Atom Counting Statistics in Ensembles of Interacting Rydberg Atoms

We show that the probability distributions for the number of Rydberg excitations in small ensembles of cold atoms, excited using short (100 ns) laser pulses, can be highly sub-Poissonian. The phenomenon occurs if the atom density and the principal quantum number of the excited Rydberg level are sufficiently high. Our observations are attributed to a blockade of the Rydberg atom excitation.

Figure 1

(a) Lowest collective states of an ensemble of $N$ atoms containing $k$ Rydberg excitations. Rydberg-Rydberg interaction causes an energy shift $V_{\mathrm{Int}}$ of the state $|N,k=2⟩$. (b) Model of an extended atomic ensemble with a Rydberg-excitation blockade of a range $R_{\mathrm{b}}$. Each “bubble” represents a region in which, ideally, there exists exactly one Rydberg excitation.

Figure 2

(a) The histogram shows the probability distribution of the number of detected $84D_{5/2}$ Rydberg atoms, obtained from 5000 realizations of the experiment. A highly sub-Poissonian $Q$ value of $-0.51\pm 0.04$ is found. To make the sub-Poissonian character of the measured distribution more apparent, the histogram is compared with a Poissonian with the same average (line). (b) Reference experiment at a Rydberg atom density that is $\sim 100$ times lower than in (a). A close-to-Poissonian $Q_D$ value of $-0.08\pm 0.04$ is found.

Figure 3

$Q_D$ values as a function of principal quantum number $n$. The average number of detected Rydberg atoms is kept constant at about 30.

Figure 4

State-selective field ionization spectra taken under the same conditions as in Fig. 3 for the indicated principal quantum numbers. The linear field ionization ramp pulse starts at time $t=0$. Only the case $n=79$ shows a very small free-electron component.