Full Counting Statistics of Laser Excited Rydberg Aggregates in a One-Dimensional Geometry

We experimentally study the full counting statistics of few-body Rydberg aggregates excited from a quasi-one-dimensional atomic gas. We measure asymmetric excitation spectra and increased second and third order statistical moments of the Rydberg number distribution, from which we determine the average aggregate size. Estimating rates for different excitation processes we conclude that the aggregates grow sequentially around an initial grain. Direct comparison with numerical simulations confirms this conclusion and reveals the presence of liquidlike spatial correlations. Our findings demonstrate the importance of dephasing in strongly correlated Rydberg gases and introduce a way to study spatial correlations in interacting many-body quantum systems without imaging.

Figure 1

(a) Level scheme and many-body energies in a rotating frame for Rydberg aggregates of size $m$ as a function of laser detuning $\mathrm{\Delta }$. The shaded areas indicate the manifold of excited states corresponding to different spatial configurations. Zero energy crossings for the lowest energy states occur at ${\mathrm{\Delta }}_m=C_6{(m-1)}^7/(m{L}^6)$, where $L$ is the system length and $C_6$ is the van der Waals interaction strength. For a given detuning and laser dephasing, aggregates of different sizes are formed (dotted rectangle), either through sequential growth or by multiphoton excitation. (b) Measured histograms of the Rydberg atom number distribution for different detunings. The solid lines are the results of the numerical simulations (see text).

Figure 2

Rydberg excitation spectra for different atomic densities: $5\times 10^{10}{\mathrm{cm}}^{-3}$ (blue circles), $2\times 10^{11}{\mathrm{cm}}^{-3}$ (cyan triangles), $8\times 10^{11}{\mathrm{cm}}^{-3}$ (green triangles), $1.2\times 10^{12}{\mathrm{cm}}^{-3}$ (magenta diamonds), and $1.5\times 10^{12}{\mathrm{cm}}^{-3}$ (red squares). With increasing density we find enhanced excitation probabilities on the blue side of the resonance due to repulsive Rydberg-Rydberg interactions. The solid lines show the result of the rate equation model.

Figure 3

$Q$ (a) and $Q_3$ (b) as a function of the detuning $\mathrm{\Delta }$ at a density of $1.5\times 10^{12}{\mathrm{cm}}^{-3}$. The red diamonds (blue circles) are extracted from a data set with 200 (800) experiments per data point. Error bars represent 68% confidence intervals determined via bootstrapping. The dashed lines indicate the expected $Q$ and $Q_3$ factors corresponding to the excitation of exclusively single atoms, pairs, and triples. The solid lines show the statistical moments as obtained from the rate equation model.

Figure 4

Pair correlation functions $G_2(r)$ obtained from the RE model. The blue curve shows the correlation function for $\mathrm{\Delta }=5\mathrm{MHz}$, the red curve for $\mathrm{\Delta }=15\mathrm{MHz}$. The inset shows MCWF simulations for $\mathrm{\Delta }=15\mathrm{MHz}$, and dephasing rates $\mathrm{\Gamma }=0$ (green, dotted) and $\mathrm{\Gamma }=1\mathrm{MHz}$ (green, dashed), compared to the RE simulation with $\mathrm{\Gamma }=1\mathrm{MHz}$ (red, solid). To improve visibility, the dotted curve is scaled by a factor of $1/10$. The different peak amplitudes between the inset and main figure are due to the different simulation volumes and finite-size effects.