Control and Entanglement of Individual Rydberg Atoms near a Nanoscale Device

Coherent control of Rydberg atoms near dielectric surfaces is a major challenge due to the large sensitivity of Rydberg states to electric fields. We demonstrate coherent single-atom operations and two-qubit entanglement as close as $100\mathrm{\mu }\mathrm{m}$ from a nanophotonic device. Using the individual atom control enabled by optical tweezers to study the spatial and temporal properties of the electric field from the surface, we employ dynamical decoupling techniques to characterize and cancel the electric-field noise with submicrosecond temporal resolution. We further use entanglement-assisted sensing to accurately map magnitude and direction of electric-field gradients on a micrometer scale. Our observations open a path for integration of Rydberg arrays with micro- and nanoscale devices for applications in quantum networking and quantum information science.

Figure 1

Rydberg spectral shift. (a) Experimental setup. (b) Two-photon excitation to the Rydberg state, which is shifted by electric fields (yellow shade). (c) Ground state population $P_g$ as a function of the two-photon detuning $\mathrm{\Delta }$ at $150\mathrm{\mu }\mathrm{m}$ from the device, where the spectrum center (dashed line) is determined via a Lorentzian fit (black line). (d) Measured spectral shift as a function of distance from the device fitted to a point-charge model (yellow line, Supplemental Material [37], Sec. 2.1). The shift only exceeds the Rabi-broadened linewidth (shaded gray region) for distances less than $250\mathrm{\mu }\mathrm{m}$. Inset: spectral shift dependence on UV power at $160\mathrm{\mu }\mathrm{m}$.

Figure 2

Ground-Rydberg qubit coherence. Ground state population $P_g$ as measured after a Ramsey (a), spin-echo (b), and Carr-Purcell (CP) $N=2$ (c) pulse sequences at $130\mathrm{\mu }\mathrm{m}$ [dotted line in (d)]. A decaying sinusoid fit (blue line) gives $T_2^{*}=200(40)\mathrm{ns}$ and a Gaussian decay function (red line) gives $T_2=4.1(2)\mathrm{\mu }\mathrm{s}$. The CP $N=2$ data exhibits no decay within the measurement time. (d) Measured $T_2$ (red circles) and $T_2^{*}$ (blue circles) as a function of distance from the device. The solid lines are fits to the data given our decoherence model (Supplement Material [37], Sec. 4). The shaded green region is a lower bound on the CP $N=2$ coherence time.

Figure 3

Two-atom entangled state. (a) The Rydberg interaction $U$ shifts the $|rr⟩$ state and allows the preparation of the $|W⟩=(1/\sqrt{2})(|gr⟩+|rg⟩)$ state. (b) Tomography of the $|W⟩$ state (purple) at $170\mathrm{\mu }\mathrm{m}$. We measure population ${\rho }_{rg,rg}+{\rho }_{gr,gr}=0.87(5)$ and coherence $2|{\rho }_{gr,rg}|=0.78(7)$ with correction for preparation error and loss (light purple). (c) Comparison between the two-atom $|W⟩$ state lifetime $T_W$ (purple circles) and the single-atom ground-Rydberg coherence time $T_2^{*}$ {gray circles, data and fit from [Fig. 2]}. The dotted purple line is a theoretical prediction (Supplemental Material [37], Sec. 5.4).

Figure 4

Entanglement-assisted sensing of electric-field gradients. (a) The orientation of an entangled atom pair is varied with respect to the device. (b) The $|W⟩$ state lifetime measurement (blue circles) reveals gradient-induced oscillations by fitting to a decaying sinusoid (blue lines) for different $\theta$ (offset for clarity). (c) Angular dependence of the fitted oscillation frequency at different $x$ (circles) with solid curves being simultaneous fit (Supplemental Material [37], Sec. 6) to extract background field orientation. (d) A 200 nW UV-power reduction from its optimized value causes a rotation (53°) of the gradient. (e) Reconstructed electric-field magnitude $|\overrightarrow{E}|$ (contour scale) and direction (white arrows) given the measurements in (c) at the positions of the black circles. (f) Electric-field contour plot reconstructed from (d) showing direction at the optimal UV value (gray arrow) and shifted UV value (orange arrow).