Research ArticleQUANTUM PHYSICS

Quantum entanglement at ambient conditions in a macroscopic solid-state spin ensemble

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Science Advances  20 Nov 2015:
Vol. 1, no. 10, e1501015
DOI: 10.1126/sciadv.1501015
  • Fig. 1 Hybrid registers in silicon carbide.

    (A) A hybrid two-qubit register comprising a PL6 color-center defect’s intrinsic electron spin and a nearby 29Si nuclear spin. The PL6 defect, whose physical structure is unknown, is depicted as a pyramid to indicate its known C3v symmetry. (B) The hybrid system forms an atom-like state with an optical, fine, and hyperfine structure. Optical pumping from the ground state |GS〉 to the excited state |ES〉 with nonresonant laser light initializes registers into |0, ↑〉. The mechanisms responsible for initialization are a series of electron spin–dependent intersystem crossings (dashed arrows), through some intermediate states |IS〉, and dynamic nuclear polarization. These mechanisms also lead the intensity of the emitted photoluminescence to be dependent on both the electron and nuclear spin, enabling registers to be read out. The energy levels are split by the crystal field, the electron and nuclear Zeeman effects (2γeB|| and −γnB||, where γe = 28 MHz/T, γn = −8.5 MHz/T for 29Si, and B|| is a magnetic field co-aligned with the PL6 symmetry axis), and the hyperfine interaction (A). The register states are |−1, ↑〉, |0, ↓〉, |−1, ↓〉, and |0, ↑〉. Radio-frequency (RF) and microwave (MW) pulses are used to drive nuclear and electron spin transitions, respectively. (C) A register’s electron and nuclear spin can be entangled by using MW and RF pulses to produce coherences (indicated by double-ended arrows) between the |−1, ↑〉 and |0, ↓〉 states or between the |−1, ↓〉 and |0, ↑〉 states. We prepare 103 identical registers into each of the four Bell states, |Ψ±〉 and |Φ±〉.

  • Fig. 2 Register characterization.

    (A) ODMR measurement sequence. (B) ODMR returns a structured line that can be decomposed into a strong central resonance and three doublets (the model curves, which are derived from fits to the data, are offset). The central peak (black trace) is the |0〉 ↔ |−1〉 resonance of PL6 electron spins that are not strongly coupled to any nuclei. The two pronounced doublets (blue and purple traces) are the |0, ↑〉 ↔ |−1, ↑〉 and |0, ↓〉 ↔ |−1, ↓〉 transitions of two inequivalent types of register (labeled R1 and R2; the arrows are color-coded to the model curves). The third doublet (green trace) was not considered in this study because of its weak signal. (Right) At B|| = 33 mT, dynamic nuclear polarization strongly initializes the nuclei in R1 and R2 into their mI = ↑ states. This is observed in ODMR as a strong asymmetry in the amplitudes of the individual peaks in each doublet. a.u., arbitrary units. (C) ODNMR measurement sequence. (D) ODNMR returns two sharp peaks, which are the |−1, ↑〉 ↔ |−1, ↓〉 resonances of R1 and R2. (Inset) Both resonances evolve with magnetic field according to the 29Si gyromagnetic ratio. ODMR and ODNMR are obtained through differential photoluminescence measurements, which are described in Materials and Methods.

  • Fig. 3 Register entanglement.

    (A) Quantum gates within the circuit model of quantum information processing and their implementation in our system. Initialization and readout use the same optical cycling process. (B) The density matrix ρ is reconstructed by making 15 differential measurements between distinct quantum circuits U1 and U2. Each measurement allows us to infer either a single element or a relationship between two elements of ρ. (C) The three circuit pairs used to determine the relationships between the four populations. U1 and U2 are labeled to serve as a guide for all circuit pairs. (D) The 12 circuit pairs used to determine the real and imaginary components of the six unique coherences. We use a condensed notation in which half-filled circles are used to combine circuit pairs that differ in the condition of a gate and brackets to combine those that differ in the phase of a gate. (E) Entangling algorithm. The Bell state is chosen by the phase of the last nuclear gate and the condition of the last electronic gate. (F) The real (upper panel) and imaginary (lower panel) components of the R2 ensemble density matrix after optical pumping and after the entangling algorithm. The overlaid transparent bars represent the ideal density matrices. The normalization for these reconstructions is derived from the mean electron spin polarization. The coherences 〈0, ↑|ρ|−1, ↑〉 and 〈0, ↓|ρ|−1, ↓〉, which are shown as gray squares in the initial ρ, are not measured in our experiments. See section S5 for details of the tomography procedure.

  • Fig. 4 Entanglement metrics.

    (A) The fidelity (upper panel) and the PPT test value (lower panel) as calculated from Monte Carlo and maximum likelihood techniques applied to the measured density matrices (see Materials and Methods for details). The lower labels show the ideal states. The initialized states are classical (PPT test ≥0), and the Bell states are unambiguously entangled (PPT test <0). (B) The entanglement coherences, 〈–1, ↑|ρ|0, ↓〉 for |Φ±〉 and 〈–1, ↓|ρ|0, ↑〉 for |Ψ±〉, as a function of the entanglement free-evolution time. The error bars are 95% confidence intervals.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/1/10/e1501015/DC1

    Section S1. Multinuclear spin registers.

    Section S2. Electron spin polarization.

    Section S3. Register-density calculation.

    Section S4. Coherent nuclear spin control.

    Section S5. Quantum-state tomography.

    Fig. S1. Optically pumped electron spin polarization.

    Fig. S2. Coherent nuclear spin control in SiC.

    Fig. S3. Entanglement of the R1 ensemble.

    Fig. S4. Experimental apparatus.

    Table S1. The relative signal calculated for various registers.

    Table S2. Quantum gate sequences used to measure the density matrix coherences.

    Table S3. Quantum gate sequences used to measure the density matrix populations.

    Table S4. Consolidated initialization and entanglement data.

    References (4348)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Multinuclear spin registers.
    • Section S2. Electron spin polarization.
    • Section S3. Register-density calculation.
    • Section S4. Coherent nuclear spin control.
    • Section S5. Quantum-state tomography.
    • Fig. S1. Optically pumped electron spin polarization.
    • Fig. S2. Coherent nuclear spin control in SiC.
    • Fig. S3. Entanglement of the R1 ensemble.
    • Fig. S4. Experimental apparatus.
    • Table S1. The relative signal calculated for various registers.
    • Table S2. Quantum gate sequences used to measure the density matrix coherences.
    • Table S3. Quantum gate sequences used to measure the density matrix populations.
    • Table S4. Consolidated initialization and entanglement data.
    • References (43–48)

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