Vibronic quantum dynamics of ultralong-range high-$\ell$ Rydberg molecules

Abstract

We investigate the non-adiabatic quantum dynamics of ultralong-range Rydberg molecules using a vibronically coupled two-channel treatment. The two channels are composed of coupled trilobite and butterfly electronic states, formed as a result of $S$-wave and $P$-wave scattering of high angular momentum Rydberg electrons with perturbing ground state atoms. Within the Born-Oppenheimer treatment, the $P$-wave scattering channel introduces an adiabatic decay pathway that affects the stability and lifetimes of trilobite states. Our numerical results show that the vibronic coupling is dependent on the principal quantum number $n$, and for certain $n$ there is non-adiabatic stabilization against internal molecular decay, facilitating previously studied dynamical effects in pure trilobite molecules. Apart from the internal diffraction effect we also observe interesting multi-well tunneling effects, during low-energy oscillations for certain $n$-values. Our work serves to highlight that the unique $R$-dependent electronic structure of these polar molecules, along with high level densities, promise many exciting dynamical effects.

Figures (5)

• Figure 1: The Born-Oppenheimer potentials of the $n$=55 ULRM, obtained by solving the electronic Schrödinger equation. The two-state system corresponds to the highlighted $V_1$ (violet) and $V_2$ (orange) potentials, ignoring the grey curves for low energy dynamics. The wavepackets and arrows are used to illustrate the possible trajectories of a time evolving nuclear wavefunction. The probability density plots of $\phi_1(\textbf{r},R)$ (corresponding to the PEC $V_1$) calculated at $R$=1400 a$_0$ and $R$=4880 a$_0$, portray the change of electronic structure from trilobite to butterfly states as $R$ changes.
• Figure 2: (a) The first order derivative coupling element $P_{12}/\mu \mathrm{a}_0$ as a function of the internuclear distance $R$, for varying $n$-values. The inset depicts the magnitude of $P_{12}$ with log-scaling of the $y$-axis. The adiabatic and diabatic PECs of the $n=55$ and $n=57$ ULRM are shown in (b) and (c) respectively, with (d) and (e) being the corresponding magnified plots showcasing the avoided crossing.
• Figure 3: Two channel wavepacket diffraction dynamics. The potential energy structure of the $n=55$ and $n=57$ ULRM in the relevant region, are shown in (a) and (b). The time evolving total probability density $\rho(R,t)$ in the position representation is shown for $n=55$ (c) and $n=57$ (d). The corresponding total probability density in momentum representation, i.e. $\tilde{\rho}(P,t)$ is shown for $n=55$ (e) and $n=57$ (f).
• Figure 4: Time evolution of the diabatic populations $p_{d}$ (dashed curves), and the adiabatic populations $p_{a}$ (solid curves) for channel 1 and 2, as well as the the total population $p_{tot}$ (dotted curve). (a) Depicts the population dynamics for $n=55$, and (b) depicts the population dynamics for $n=57$.
• Figure 5: Multi-well interference effects due to low energy dynamics. (a) Shows the adiabatic potential energy curve $V_1$ for the $n=49$ ULRM, along with probability density of the initial Gaussian wavepacket $\rho(R,t=0)$. (b) The time evolving total probability density $\rho(R,t)$. (c) The vibronic molecular resonances (dashed lines). The three bound eigenstates responsible for the observed multiwell dynamics are highlighted and labelled.