Advanced Photonics, Volume. 6, Issue 3, 036003(2024)

Parallelization of frequency domain quantum gates: manipulation and distribution of frequency-entangled photon pairs generated by a 21 GHz silicon microresonator

Antoine Henry1、*, Dario A. Fioretto2, Lorenzo M. Procopio3, Stéphane Monfray4, Frédéric Boeuf4, Laurent Vivien2, Eric Cassan2, Carlos Alonzo-Ramos2, Kamel Bencheikh2, Isabelle Zaquine1, and Nadia Belabas2、*
Author Affiliations
  • 1Institut Polytechnique de Paris, LTCI, Télécom Paris, Palaiseau, France
  • 2Université Paris-Saclay, CNRS, Centre for Nanosciences and Nanotechnology, UMR 9001, Palaiseau, France
  • 3Weizmann Institute of Science, Rehovot, Israel
  • 4STMicroelectronics SAS, Crolles, France
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    Figures & Tables(12)
    (a) Waveguide dispersion as a function of the wavelength, calculated for a waveguide height of 300 nm and different waveguide widths. (b) SEM image of the resonator. (c) Normalized transmission spectrum of the resonator. (d) Measured quality factor as a function of the wavelength.
    Measured FSR as a function of wavelength and optical frequency around 1540 nm.
    (a) Setup for measurement of the joint spectral intensity. BP, bandpass filter; NF, notch filter; PF, programmable filter; PC, polarization controller; and SNSPDs, superconducting single-photon detectors. (b) Anti-diagonal elements of the JSI measurement for every accessible signal-idler pair from n=3 to n=83.
    Photon pair generation and heralded single-photon characterization of the SOI MR. (a) Setup for measuring single counts, two-photon coincidences, and three-photon coincidences. NF, notch filter; PF, programmable filter; and TT, time tagger. (b) Single counts, (c) coincidences, (d) generated number of pairs, (e) heralded g(2)(0), and (f) CAR, each as a function of input power (refer to text).
    Setup for the quantum state tomography. PF, programmable filter; EOM, electro-optic phase modulator. Insets are the action of the PFs on the frequency modes. PF1 is used both as an amplitude filter to select the four modes of the two qubits, and as a phase gate implementing a phase ϕi and ϕs on the frequency modes In and Sn. The boxed devices implement identity or Hadamard gate on the qubits. All the projections required for the tomography are accessible with these two gates. PF3 selects two modes Ip and Sq, where p,q∈{n,n+1}.
    Numerical reconstruction of the experimental density matrix of a two-qubit frequency-bin entangled state generated by the SOI resonator + PF1. (a) Real part and (b) imaginary part.
    Fidelity to a maximally entangled state for several frequency-bin entangled photon pairs. The x-axis corresponds to the number of resonances between the frequency qubit and the pump mode.
    (a) Raw coincidences (bars) and QBER (dots) between two users and (b) sifted key rate, calculated using the method in Ref. 34 as a function of n, spectral detuning from the pump. Each link between two users is a two-qubit frequency-bin entangled pair and is color-coded. For example, the bottom users of the network in the inset of (b) receive, respectively, the two frequency channels |I10⟩, |I11⟩ and |S10⟩, |S11⟩, which connect them in the network.
    Classical characterization of the quantum gate. (a) Principle of a frequency-domain operation. (b) Principle of a frequency-domain quantum gate. (c) Phase pattern applied by the PF. (d) Measured tunability of the quantum gate operation.
    (a) Light coupling from mode |ω0⟩ (black) or |ω1⟩ (red) into nine neighboring modes. The gray shaded areas represent the guard modes that are not used for parallelization. (b) Transmission measurement for nine frequency modes when a Hadamard gate is applied to two qubits separated by two guard modes.
    • Table 1. Comparison of internal brightness, FSR, and frequency channels accessible with commercial EOMs and other SOI implementations. We measured the brightness B on the signal-idler pair |I15,S15. *: Clementi et al.9 and Borghi et al.10 used several coupled rings to achieve, respectively, an effective 18 GHz and a 15 GHz mode spacing.

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      Table 1. Comparison of internal brightness, FSR, and frequency channels accessible with commercial EOMs and other SOI implementations. We measured the brightness B on the signal-idler pair |I15,S15. *: Clementi et al.9 and Borghi et al.10 used several coupled rings to achieve, respectively, an effective 18 GHz and a 15 GHz mode spacing.

      WorkB (pairss1mW2GHz1)QFSR (GHz)Number of frequency channels
      Oser et al.435×1053×104200
      Mazeas et al.421.6×1064×104230
      Jiang et al.456.24×1073.47×105/4.94×1052315
      Clementi et al.94.80×1071.5×105*Two signal-idler pairs
      Borghi et al.101.80×105/2.50×1055.7×104/7.8×104*Four signal-idler pairs
      This work(5.1±3)×1074.75×1052180 signal-idler pairs
    • Table 2. Coincidences for the two-photon projections Ca,b integrated for 125 s, in a coincidence window of 1 ns.

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      Table 2. Coincidences for the two-photon projections Ca,b integrated for 125 s, in a coincidence window of 1 ns.

      ProjectionsCoincidencesProjectionsCoincidences
      C0,01548C+,0716
      C0,136C+,1767
      C0,+622C+,+1275
      C0,+i663C+,+i608
      C1,022C+i,0837
      C1,11553C+i,1695
      C1,+692C+i,+723
      C1,+i664C+i,+i42
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    Antoine Henry, Dario A. Fioretto, Lorenzo M. Procopio, Stéphane Monfray, Frédéric Boeuf, Laurent Vivien, Eric Cassan, Carlos Alonzo-Ramos, Kamel Bencheikh, Isabelle Zaquine, Nadia Belabas, "Parallelization of frequency domain quantum gates: manipulation and distribution of frequency-entangled photon pairs generated by a 21 GHz silicon microresonator," Adv. Photon. 6, 036003 (2024)

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    Paper Information

    Category: Research Articles

    Received: Sep. 30, 2023

    Accepted: May. 22, 2024

    Published Online: Jul. 1, 2024

    The Author Email: Antoine Henry (antoine.henry@telecom-paris.fr), Nadia Belabas (nadia.belabas@c2n.upsaclay.fr)

    DOI:10.1117/1.AP.6.3.036003

    CSTR:32187.14.1.AP.6.3.036003

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