Deterministic Time-Bin Entanglement between a Single Photon and an Atomic Ensemble

Peng-Fei Sun, Yong Yu, Zi-Ye An, Jun Li, Chao-Wei Yang, Xiao-Hui Bao, and Jian-Wei Pan

Phys. Rev. Lett. 128, 060502 – Published 10 February 2022

Abstract

Hybrid matter-photon entanglement is the building block for quantum networks. It is very favorable if the entanglement can be prepared with a high probability. In this Letter, we report the deterministic creation of entanglement between an atomic ensemble and a single photon by harnessing the Rydberg blockade. We design a scheme that creates entanglement between a single photon’s temporal modes and the Rydberg levels that host a collective excitation, using a process of cyclical retrieving and patching. The hybrid entanglement is tested via retrieving the atomic excitation as a second photon and performing correlation measurements, which suggest an entanglement fidelity of 87.8%. Our source of matter-photon entanglement will enable the entangling of remote quantum memories with much higher efficiency.

Received 5 August 2021
Accepted 20 January 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.060502

Physics Subject Headings (PhySH)

Entanglement production Quantum memories Quantum networks Quantum repeaters Quantum state engineering

Atomic ensemble Rydberg atoms & molecules

Quantum Information, Science & Technology

Authors & Affiliations

Peng-Fei Sun ^1,2,*, Yong Yu ^1,2,*, Zi-Ye An^1,2, Jun Li ^1,2, Chao-Wei Yang^1,2, Xiao-Hui Bao ^1,2, and Jian-Wei Pan^1,2

¹Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
²CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

^*These authors contributed equally to this work.

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Vol. 128, Iss. 6 — 11 February 2022

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Figure 1
Scheme of generating deterministic time-bin entanglement. In the first phase, we prepare a Rydberg superposition state $(| R_{1} ⟩ + | R_{2} ⟩) / \sqrt{2}$ . In the second phase, we apply the cyclical “retrieving and patching” process for $| R_{1} ⟩$ and $| R_{2} ⟩$ in sequence, which results in a retrieval photon whose temporal mode is entangled with the Rydberg levels of the collective excitation. In the last phase, we detect the atomic state via retrieving it to the temporal mode of a second photon. The excitation and patching process involve a two-photon Raman process. Spatial arrangement of the Raman beams is shown in Fig. 2. Numerically filled circles indicate relative time sequences of all the steps.
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Figure 2
Experimental setup. (a) Observed collective Rabi oscillations. Light blue dots represent the oscillation between $| G ⟩$ and $| R_{1} ⟩$ and dark blue dots represent the oscillation between $| G ⟩$ and $| R_{2} ⟩$ . Dashed lines are the fitting results, indicating a $π$ pulse duration of 92.95 ns and 92.18 ns for $| R_{1} ⟩$ and $| R_{2} ⟩$ , respectively. (b) Layout of the experiment. The 795 nm beam counterpropagates with the 474 nm beams, all of which are tightly focused to address a small region of the atomic cloud to define a mesoscopic ensemble with full blockade (more details available in [56]). Single photons are retrieved in the $x$ direction, and are afterwards subjected to fiber coupling, temporal filtering, interfering through an unbalanced MZ interferometer, switching, rotating in polarization, and final detecting sequentially. The fibers used in the two arms of the MZ interferometer are 65 m and 5 m which give a relative photon delay of about 300 ns. The interferometer is actively stabilized by injecting a locking beam into the idle port. Our experiment involves four blue beams ( $B_{1} / B_{2} / C_{1} / C_{2}$ ), which differentiate from each other in polarization, frequency, or both. We make use of a multiplexing scheme shown as the inset of Fig. 2 to adjust the frequencies dynamically and combine the beams into a single-mode fiber. ${AOM}_{2}$ is merely used for the Bell measurement. Polarization of the retrieved single photons is $σ^{-}$ , which is later rotated to vertical ( $V$ ) with the wave plates before ${AOM}_{1}$ . The electro-optic modulator (EOM) preserves the vertical polarization for the $| E ⟩$ mode, while switches it to horizontal ( $H$ ) for the $| L ⟩$ mode. Thus the interferometer makes an effective degree-of-freedom transformation of $| E ⟩ \to | V ⟩$ and $| L ⟩ \to | H ⟩$ . The setting for the wave plates in front of the detectors varies for different measurement bases. Some abbreviations: half-wave plate (HWP), quarter-wave plate (QWP), polarizing beam splitter (PBS), high reflection mirror (HR), dichroic mirror (DM), photodiode (PD).
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Figure 3
Temporal profile for the single photons. Pulse labels in the time sequence are defined in Fig. 1. Measurement is performed in the eigenbasis of $| E ⟩ / | L ⟩$ . Temporal delays through the unbalanced interferometer are corrected to differentiate different time-bin modes. The four peaks in the profile refer to the modes of $| E ⟩$ , $| L ⟩$ , $| E ⟩^{'}$ , and $| L ⟩^{'}$ in sequence. Amplitudes for the last two modes are slightly smaller, which is mainly due to incomplete retrieval of the Rydberg excitations.
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Figure 4
Photon counting result. (a) Verification of the initial Rydberg state preparation. $(| R_{1} ⟩ + | R_{2} ⟩) / \sqrt{2}$ is converted to $(| E ⟩^{'} + e^{i ϕ} | L ⟩^{'}) / \sqrt{2}$ and measured in the basis of $(| E ⟩^{'} \pm | L ⟩^{'}) / \sqrt{2}$ . Dependence on the internal phase $ϕ$ is plotted. Dashed lines are the fitting results. (b) Characterization of the entanglement $| Ψ ⟩_{p p} = (1 / \sqrt{2}) (| E ⟩ | E ⟩^{'} + e^{i ψ} | L ⟩ | L ⟩^{'})$ via correlation measurement. In the eigenbasis, the sum of $| E ⟩ | E ⟩^{'}$ and $| L ⟩ | L ⟩^{'}$ coincidences is shown in dark blue, while the sum of $| E ⟩ | L ⟩^{'}$ and $| L ⟩ | E ⟩^{'}$ coincidences is shown in orange. In the superposition basis, the sum of $| + ⟩ | + ⟩^{'}$ and $| - ⟩ | - ⟩^{'}$ coincidences is shown in red, while the sum of $| + ⟩ | - ⟩^{'}$ and $| - ⟩ | + ⟩^{'}$ is shown in light blue. The dashed lines are the fitting results.
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