Atom-Pair Kinetics with Strong Electric-Dipole Interactions

Rydberg-atom ensembles are switched from a weakly to a strongly interacting regime via adiabatic transformation of the atoms from an approximately nonpolar into a highly dipolar quantum state. The resultant electric dipole-dipole forces are probed using a device akin to a field ion microscope. Ion imaging and pair-correlation analysis reveal the kinetics of the interacting atoms. Dumbbell-shaped pair-correlation images demonstrate the anisotropy of the binary dipolar force. The dipolar $C_3$ coefficient, derived from the time dependence of the images, agrees with the value calculated from the permanent electric-dipole moment of the atoms. The results indicate many-body dynamics akin to disorder-induced heating in strongly coupled particle systems.

Figure 1

(a) Experimental setup. Rydberg atoms are laser-excited above a tip imaging probe (TIP) and ionized by application of a high voltage to the TIP. Ions are detected by a microchannel plate (MCP). (b) Rydberg atoms initially prepared in an $S$-like state (blue circle) become adiabatically transferred into a highly dipolar state (pink oval), when passing through an avoided crossing in the Stark energy level diagram in the applied electric field $\mathbf{E}$. The diameters of the dashed circles indicate binary-interaction strengths. (c) Measured Stark spectra at the sixth crossing between the $50S_{1/2}$ state and $n=47$ hydrogenlike states. (d) Timing sequence.

Figure 2

Experimental pair-correlation images for the indicated wait times. The linear gray scale ranges from 0.4 (white) to 1.5 (black), where values of 1, $<1$, and $>1$ indicate no correlation, anticorrelation, and positive correlation, respectively. The illustrations on the left show the electric-field and dipolar alignments relative to the object plane (which is the same as the image plane) for the three data rows. (a) Zero field. Atoms undergo weak van der Waals interaction. (b) Applied electric field in $z$ direction. The atomic dipoles are aligned along $z$, perpendicular to the image ($xy$) plane. Binary interactions are azimuthally symmetric about $z$ and primarily repulsive. (c) Applied electric field in $y$ direction. The atomic dipoles are aligned along $y$, in plane with the image plane. Binary interactions are mixed attractive or repulsive, leading to anisotropic images showing repulsion along $x$ and attraction along $y$. The dark rings immediately around the centers are experimental artifacts.

Figure 3

(a) Angular integrals $I(R)$ of the pair-correlation images in Fig. 2 at wait times (from top to bottom) 0, 2, 4, 6, 8, and $10\mu \mathrm{s}$. The $y$ axis is for the $0\mu \mathrm{s}$ curve; for clarity, the other curves are shifted down in equidistant steps of 0.3. (b) Interatomic separations $R_c(t)$ between Rydberg-atom pairs as a function of interaction time (left axis) from experiment (blue circles) and simulation (red line). The blue dashed line shows a linear fit to the experimental data between 6 and $10\mu \mathrm{s}$. The gray squares show the visibility of the experimental pair-correlation enhancement (right axis).

Figure 4

(a) Color map of the dipolar potential and corresponding force vectors as a function of $\mathbf{R}$ for a pair of dipoles pointing along $y$. Atoms repel each other in the equatorial direction $x$ and attract each other in the polar direction $y$. Because of the combination of radial and angular forces, the atom pairs become funneled into narrow conical sections at the poles. This leads to characteristic pair-correlation images as shown in (b) (from the experiment) and (c) (from a simulation). The images in (b) and (c) are for $t=4\mu \mathrm{s}$.