Enhanced Rydberg Blockade through RF-tuned Förster Resonance

Abstract

Enhancing interactions between Rydberg atoms is a key challenge in contemporary quantum technologies. Stronger interactions enable faster Rydberg gates in digital processors and larger entangled states in analog simulation. Achieving the same interaction strength at lower principal quantum number addresses current constraints in available Rabi frequency and field sensitivity in large scale tweezer or cavity QED experiments. Here, we demonstrate a new technique using AC Stark shifts from a microwave drive to tune into a Förster resonance, thereby modifying the interaction scaling with distance from $1/R^6$ to $1/R^3$. We validate enhanced Rydberg interactions (in strength and range) by probing cavity Rydberg polariton blockade at $n=44$ in $^{87}$Rb, improving from $g^{(2)}(0) = 1.0 (1)$ in the Van-der-Waals regime to $g^{(2)}(0) = 0.38 (1)$ in the dipolar regime on the Förster resonance. Importantly, our technique allows minimal shifts of the original Rydberg state, suppressing detuning errors in gate protocols while maintaining quadratic insensitivity to DC electric fields.

Figures (10)

• Figure 1: Overview of experiment and Förster Resonance mechanism. (a) Schematic of the experimental setup: a cloud of ultracold $^{87}$Rb atoms is transported into a lens-focused cavity at $780$ nm (red) while a control field at $480$ nm (blue) excites to the Rydberg state. A microwave horn (gold) is used to inject RF fields that selectively shift different Rydberg states into a Förster resonance. Arrows indicate quantization axis $\hat{z}$ (blue) and microwave propagation direction $\hat{k}_\mu$ (orange). (b) The atomic ground $\ket{g}$, excited $\ket{e}$, and Rydberg $\ket{d}$ state are coupled by a cavity mode with collective coupling $g$ and a classical control field $\Omega_c$ to realize cavity electromagnetically induced transparency (EIT). The Rydberg state $\ket{d}$ is dipole-dipole coupled to two other Rydberg states $\ket{p}$ and $\ket{f}$ with strength $V$, where $\ket{p}$ is AC Stark shifted by driving a tuning transition to a state $\ket{t}$ far off resonance with microwave Rabi frequency $\Omega_\mu$. (c) Förster defect $\Delta_F$ as a function of principal quantum number $n$ for the two dominant channels shown in purple and green (see inset for $n=44$). At $n=43$ (gold star) a natural Förster near resonance $\Delta_F \approx 8$ MHz occurs. (d) Blockade mechanism for tuned Förster resonance: In the Van-der-Waals regime at zero tuning field, the defect between pair states $\ket{dd}$ (red) and $\ket{pf}$ (blue) is large and leads to only a small interaction shift (solid line) compared to the non-interacting case (dashed line). With increasing tuning strength and resulting $\ket{pf}$ shift, the interaction becomes dipolar and the two pair states show an avoided crossing at $\Delta_F=0$; the splitting is given by the dipolar interaction strength and the eigenstates are symmetric superpositions, indicated by the color. While the single-excited Rydberg state $\ket{d}$ is unperturbed, the second Rydberg excitation is now strongly blockaded from entering the system.
• Figure 2: AC Stark shift calculation of Rydberg states. We explore the optimal way of tuning the pair state $\ket{pf}=\ket{(n+2)P_{3/2},(n-2)F_{7/2}}$ into resonance with our target state $\ket{dd}=\ket{n D_{5/2},n D_{5/2}}$ while minimizing the shift of the latter one. We compute the AC Stark shift for the three Rydberg states (color) over a wide range of microwave driving frequencies for $\pi$- (a) and $\sigma$- (b) polarization at a field strength of $E=0.1$ V/m, see \ref{['SI:theory']}. Driving with $\pi$ polarization is optimal as it maximizes the frequency separation of the $\ket{(n+2)P_{3/2}}$ from the target state and eliminates any vector shifts that would cause a transverse coupling between magnetic sublevels. The microwave driving frequency used in the experiment of $f_{MW}=23.7$ GHz is indicated by the vertical red line.
• Figure 3: Locating the Förster Resonance: Mean field non-linearity. The condition for the Förster resonance $\Delta_F=0$ is narrow and needs careful tuning of the microwave frequency and power. To achieve this, we measure the mean-field interaction between Rydberg polaritons. (a) Depending on the intermediate state detuning $\Delta_e$ in our EIT scheme, the character of the interaction can be changed. On resonance ($\Delta_e=0$, left inset) the interaction potential is mostly imaginary leading to loss of additional polaritons, while at positive detuning the interactions are predominantly real and lead to a dispersive shift of the transmission peak and increased overall transmission (right inset). The interaction regimes are highlighted with a sigmoid function (solid line). (b) We find the exact resonance condition by measuring the EIT spectrum as a function of the microwave frequency, $f_{MW}$. (c) Corresponding Lorentzian fits to the data in (b) show a dip in transmission (orange) and a peak in line width (purple) at Förster resonance.
• Figure 4: Observation of photon blockade via Förster resonance. We measure the temporal correlation function $g^{(2)}(\tau)$ of photons transmitted through the cavity QED system. (a) Away from the resonance, interactions in the $\ket{44D_{5/2}}$ state are insufficient to blockade the $LG_{0,0}$ mode, yielding $g^{(2)}(0) = 1.0 (1)$. (b) At the Förster resonance, interactions are enhanced, resulting in a suppression of multi-photon events with $g^{(2)}(0) = 0.38 (1)$. The atomic cloud is confined to a quasi-2D geometry ($\sigma < R_b \lessapprox w_0$), ensuring that the blockade radius covers the transverse optical mode. Solid line is an analytical fit while shaded bands indicate ab initio atomistic calculations (see \ref{['SI:theory']}) using experimentally measured cloud thickness $\sigma_z$. In (a) the microwave drive is still present but intentionally detuned in frequency to exclude effects of state admixture.
• Figure S1: Experiment Setup Running wave cavity formed by four flat mirrors (only one shown) and two intra-cavity lenses at $780$ nm (red) with crossed buildup cavity (not shown) for the $480$ nm Rydberg excitation (blue). The atomic cloud (stylized atoms) is held in an elliptical lattice (light red) to confine them to a quasi two-dimensional system. Microwaves for tuning the pair state are sent in via a horn transversely to the quantization axis.