Evidence for Strong van der Waals Type Rydberg-Rydberg Interaction in a Thermal Vapor

We present evidence for Rydberg-Rydberg interaction in a gas of rubidium atoms above room temperature. Rabi oscillations on the nanosecond time scale to different Rydberg states are investigated in a vapor cell experiment. Analyzing the atomic time evolution and comparing to a dephasing model, we find a scaling with the Rydberg quantum number $n$ that is consistent with van der Waals interaction. Our results show that the interaction strength can be larger than the kinetic energy scale (Doppler width), which is the requirement for realization of thermal quantum devices in the GHz regime.

Figure 1

Schema of the experiment. (a) Relevant level scheme and excitation wavelengths. We use a two-photon excitation scheme for addressing a Rydberg $S$ state via the $D2$ line. The excitation is performed off resonantly with a (blue) detuning $\Delta /2\pi$ of $\sim 2.3\mathrm{GHz}$ with respect to the intermediate state. (b) Optical setup. The two beams are overlapped in the vapor cell in almost counterpropagating configuration. We are detecting the transmission of the 780 nm laser in which the Rabi oscillations manifest themselves during the excitation pulse. (c) Oscillation signals of a detuning scan of the 480 nm laser. We fix the frequency position for the analysis to the point of slowest oscillation (dashed line).

Figure 2

Rabi oscillations for different atomic densities. Oscillations in the transmission of the 780 nm laser for different atomic densities are shown here for the Rydberg state $37S$. The numbers on the right-hand side give the atomic ground state density in ${10}^{12}{\mathrm{cm}}^{-3}$. The experimental data are averaged over 20 shots and normalized in amplitude. A curve derived from a 3-level-atom model is fitted to the data. The only fit parameters are the dephasing rate of the Rydberg state and the signal amplitude. The gray-shaded curve in the background depicts the measured temporal shape of the excitation pulse intensity.

Figure 3

Dephasing parameters versus density. (a) The dephasing parameter of the Rydberg state ${\Gamma }_{{\rho }_{33}}$ corresponding to the Rydberg-Rydberg interaction is shown as a function of the atomic ground state density $N_g$. For each Rydberg state the data are fitted by a linear curve. (b) When scaling the density axis with the critical density $N_{\mathrm{crit}}$, all data points collapse onto a single line. $N_{\mathrm{crit}}$ is determined by the van der Waals blockade radius for each Rydberg state individually. The dashed line is a linear fit to all data points.

Figure 4

Slope of the dephasing versus principal quantum number. Double-logarithmic plot of the dephasing slopes $\partial {\Gamma }_{{\rho }_{33}}/\partial N_g$ versus the effective principal quantum number $n_{*}$. The fit of a power law $\propto n_{*}{}^p$ yields an exponent of $p=5.58\pm 0.48$ (solid line). This is in excellent agreement with an $n_{*}{}^{11/2}$ van der Waals scaling. Fitting an $n_{*}{}^4$ scaling curve to the data (dashed line), it can be seen that resonant dipole-dipole interaction is not consistent with the data. The inset shows the dephasing at the van der Waals critical density. For $N_g=N_{\mathrm{crit}}$ all examined Rydberg states show the same dephasing.