Imaging Spatial Correlations of Rydberg Excitations in Cold Atom Clouds

We use direct spatial imaging of cold ${}^{85}\mathrm{Rb}$ Rydberg atom clouds to measure the Rydberg-Rydberg correlation function. The results are in qualitative agreement with theoretical predictions [F. Robicheaux and J. V. Hernández, Phys. Rev. A 72, 063403 (2005)]. We determine the blockade radius for states $44D_{5/2}$, $60D_{5/2}$, and $70D_{5/2}$ and investigate the dependence of the correlation behavior on excitation conditions and detection delay. Experimental data hint at the existence of long-range order.

Figure 1

(a) Overview of excitation region and ion detection. (b) Exploded view of electrodes that surround the excitation region, used for electric-field control. The purple, blue, and yellow electrodes allow electric-field control in the $z$, $y$, and $x$ directions, respectively. Green and red electrodes are grounded.

Figure 2

Stages in the image analysis process, using state $44D_{5/2}$. All have the same scale. (a) Raw image (cropped), (b) $X$, filtered image, (c) sum of filtered images, (d) $\overline{A}$, sum of autocorrelations, (e) $B$, autocorrelation of the sum of images, (f) ${\overline{A}}^1$, normalized autocorrelation.

Figure 3

Autocorrelations $\overline{A}$ for $44D_{5/2}$, $60D_{5/2}$, and $70D_{5/2}$. In the data sets shown we use a laser intensity of $3.4I_{\mathrm{sat}}$ for the lower transition and the lowest intensity setting (nearest the saturation knee) for the upper transition.

Figure 4

Angular average of ${\overline{A}}^1$, $I(r)$, for $44D_{5/2}$, $60D_{5/2}$, and $70D_{5/2}$. Curves correspond to images in Fig. 3.

Figure 5

Comparison of blockade radius measurements ($+$) with predictions ($\times$) based on Ref. 15.

Figure 6

Some autocorrelations ($\overline{A}$) showing possible long-range and angular structure for state $44D_{5/2}$.