Observation of Vibrational Dynamics of Orientated Rydberg-Atom-Ion Molecules

Vibrational dynamics in conventional molecules usually takes place on a timescale of picoseconds or shorter. A striking exception are ultralong-range Rydberg molecules, for which dynamics is dramatically slowed down as a consequence of the huge bond length of up to several micrometers. Here, we report on the direct observation of vibrational dynamics of a recently observed Rydberg-atom-ion molecule. By applying a weak external electric field of a few millivolts per centimeter, we are able to control the orientation of the photoassociated ultralong-range Rydberg molecules and induce vibrational dynamics by quenching the electric field. A high resolution ion microscope allows us to detect the molecule’s orientation and its temporal vibrational dynamics in real space. Our study opens the door to the control of molecular dynamics in Rydberg molecules.

Figure 1

(a) Potential energy curves of ${}^{87}{\mathrm{Rb}}_2^{+}$ as a function of internuclear distance $R$. $h$ is Planck’s constant. Molecular potential wells are formed at the avoided crossings between the $69P$ states and the hydrogenic manifolds. The potential well marked with a red rectangle is the relevant binding potential studied in this Letter. (b) Rydberg-atom-ion molecule in an external electric field. $R$ is the internuclear distance and $\theta$ the angle between the molecular axis and the external field ${\mathit{E}}_{\mathrm{ext}}$. In our experiment, ${\mathit{E}}_{\mathrm{ext}}$ is pointing along the $+y$ direction. The imaging axis is along the $z$ axis. (c) Left panel: molecular potential along the $y$ axis in the presence of an external field of $10\mathrm{mV}/\mathrm{cm}$ (blue curve for $\theta =0$ and orange curve for $\theta =\pi$). Gray curves represent the field free potential. Zero detuning refers to the lowest vibrational energy at zero external field. Shaded areas indicate the ground vibrational wave functions. Horizontal dashed lines show computed vibrational levels. Right panel: photoassociation spectroscopy for molecules orientated to $\theta \approx 0$ (blue) and $\theta \approx \pi$ (orange). Molecules detected within an angle window of $\pm 0.2\pi$ are taken into account. Data points represent a bin of the raw data in 1 MHz steps. Error bars denote the standard error of the mean.

Figure 2

Molecular image and orientation. Image of molecules for ${\mathit{E}}_{\mathrm{ext}}=0\mathrm{mV}/\mathrm{cm}$ (a) and ${\mathit{E}}_{\mathrm{ext}}=10\mathrm{mV}/\mathrm{cm}$ (b). The corresponding detunings are 0 MHz and $-6\mathrm{MHz}$, which is resonant to the lowest vibrational level at $\theta =\pi$. $x$ and $y$ represent the relative position of the Rydberg atom with respect to the ion. (c) Molecular orientation $\overline{O}\equiv ⟨\cos (\theta )⟩$ as a function of the laser detuning for ${\mathit{E}}_{\mathrm{ext}}=0$, 5, 10, and $15\mathrm{mV}/\mathrm{cm}$. Data points represent a bin of the raw data in 1 MHz steps.

Figure 3

Vibrational wave packet dynamics. (a) Experimental sequence. (b) Radial density distribution of the wave packet, integrated over an azimuthal segment of $0.4\pi$ around $\theta =\pi$, detected after separation for variable dynamics time $t_{\mathrm{dyn}}$. White dots represent the fitted center $R_c$ of the wave packet with a Gaussian function. (c) Plot of the center $R_c$. Error bars denote the fitting uncertainties. The solid line is a fit of the oscillation based on a damped sinusoid. (d) Calculated mean radial position $\overline{R}$ (blue line) and mean radial velocity $\overline{v_R}$ (orange line) of the wave packet before separation with a classical trajectory simulation. (e) Fitted center of the wave packet after separation from theoretical simulations modeled by classical and quantum mechanical calculations.

Figure 4

Rydberg electron dynamics during the periods of nuclear vibration. Dotted lines mark the equilibrium position of the Rydberg atom’s core. Blue dots indicate the position of the Rydberg core at different evolution times $t_{\mathrm{dyn}}$. $\mathrm{\Delta }R$ is the displacement of the Rydberg core relative to the equilibrium position. Arrows show the direction and relative magnitude of the Rydberg atom’s dipole moment. The ion is located on the $y$ axis about $4\mathrm{\mu }\mathrm{m}$ above the Rydberg core, which is not shown in the figure.