Kilometer-Scale Ion-Photon Entanglement with a Metastable $^{88}$Sr$^{+}$ Qubit

TL;DR

The paper demonstrates direct infrared ion-photon entanglement between a metastable $^{88}$Sr$^{+}$ ion qubit and a polarization-encoded $1092$ nm photon, with the photon transmitted over a field-deployed $2.8$ km fiber. Tomography yields high fidelities in both lab ($F=0.949(4)$) and field ($F=0.929(5)$) settings, establishing Sr$^{+}$ as a telecom-compatible node for metropolitan quantum networks. The demonstrated entanglement rates ($350(4)$ s$^{-1}$ lab; $15.9(4)$ s$^{-1}$ field) and identified error sources (magnetic noise, polarization drift) provide a concrete roadmap for improving reliability via stabilization or alternative encodings. Overall, the work presents a significant step toward city-scale quantum networking using infrared transitions that align with existing fiber infrastructure.

Abstract

We demonstrate entanglement between the polarization of an infrared photon and a metastable $^{88}$Sr$^+$ ion qubit. This entanglement persists after transmitting the photon over a $2.8\:$km long commercial fiber deployed in an urban environment. Tomography of the ion-photon entangled state yields a fidelity of $0.949(4)$ within the laboratory and $0.929(5)$ after fiber transmission, not corrected for readout errors. Our results establish the Strontium ion as a promising candidate for metropolitan-scale quantum networking based on an atomic transition at $1092\:$nm, a wavelength compatible with existing telecom fiber infrastructure.

Figures (7)

• Figure 1: Quantum networking scheme. a) Reduced level diagram in $^{88}$Sr$^+$. The atomic qubit states $|0\rangle$ and $|1\rangle$ are $|4D_{3/2},-3/2\rangle$ and $|4D_{3/2},+1/2\rangle$ respectively. A short pulse of $\sigma^-$ light at $422\:$nm excites population from $|5S_{1/2},+1/2\rangle$ to $|5P_{1/2},-1/2\rangle$. Ion-photon entanglement at $1092\:$nm is generated upon decay to $4D_{3/2}$. b) Experimental setup. The emission patterns of the $\pi$ and $\sigma$ polarizations are shown with the ion at the center. By symmetry, $\pi$ light is not collected into the fiber, since the collection optics are parallel to the magnetic field. The photons are sent through SMF-$28$ optical fiber of length $2\:$m or $2.8\:$km. A series of three waveplates ($\lambda/4$, $\lambda/2$, and $\lambda/4$) provides full control over the polarization state of the photon. A Wollaston prism acts as a beam splitter before two detectors (SNSPDs).
• Figure 2: Experimental sequence for generation of ion-photon entanglement. After laser cooling, up to $50$ attempts of entanglement generation are made. Each includes optical pumping to $|5S_{1/2},+1/2\rangle$ and then excitation to $|5P_{1/2},-1/2\rangle$. The wait time before detection depends on the length of fiber. If a photon click is registered on one of the two detectors during the detection window, the sequence proceeds to ion state rotation and measurement. Each attempt includes about $500\:$ns of latency.
• Figure 3: Results. The density matrix is reconstructed using Maximum Likelihood Estimation for the ion-photon entangled state through (a) $2\:$m of optical fiber in the laboratory, resulting in a fidelity of $0.949(4)$ and a purity of $0.908(7)$, and (b) $2.8\:$km of optical fiber deployed underground, resulting in a fidelity of $0.929(5)$ and a purity of $0.899(9)$. No active polarization stabilization is used for the deployed fiber. Due to the imbalanced coefficients in the entangled state, the diagonal elements are not equal. Ideal values are shown as outlines on the bars.
• Figure 4: Map of the fiber loop in downtown Durham, NC. The laboratory is located at the Duke Quantum Center (DQC). The fiber runs underground except for the locations marked by the green circles, which are network utility rooms. The fiber contains three splices and no connectors along its length.
• Figure A1: Qubit detection scheme. We use two different readout sequences for the two state populations. To detect the $|0\rangle$ state, shown in (a), we first optically pump the $|1\rangle$ state to $4D_{5/2}$, using a 408 nm $\sigma^+$ beam and a 1004 nm $\sigma^-$ beam. These beams also pump the $|4D_{3/2},-1/2\rangle$ and $|4D_{3/2},+3/2\rangle$ states to $4D_{5/2}$. We then turn on the 422 and 1092 nm lasers to detect the population that remains in $4D_{3/2}$, which is any population in $|0\rangle$. Detection of bright indicates $|0\rangle$ population. If the experimental errors that lead to population in $|4D_{3/2},-1/2\rangle$ and $|4D_{3/2},+3/2\rangle$ were negligible, detection of dark would indicate population in $|1\rangle$ with high fidelity. However, such leakage errors are non-negligible in our experiment. Thus, a separate detection method is required to measure $|1\rangle$. The experiment is re-run, this time with the measurement scheme shown in (b). A Raman $\pi$-pulse first flips the $|0\rangle$ and $|1\rangle$ states. The 408 and 1004 nm beams are then turned on to shelve. Finally, 422 and 1092 nm are used to detect the population remaining in $4D_{3/2}$, which this time corresponds to $|1\rangle$. In both sequences, population that has left the qubit manifold is detected as dark. Therefore, by post-selecting on bright events only, we are able to exclude those errors.