Research ArticlePHYSICS

Experimental entanglement of 25 individually accessible atomic quantum interfaces

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Science Advances  20 Apr 2018:
Vol. 4, no. 4, eaar3931
DOI: 10.1126/sciadv.aar3931
  • Fig. 1 Experimental setup for generation and verification of multipartite entanglement between a 2D array of atomic quantum interfaces.

    (A) We use a combination of the DLCZ scheme and the programmable AOD multiplexer to generate multipartite entanglement of the W-state type between the atomic spin waves in a 2D array of micro-ensembles. For clarity, we show a 3 × 3 array, albeit we have also entangled 4 × 4 and 5 × 5 ensemble arrays. The write laser beam is split coherently into nine paths to simultaneously excite the 3 × 3 87Rb ensemble array by the write AOD multiplexer, which contains two orthogonal deflectors placed in the x and y directions. The lens after the AOD multiplexer focuses the beams and, at the same time, maps different angles of the deflected beams to different positions in a big atomic cloud forming individual micro-ensembles. The scattered signal photon modes are combined phase coherently by lens 2 and the signal AOD de-multiplexer and then coupled into a single-mode fiber with output detected by the single-photon detector (SPD1). To verify multipartite entanglement, we use a programmable AOD multiplexer and de-multiplexer in the paths of the read beam and the idler photon mode to detect the atomic spin waves from different micro-ensembles in several complementary bases. To bound the double excitation probability, the idler photon mode is split by a 50/50 beam splitter (BS) and detected by two single-photon detectors (SPD2 and SPD3) for registration of the three-photon coincidence (together with the SPD1). (B) Illustration of the 5 × 5 array from multiplexing of a laser beam at the position of the atomic ensemble. This image is obtained by shining a laser beam into the signal single-mode fiber, which is multiplexed by the signal AOD and captured by a charge-coupled device camera at the position of the atomic ensemble. The separation between adjacent signal modes is 180 μm in both the x and y directions, and the Gaussian diameter of both the signal and the idler modes is 70 μm. (C) Relevant atomic energy levels and their couplings to the write/read laser beams and the signal/idler photon modes, with |g〉 ≡ |5S1/2, F = 2〉, |s〉 ≡ |5S1/2, F = 1〉, and |e〉 ≡ |5P1/2, F′ = 2〉. The write (read) laser beam is red-detuned at Δ = 10 MHz (Δ′ = 0), respectively, at the center micro-ensemble.

  • Fig. 2 Programmable coupling configurations for entanglement generation and verification.

    (A) The coupling configuration to generate multipartite entanglement, where the write AODs split the optical paths and the signal AODs coherently combine the paths. (B) The detection configuration for the measurement of fidelity, where the read AODs deliver the read beams to all the micro-ensembles to transfer the atomic spin-wave excitations to idler photons, and the idler AODs combine coherently the idler modes from different ensembles with equal weight for detection in the superposition basis. (C and D) The write and the read AODs in (C) and (D) are configured in the same way as those in (A) and (B), but the signal and the idler AODs are programmed to successively detect the signal/idler photon from each individual micro-ensemble. The configurations (C) and (D) combined are used to calibrate the retrieval efficiency for each micro-ensemble, and the configurations (A) and (D) combined are used to detect the excitation population in each ensemble after the W-state preparation (see section S2 for details).

  • Fig. 3 Entanglement verification for the 3 × 3 array of atomic ensembles.

