Continuously tunable single-photon level nonlinearity with Rydberg state wave-function engineering

TL;DR

This work addresses the challenge of achieving tunable nonlinear optical interactions at the single-photon level by introducing microwave-assisted wave-function engineering of Rydberg–Rydberg interactions, allowing continuous control of the effective interaction $V^{++}$ over two orders of magnitude. The authors develop a four-state model and derive an expression for $V^{++}$ that includes both dipole-dipole and van der Waals contributions, then demonstrate, via Rydberg-EIT storage in a cold $^{87}$Rb ensemble, that the nonlinear interaction and associated dephasing can be tuned by adjusting the microwave detuning $\Delta$ and the mixing angle $\theta$. Experimentally, they show that $g^{(2)}(0)$ decays faster under MW dressing, achieving $g^{(2)}(0) \approx 5\times10^{-3}$ at ~400 ns for resonant dressing and reaching $\approx 0.082(23)$ at 500 ns for low-$n$ states, with dynamic MW-on/off control enabling on-demand tuning. These results imply significant potential for fast, high-purity single-photon generation and enhanced circuit depth/connectivity in Rydberg-based quantum information processing, and offer a pathway to broader photonic quantum operations using low-lying Rydberg states.

Abstract

Extending optical nonlinearity into the extremely weak light regime is at the heart of quantum optics, since it enables the efficient generation of photonic entanglement and implementation of photonic quantum logic gate. Here, we demonstrate the capability for continuously tunable single-photon level nonlinearity, enabled by precise control of Rydberg interaction over two orders of magnitude, through the use of microwave-assisted wave-function engineering. To characterize this nonlinearity, light storage and retrieval protocol utilizing Rydberg electromagnetically induced transparency is employed, and the quantum statistics of the retrieved photons are analyzed. As a first application, we demonstrate our protocol can speed up the preparation of single photons in low-lying Rydberg states by a factor of up to ~ 40. Our work holds the potential to accelerate quantum operations and to improve the circuit depth and connectivity in Rydberg systems, representing a crucial step towards scalable quantum information processing with Rydberg atoms.

Figures (7)

• Figure 1: Interaction control via Rydberg-Rydberg wave-function dressing. (a) The relevant atomic levels: the ground state $\ket{g} = \ket{5S_{1/2}, F=2, m_F=2}$, the intermediate state $\ket{e} = \ket{5P_{3/2}, F=3, m_F=3}$, two Rydberg states $\ket{r_1}$ and $\ket{r_2}$ with different parities, and the MW-dressed Rydberg states $\ket{+}$ and $\ket{-}$ when the microwave is in resonance with two Rydberg states $\ket{r_1}$ and $\ket{r_2}$. The 780nm photons is resonant with $\ket{g} \leftrightarrow \ket{e}$, and the 480nm control field resonantly couples the $\ket{e}$ and $\ket{+}$ states.
• Figure 2: Simulation of Rydberg dephasing dynamics. (a) The exponential distribution $e^{iV^{vdW}_{jj\prime}t/\hbar}$ of the Rydberg interaction-induced phase at different interaction time. The x-axis represents the real part of the $e^{iV^{vdW}_{jj\prime}t/\hbar}$, while the y-axis represents its imaginary part. The z-axis corresponds to the normalized probability for a given phase. The result is simulated under the vdW interaction for bare state $\ket{r_1}=\ket{47D_{5/2}, J=5/2, m_J=5/2}$, via the Monte-Carlo method. (b) (c) Similar to (a) but displaying the exponential distribution $e^{iV^{++}_{jj\prime}t/\hbar}$ for the Rydberg MW-dressed states with $\Delta=-2\Omega_\mathrm{MW}$ (b) and $\Delta=0$ (c).
• Figure 3: Acceleration of quantum operations via Rydberg-Rydberg dressing. Simulated $g^{(2)}(0)$ as a function of interaction time $t$ for atoms in the bare state $\ket{r_1}=\ket{47D_{5/2}, J=5/2, m_J=5/2}$, and dressed states. The orange-colored dashed line is the threshold for $g^{(2)}(0)=0.1$.
• Figure 4: Enhanced interactions and dephasing dynamics with low-lying Rydberg states. (a) The interaction strength on a logarithmic scale as a function of inter-atomic distance $R$ for low-lying Rydberg state $\ket{r_1}=\ket{29D_{5/2}, J=5/2, m_J=5/2}$ and dressed states with different MW detunings. (b) Simulated $g^{(2)}(0)$ as a function of interaction time $t$ for the bare state and for the MW-dressed Rydberg states under the interactions shown in (a).
• Figure 5: Illustration of the experimental protocol. (a) A cold $^{87}$Rb atomic ensemble with a temperature of $\sim$ 10µK and an optical depth of $\sim 3.5$ is confined in a 1012nm optical dipole trap. The counter-propagating 780nm and 480nm laser beams are focused onto the atomic ensemble. The quantum statistics of the retrieved photons are measured using a Hanbury Brown-Twiss (HBT) setup consisting of a 50:50 beam splitter, followed by two single-photon counting modules (SPCMs). (b) Experimental timing sequence. The total duration of the storage-and-retrieval process is 5µs covered by the dressing microwave, shown as the gray wave packet. The 780nm input field is a $50ns$ long weak coherent light pulse with a mean photon number $\braket{n}=0.4$, represented by the pink wave packet. By optimizing the falling edges of the blue 480nm control field to maximize the storage efficiency ($24\%$ limited by the optical depth OD $\sim 3.5$), the input photons are stored in the atomic ensemble. The interaction time $t$ in the experiment is variable, ranging from 190ns to 1000ns in the experiment, and can be extended to its decoherence time in principle.