Quantum Storage of Three-Dimensional Orbital-Angular-Momentum Entanglement in a Crystal

Zong-Quan Zhou, Yi-Lin Hua, Xiao Liu, Geng Chen, Jin-Shi Xu, Yong-Jian Han, Chuan-Feng Li, and Guang-Can Guo

Phys. Rev. Lett. 115, 070502 – Published 13 August 2015

Abstract

Here we present the quantum storage of three-dimensional orbital-angular-momentum photonic entanglement in a rare-earth-ion-doped crystal. The properties of the entanglement and the storage process are confirmed by the violation of the Bell-type inequality generalized to three dimensions after storage ( $S = 2.152 \pm 0.033$ ). The fidelity of the memory process is $0.993 \pm 0.002$ , as determined through complete quantum process tomography in three dimensions. An assessment of the visibility of the stored weak coherent pulses in higher-dimensional spaces demonstrates that the memory is highly reliable for 51 spatial modes. These results pave the way towards the construction of high-dimensional and multiplexed quantum repeaters based on solid-state devices. The multimode capacity of rare-earth-based optical processors goes beyond the temporal and the spectral degree of freedom, which might provide a useful tool for photonic information processing.

Received 24 January 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.070502

Authors & Affiliations

Zong-Quan Zhou, Yi-Lin Hua, Xiao Liu, Geng Chen, Jin-Shi Xu, Yong-Jian Han, Chuan-Feng Li^*, and Guang-Can Guo

Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, China and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China

^*cfli@ustc.edu.cn

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Vol. 115, Iss. 7 — 14 August 2015

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Figure 1
Schematic diagram of the experimental setup. The photon pairs are generated in the 20-mm PPKTP crystal via spontaneous parametric down-conversion (SPDC). The pump source is obtained by sending the master laser to a frequency doubler. AOM1 and AOM2 are used to ensure the frequency matching between the atomic frequency comb (AFC) and the center frequency of the photon pairs. The blue pump light is then removed by the dichroic mirror (DM). The photon pairs are spectrally filtered by the two etalons. The two photons in the pair are separated by the polarization beam splitter (PBS). The signal photon of each pair is directed to the memory hardware; the idler photon is forced to propagate through a 16.4-m delay line and is then analyzed with a spatial light modulator (SLM) and a single-mode fiber (SMF). AOM3 and the two electro-optic modulators (EOMs) together generate the pump light for AFC preparation. The polarization of the signal photons is controlled by the half-wave plates (HWPs). The AFC preparation light and the signal photons overlap at the sample position, with a small angle (20 mrad) between them. The ${Nd}^{3 +} ∶ {YVO}_{4}$ crystal is placed in a cryostat (Oxford Instruments, SpectromagPT) with a temperature of 1.5 K and a magnetic field of 0.3 T. After a programmable delay, the OAM of the retrieved signal photons is analyzed using the SLM2 and a SMF. The single-photon signals are analyzed using time-correlated single-photon counting system (TCSPC). The phase-locked mechanical choppers (MC) are used to protect the single-photon detector (SPD) during the preparation procedure. The inset shows the energy structure of ${Nd}^{3 +}$ ions. The AFC is prepared in the ground state $| g ⟩$ by frequency-selective optical pumping of atoms from $| g ⟩$ to an auxiliary Zeeman state $| aux ⟩$ . An input photon resonant with the $| g ⟩ \to | e ⟩$ transition will be stored as a collective excitation of the AFC. The AFC works as a grating in the frequency domain and diffracts the photon into a temporal-delayed echo emission. Further details are provided in Ref. [26].
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Figure 2
Graphical representation of the reconstructed density matrix of the two photon states before (a) and after (b) the storage process. The density matrix of the two qutrits is reconstructed from a set of 81 measurements represented by the operators $u_{i} \otimes u_{j}$ (with $i, j = 1, 2, \dots, 9$ ) and $u_{k} = | ψ_{k} ⟩ ⟨ ψ_{k} |$ ). The kets $| ψ_{k} ⟩$ for both the idler photons and the signal photons are selected from the following set: ${| - 1 ⟩, | 0 ⟩, | 1 ⟩, (| 0 ⟩ + | - 1 ⟩) / \sqrt{2}, (| 0 ⟩ + | 1 ⟩) / \sqrt{2}, (| 0 ⟩ + i | - 1 ⟩) / \sqrt{2}, (| 0 ⟩ - i | 1 ⟩) / \sqrt{2}, (| - 1 ⟩ + | 1 ⟩) / \sqrt{2}, (| - 1 ⟩ + i | 1 ⟩) / \sqrt{2}}$ . Detailed descriptions of the tomographic measurements are presented in Ref. [26].
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Figure 3
(a) The setup for exploration of the multimode capacity in the spatial domain of the memory. The photon source is weak coherent pulse in Gaussian mode. The pulse has a temporal width of 20 ns and contains an average of 0.5 photons per pulse. Superposition states of OAM are generated though SLM1 and analyzed by SLM2. (b) Graphical representation of the real part of the reconstructed process matrix $χ_{2}$ in three dimensions. $λ_{1}$ is the identity operator, and the detailed definitions of the basis operators $λ_{1} \sim λ_{9}$ are provided in Ref. [26]. (c) The memory performance for quantum superposition states $| ψ_{+} (l) ⟩$ . The black squares and red dots represent the visibility of the states before and after storage, respectively. The blue triangles represent the AFC storage efficiency for different values of $| l |$ .
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