Depletion Imaging of Rydberg atoms in cold atomic gases

TL;DR

This work introduces depletion imaging as a fully optical, non-destructive method to map the integrated 2D density of ultracold Rydberg atoms by comparing ground-state absorption with and without pre-excitation. Using a two-photon excitation to a Rydberg state in a cold rubidium gas, the authors reconstruct the local Rydberg fraction and observe rapid center-region saturation due to Rydberg blockade, while the tails evolve more slowly. A Monte Carlo master-equation approach incorporating blockade effects quantitatively reproduces the observed dynamics and extracts spatially varying effective Rabi frequencies, enabling a 3D reconstruction of the Rydberg distribution to seed many-body spin simulations. The technique provides a robust diagnostic for local Rydberg dynamics and can be extended to three-dimensional tomography, aiding investigations of Ising-like and Heisenberg spin dynamics in higher dimensions.

Abstract

We present a depletion imaging technique to map out the spatial and temporal dependency of the density distribution of an ultracold gas of Rydberg atoms. Locally resolved absorption depletion, observed through differential ground state absorption imaging of a $^{87}\text{Rb}$ cloud in presence and absence of pre-excited Rydberg atoms, reveals their projected two-dimensional distribution. By employing a closed two-level optical transition uncoupled from the Rydberg state, the highly excited atoms are preserved during imaging. We measure the excitation dynamics of the $\vert48S\rangle$ state of $^{87}\text{Rb}$, observing a saturation of the two-dimensional Rydberg density. Such outcome can be explained by the Rydberg blockade effect which prevents resonant excitation of close-by Rydberg atoms due to strong dipolar interactions. By combining the superatom description, where atoms within a blockade radius are represented as collective excitations, with a Monte Carlo sampling, we can quantitatively model the observed excitation dynamics and infer the full three-dimensional distribution of Rydberg atoms, that can serve as a starting point for quantum simulation of many-body dynamics involving Rydberg spin systems.

Figures (3)

• Figure 1: Experimental observation of Rydberg atoms by depletion imaging. (a) Excitation scheme and experimental sequence. The two-photon excitation pulse is applied during a variable time $t_{exc}$, then resonant absorption imaging is performed with fixed exposure time $t_{exp}=5µs$. (b) Geometry of the experimental setup. The cloud of [87]Rb atoms in their electronic ground state is prepared in an ellipsoid shape by an optical dipole trap. A vertical $780nm$ laser beam is used for Rydberg excitation, in combination with an horizontal $480nm$ laser beam, tilted by $45°$ with respect to the dipole trap axis. To measure absorption, a counter-propagating probe laser beam uniformly illuminates the cloud and the transmitted photons are collected onto a CCD camera through an imaging system.
• Figure 2: Typical two-dimensional density distributions observed during depletion imaging experiments, averaged over 50 realizations and with $16\,a_{px}$ binning. (a) Ground state density without atoms excited to the Rydberg state, obtained from the optical density $\mathrm{OD}=1-A$ with a peak $\mathrm{OD}=0.7$. (b) Ground state density depleted by atoms pre-excited to the Rydberg state for $t_{exc}=3µs$. (c) Rydberg density for $t_{exc}=3µs$ (peak $\mathrm{OD}=0.2$) obtained by depletion imaging through Eq. \ref{['eq:density2D']} from the difference in cloud absorption between the realizations presented in (a) and (b). (d) Signal-to-noise ratio within the Rydberg density distribution, along a cut through $y=0$, determined from the fluctuations of the individual realizations.
• Figure 3: Spatially resolved Rydberg excitation dynamics, averaged over 50 repetitions with $16\,a_{px}$ binning. (a) Two-dimensional Rydberg fraction distribution $\rho^\mathrm{2D}_r(x,y)$, integrated over $\hat{z}$, for increasing excitation times of $0.83$, $1.55$, $2.28$ and $3.00µs$. (b) Local excitation dynamics at different cloud positions, marked with hollow squares on the $\rho^\mathrm{2D}_r(x,y)$ distribution in (a). The solid lines represent the simulated dynamics with the master equation Monte Carlo model, using a dephasing of $\gamma/2\pi = 0.25MHz$ and effective Rabi frequencies $\Omega_{\text{eff}}/2\pi = 0.17MHz$ (blue line), 0.14MHz (green line), 0.12MHz (red line) and 0.07MHz (turquoise line). Inset: evolution of the global mean Rydberg atom number with $t_{exc}$. (c) Effective Rabi frequency distribution $\Omega_{\text{eff}}(x,y)$, obtained by locally fitting the excitation dynamics with the Monte Carlo model within each $64\,a_{px}$ bin. (d) Reconstructed 3D distribution of the Rydberg atom cloud by the Monte Carlo simulations for $t_{exc}=3µs$. The dots represent a discrete Rydberg atom arrangement obtained in a single run, whereas the continuous distribution corresponds to the Rydberg density averaged over 50 realizations.