Cooperative Excitation and Many-Body Interactions in a Cold Rydberg Gas

The dipole blockade of Rydberg excitations is a hallmark of the strong interactions between atoms in these high-lying quantum states [M. Saffman, T. G. Walker, and K. Mølmer, Rev. Mod. Phys. 82, 2313 (2010); D. Comparat and P. Pillet, J. Opt. Soc. Am. B 27, A208 (2010)]. One of the consequences of the dipole blockade is the suppression of fluctuations in the counting statistics of Rydberg excitations, of which some evidence has been found in previous experiments. Here we present experimental results on the dynamics and the counting statistics of Rydberg excitations of ultracold rubidium atoms both on and off resonance, which exhibit sub- and super-Poissonian counting statistics, respectively. We compare our results with numerical simulations using a novel theoretical model based on Dicke states of Rydberg atoms including dipole-dipole interactions, finding good agreement between experiment and theory.

Figure 1

Rydberg excitation dynamics in an ultracold gas. The mean number of detected ions $⟨N_D⟩$ and $Q_D$ are shown, in (a) and (b), respectively, as a function of pulse duration for the resonant excitation of the $71D_{5/2}$ state. The blue laser detuning from the intermediate $6P_{3/2}$ $F=3$ state is 1 GHz. The number of ground state atoms is $8\times {10}^3$, the average density is $1.2\times {10}^{10}{\mathrm{cm}}^{-3}$, and the two-photon Rabi frequency is 40 kHz. The error bars are derived from 50 experimental realizations. The continuous lines are the prediction of our complete model, while the dashed line in (a) is the theoretical prediction of a model based on the Dicke symmetric states only. All quantities are rescaled by the detection efficiency.

Figure 2

Detuning dependence of collective Rydberg excitations. The mean number of detected ions $⟨N_D⟩$ and $Q_D$ are shown for a range of frequencies around the two-photon excitation of state $71D_{1/2}$ in (a) and (b), respectively. The $⟨N_D⟩$ data are well fitted by a top truncated Lorentzian line shape, except in a frequency range around the maximum. The continuous and dashed lines are the predictions of our complete model, with the calculated average coupling strength and 100 times that coupling strength, respectively. The black dot-dashed line simulates the effect of the laser jitter (assumed to be 0.5 MHz) on $Q_D$, assuming that $Q=0$ independently of the detuning, based on the data of (a). The blue laser detuning from the intermediate $6P_{3/2}$ $F=3$ state is 1 GHz. The number of ground state atoms is $5\times {10}^4$, the average density is $4\times {10}^{10}{\mathrm{cm}}^{-3}$, the two-photon Rabi frequency is 40 kHz, and the excitation pulse duration is $0.3\mu \mathrm{s}$.

Figure 3

Predictions for the detuning dependence of collective Rydberg excitations. (a) Theoretical dependence of the $Q$ parameter on the laser detuning for a range of atomic densities (in ${\mathrm{cm}}^{-3}$): $1\times {10}^{10}$ (thin blue line), $4\times {10}^{10}$ (dashed green line), $10\times {10}^{10}$ (dot-dashed orange line), and $40\times {10}^{10}$ (thick red line), respectively. (b) Dependence on the density of the on-resonant $Q$ (blue line) and the value of $Q$ (dot-dashed red line) and position (black dashed line, right-hand scale) of the first off-resonant peaks.