potentials for $M_J=0$ and $M_J=1$ in panel (c).

Figure 6

Symmetric configuration of the Rydberg PentaMol: Adiabatic electronic potential curves with varying separation between the ${\mathrm{Rb}}^{+}$ and the two diatomic molecules $R=R_1=R_2$ evolving from the Rydberg state $\mathrm{Rb}(23s$) and for the diatomic molecules in rotational excitations with wave functions in the coupled basis $|N,M_N,2,2\rangle$, with $N=0,\cdots ,4$, $|3,M_N,3,0\rangle$, and $|3,M_N,0,3\rangle$. The total magnetic quantum number of the adiabatic electronic potentials is (a) $M_J=0$ and (b) $M_J=1$. The insets show the orientation of the first diatomic molecule $\langle cos{\theta }_1\rangle$ located at ${\theta }_1={\varphi }_1=0$.

Figure 7

Symmetric configuration of the Rydberg PentaMol: Adiabatic electronic potential curves ($R=R_1=R_2$) evolving from the Rydberg state $\mathrm{Rb}(23s$) and the diatomic molecules in rotational excitations $|N,M_N,3,3\rangle$ for $N=0,\cdots ,6$. The total magnetic quantum number of the BOPs is (a) $M_J=0$ and (b) $M_J=1$. The insets show the orientation of the first diatomic molecule $\langle cos{\theta }_1\rangle$ located at ${\theta }_1={\varphi }_1=0$.

Figure 8

Matrix elements of the $Z$ component of the electric field due to the Rydberg electron $|\langle l_1,0|F_{\mathrm{Ryd}}^{e,Z}(600,0,0,\mathbf{r})|l_2,0\rangle |$. See the Appendix for the expression of the Rydberg electron electric field $F_{\mathrm{Ryd}}^{e,Z}(R_i,{\theta }_i,{\varphi }_i,\mathbf{r})$ in Eqs. (A3) and (A6).

Figure 9

Asymmetric Rydberg PentaMol: Adiabatic electronic potentials evolving from the Rydberg manifold $\mathrm{Rb}(n=20$, $l\ge 3$) versus the separation of the first dipole $R_1$ from ${\mathrm{Rb}}^{+}$. The second diatomic molecule is located at the same side of the ${\mathrm{Rb}}^{+}$ core and separated from the first one by a distance (a) $\mathrm{\Delta }R=175a_0$ and (b) $\mathrm{\Delta }R=300a_0$, which is kept constant. The first (1) and second (2) KRb molecules are shown in the sketch of Fig. 1.

Figure 10

Orientation (solid lines) and alignment (dashed lines) of the first (thick red lines) and second (thin black lines) diatomic molecules within the lowest-lying BOP for $M_J=0$ evolving from the Rydberg manifold $\mathrm{Rb}(n=20$, $l\ge 3$) for the Rydberg PentaMol in an asymmetric configuration as a function of $R_1$. The relative separation between the two diatomic molecules is kept fixed to (a) $\mathrm{\Delta }R=175a_0$ and (b) $\mathrm{\Delta }R=300a_0$, and they are both located on the same side of the ${\mathrm{Rb}}^{+}$ core. The first (1) and second (2) KRb molecules are shown in the sketch of Fig. 1.

Figure 11

Asymmetric Rydberg PentaMol: Adiabatic electronic potentials evolving from the Rydberg manifold $\mathrm{Rb}(n=20$, $l\ge 3$) versus the separation of the second diatomic molecule $R_2$ from ${\mathrm{Rb}}^{+}$. The position of the first diatomic molecule is fixed at (a) $R_1=400a_0$ and (b) $R_1=500a_0$. Both diatomic molecules are located at the same side of the ${\mathrm{Rb}}^{+}$ core, see Fig. 1.

Figure 12

Orientation (solid lines) and alignment (dashed lines) of the first (thick red lines) and second (thin black lines) diatomic molecules within the lowest-lying BOP for $M_J=0$ evolving from the Rydberg manifold $\mathrm{Rb}(n=20$, $l\ge 3$) in the Rydberg PentaMol in an asymmetric configuration where the position of the first diatomic molecule is fixed on (a) $R_1=400a_0$ and (b) $R_1=500a_0$. Both diatomic molecules are located at the same side of the ${\mathrm{Rb}}^{+}$ core. The first (1) and second (2) KRb molecules are shown in the sketch of Fig. 1.