    (A) The measured values, together with the 68% confidence intervals (corresponding to the region within 1 SD if the distribution is Gaussian), for the population Embedded Image, the fidelity F′, and the entanglement witness Embedded Image for the idler photon modes that are directly measured. The entanglement in the retrieved idler photon modes provides a lower bound to the entanglement in the collective spin-wave modes in different atomic ensembles. The optimized parameters in the witness Embedded Image are given by Embedded Image, Embedded Image, and Embedded Image. (B) The distribution of entanglement witness Embedded Image, where Embedded Image implies eight-partite genuine entanglement. The probability with Embedded Image is 99.5% from this measurement. (C) The measured retrieval efficiency for each of the 3 × 3 atomic ensemble arrays. (D) The measured spin-wave excitation population in each of the 3 × 3 atomic ensemble arrays after the W-state preparation. (E) The measured values, together with the 68% confidence intervals for the population p0, p1, p2, the fidelity F, and the entanglement witness W9 for the collective spin-wave modes in different atomic ensembles after correction of the retrieval efficiency through the above measurements. The optimized parameters in the witness W9 are given by α9 = 0.369, β9 = 0.889, and γ9 = 0.268. (F) The distribution of entanglement witness W9, where W9 < 0 implies nine-partite genuine entanglement. The probability with W9 < 0 is 99.98% from this measurement.

  • Fig. 4 Entanglement verification for the 4 × 4 array of atomic ensembles.

    (A) The measured values, together with the 68% confidence intervals, for the population Embedded Image, the fidelity F′, and the entanglement witness Embedded Image for the directly measured idler photon modes retrieved from the 4 × 4 atomic ensemble array. The optimized parameters in the witness Embedded Image are given by Embedded Image, Embedded Image, and Embedded Image. (B) The distribution of entanglement witness Embedded Image for the 4 × 4 idler photon modes. The probability with Embedded Image is 99.7% from these measurements. (C) The measured values, together with the 68% confidence intervals, for the population p0, p1, p2, the fidelity F, and the entanglement witness W14, for the 4 × 4 atomic ensemble array after correction of the retrieval efficiency. The optimized parameters in the witness W14 are given by α14 = 0.635, β14 = 0.813, and γ14 = 0.240. (D) The distribution of entanglement witness W14 for the 4 × 4 case. The probability with W14 < 0 is 99.997% from these measurements.

  • Fig. 5 Entanglement verification for the 5 × 5 array of atomic ensembles.

    (A) The measured values, together with the 68% confidence intervals, for the population Embedded Image, the fidelity F′, and the entanglement witness Embedded Image for the directly measured idler photon modes retrieved from the 5 × 5 atomic ensemble array. The optimized parameters in the witness Embedded Image are given by Embedded Image, Embedded Image, and Embedded Image. (B) The distribution of entanglement witness Embedded Image for the 5 × 5 idler photon modes. The probability with Embedded Image is 98.4% from these measurements. (C) The measured values, together with the 68% confidence intervals, for the population p0, p1, p2, the fidelity F, and the entanglement witness W22 for the 5 × 5 atomic ensemble array after correction of the retrieval efficiency. The optimized parameters in the witness W22 are given by α22 = 0.550, β22 = 0.840, and γ22 = 0.244. (D) The distribution of entanglement witness W22 for the 5 × 5 case. The probability with W22 < 0 is 96.5% from these measurements.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/4/eaar3931/DC1

    section S1. Entanglement witness for W-type states

    section S2. Experimental measurement of the entanglement witness

    section S3. Discussion of the experimental noise

    fig. S1. Coupling configuration for the measurement of the retrieval efficiency of each micro-ensemble.

    fig. S2. Coupling configuration for the measurement of the excitation population of each micro-ensemble.

    fig. S3. Coupling configuration for the measurement of the W-state fidelity.

    fig. S4. Measurement of the three-photon correlation and the double excitation probability.

  • Supplementary Materials

    This PDF file includes:

    • section S1. Entanglement witness for W-type states
    • section S2. Experimental measurement of the entanglement witness
    • section S3. Discussion of the experimental noise
    • fig. S1. Coupling configuration for the measurement of the retrieval efficiency of each micro-ensemble.
    • fig. S2. Coupling configuration for the measurement of the excitation population of each micro-ensemble.
    • fig. S3. Coupling configuration for the measurement of the W-state fidelity.
    • fig. S4. Measurement of the three-photon correlation and the double excitation probability.

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