Spin Squeezing by Rydberg Dressing in an Array of Atomic Ensembles

We report on the creation of an array of spin-squeezed ensembles of cesium atoms via Rydberg dressing, a technique that offers optical control over local interactions between neutral atoms. We optimize the coherence of the interactions by a stroboscopic dressing sequence that suppresses super-Poissonian loss. We thereby prepare squeezed states of $N=200$ atoms with a metrological squeezing parameter ${\xi }^2=0.77(9)$ quantifying the reduction in phase variance below the standard quantum limit. We realize metrological gain across three spatially separated ensembles in parallel, with the strength of squeezing controlled by the local intensity of the dressing light. Our method can be applied to enhance the precision of tests of fundamental physics based on arrays of atomic clocks and to enable quantum-enhanced imaging of electromagnetic fields.

Figure 1

Experimental setup. (a) An array of atomic ensembles is locally illuminated with 319 nm Rydberg dressing light, inducing interactions of characteristic range $r_c$. (b) Level diagrams for one atom (left) and a pair of atoms (right), where $|+⟩=(|r\uparrow ⟩+|\uparrow r⟩)/\sqrt{2}$ and $|\tilde{\uparrow }⟩$ denotes the Rydberg-dressed state. (c) Interactions generate an $S_z$-dependent precession (twisting) of the collective spin $\mathbf{S}$ that shears a coherent state (left) into a squeezed spin state (right).

Figure 2

Stroboscopic Rydberg dressing. (a) An equal superposition of states $|\uparrow ⟩$ and $|\downarrow ⟩$ is prepared by a $\pi /2$ microwave rotation (purple) and subjected to dressing pulses of length ${\tau }_p$ (blue) at intervals ${\tau }_d$. (b) Atoms in contaminant states $|c⟩$ (orange) influence dressed atoms $|\tilde{\uparrow }⟩$ (purple-blue). (c) Histograms of $S_z$ for one microtrap with (blue) or without (gray) dressing light. Broadening observed for continuous dressing (top, ${\tau }_d=0$) is suppressed by pulse delay ${\tau }_d=100\mathrm{\mu }\mathrm{s}$ (bottom). (d) Normalized variance versus loss, plotted across microtraps for ${\tau }_d=0\mathrm{\mu }\mathrm{s}$. Linear fit (red) reports atoms being lost in groups of size $g=17(1)$. Green shows Poissonian loss ($g=1$). (e) Normalized variance, averaged across three central microtraps, versus pulse delay for ${\tau }_p=628\mathrm{ns}$, $M=48$. Fitting to ${\sigma }^2=A\exp (-\gamma {\tau }_d)+1$ yields ${\gamma }^{-1}=29(9)\mathrm{\mu }\mathrm{s}$. “$\mathbf{\times }$” markers in (d) and (e) denote data shown in (c).

Figure 3

Quantifying interactions. (a) Microwave (purple) and dressing (blue) pulse sequence for measuring the ac Stark shift $U$ by Ramsey spectroscopy. (b) $U(\mathrm{\Delta })$ measured at $\theta =(\pi /4,\pi /2,3\pi /4)$ (green squares, orange triangles, blue circles). Solid lines show fits that determine ${\mathrm{\Omega }}_{\mathrm{p}}$ and $N_c^{\uparrow }$. Inset: visualization of accumulated phase $\varphi$. (c) $N_c^{\uparrow }({\mathrm{\Delta }}_{*})$ versus ${\cos }^2(\theta /2)$, with linear fit (red line) of slope $N_c$. (d) Fitted number of neighbors (bottom) and Rabi frequency (top).

Figure 4

Spin squeezing. (a) Sequence of microwave (purple) and dressing (blue) pulses for preparing the initial state $|\pi /2⟩$, implementing one-axis twisting with spin echo, and measuring $S_{\alpha }$. (b) Squeezing parameter ${\xi }^2$ versus $\alpha$ for one microtrap, measured with (blue circles) and without (gray squares) dressing. (c) Top: fluorescence image of microtraps. Middle: minimum (${\xi }_{\min }^2$, green circles) and maximum (${\xi }_{\max }^2$, orange diamonds) squeezing parameters after dressing. Bottom: twisting strength $Q$ (blue circles). Gray squares represent ${\xi }^2({\alpha }_{\mathrm{opt}})$ with no dressing light. Gray dotted line denotes ${\mathcal{C}}_0^{-2}$. Blue shaded region is a guide to the eye for the twisting strength used to predict squeezing (green shaded) and antisqueezing (orange shaded). Yellow shading indicates microtrap shown in (b). (d) Squeezing (green circles) and antisqueezing (orange diamonds) versus $Q$. Solid lines denote parameter-free model of one-axis twisting for $N_c$ atoms with initial contrast ${\mathcal{C}}_0$. Dotted lines add 7% technical noise, consistent with excess noise observed without dressing in (c).