Research ArticleQUANTUM PHYSICS

A photonic platform for donor spin qubits in silicon

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Science Advances  26 Jul 2017:
Vol. 3, no. 7, e1700930
DOI: 10.1126/sciadv.1700930
  • Fig. 1 Orbital levels of 28Si:77Se+.

    (A) Valley composition of the six sublevels of the 1s hydrogenic manifold of 28Si:77Se+, ignoring spin interactions. (B) With electron spin interactions, the six 1s:T2 levels are split into 1s:Γ7 (two states) and 1s:Γ8 (four states) by the spin-valley interaction. With nuclear spin interactions, the 1s:A states are split by the hyperfine interaction into electron-nuclear spin singlet S0 and triplet {T,T0,T+} states (not to scale). (C) These eigenstates change according to an applied magnetic field. The spin-valley composition of the 1s:Γ7 states in a magnetic field are shown with spin (anti) alignment with the background magnetic field indicated by arrows and valley phase indicated by color. In the high-field limit, the 1s:A and 1s:Γ7 states are labeled according to nuclear spin (⇑,⇓) and electron spin (↑,↓). (D) Transmission spectra (top) and photoluminescence (PL) spectra (bottom) collected with different resolutions as indicated. The small side peaks (⋄ and ⋆) are because of small concentrations of 76Se+ and 78Se+, respectively. (E) Unpolarized (yellow) and singlet/triplet hyperpolarized (green and purple, respectively) transmission scans of the 1s:A ⇔ 1s:Γ7 optical transitions (see main text).

  • Fig. 2 Singlet ⇔ triplet magnetic resonance of 77Se+ in Earth’s magnetic field.

    (A) Frequencies of the singlet ⇔ triplet transitions as a function of magnetic field B. The S0T± transitions vary linearly with B, whereas the S0T0 transition is first-order insensitive to changes in B, giving rise to a quadratic clock transition (see text). A y-axis magnification of the S0T0 transition is displayed with a dashed line, corresponding to the right dashed y axis. (B) Magnetic resonance spectra, as a function of B1 frequency, measured via the change in triplet absorption after hyperpolarization, were taken at T = 2.0 K. All three singlet ⇔ triplet transitions are well resolved in Earth’s magnetic field (here, 70 μT). (C) Measured polarization decay showing the relaxation time constant, T1, to be over 6 min at T = 1.2 K. Inset: Pulse sequence used to measure T1. For each wait duration τ, polarization was measured as the difference between two integrated absorption transients, one with (B) and one without (A) a leading population inversion π pulse. These absorption transients also served to fully reinitialize the S0T0 qubit ensemble.

  • Fig. 3 Spin coherence properties of 77Se+.

    (A) Center: Hahn-echo T2 measurements with rf pulse sequence (inset) showing a coherence time of 2.14 ± 0.04 s at T = 1.2 K, collected with a phase-cycled leading π/2 pulse and varied τ. (A) Top right: Varying the amount of rotation in the refocusing pulse of a Hahn-echo experiment (a tip-angle measurement) can be used to deduce the concentration of the sample. We confirm a 77Se+ concentration upper limit of 2 × 1013 cm−3 under these experimental conditions. (A) Bottom left: These Hahn-echo times can be extended with dynamic decoupling sequences. We see square-root extension of coherence times as a function of N, the number of refocusing pulses, here applied as an alternating CPMG sequence (see main text). (B) Rabi oscillations of the S0T0 qubit ensemble. (C) Ramsey fringes of the S0T0 qubit ensemble. The fitted envelope (red) gives a T2* value of approximately 1 ms, arising from static magnetic field inhomogeneities.

  • Fig. 4 Coupled cavity-donor system.

    (A) Simulated electric field intensity of a silicon photonic L3 cavity mode at ~427.3 meV (2902 nm), viewed top-down, modeled after the work of Shankar et al. (63). Inset: Fourfold magnification of the mode maximum region. The white crosshair indicates the calculated lateral implantation straggle. (B) Cross-sectional view of the long axis of the same 0.5 μm thick photonic L3 cavity mode at ~427.3 meV (2902 nm). Inset: Fourfold magnification of the mode maximum region with indicated implantation straggle. (C) The Jaynes-Cummings ladder of available energy eigenstates in a single chalcogen-cavity coupled system. At zero field, with a zero nuclear spin isotope and the cavity frequency, ωc, on resonance with the 1s:A ⇔ 1s:Γ7 transition, the regular ladder of states exists (orange). With an applied magnetic field (blue), the ground-state electron states split according to gA = 2.0057 and the excited state splits according to gΓ7 = 0.644. Detuning the 1s:Γ7 excited state (Δω) with, for example, electric fields, brings these excited-state levels into alignment to observe spin-dependent strong coupling r. (D) Calculated spin-dependent strong coupling of the donor-implanted L3 cavity, neglecting cavity losses: Only one spin state (bottom) has a split optical spectrum near the bare cavity frequency.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/7/e1700930/DC1

    Hyperfine constant

    T1 decoherence

    T2 decoherence

    fig. S1. Linewidth measurements using hole burning.

    fig. S2. Impact of room temperature blackbody radiation on T1 lifetimes.

    fig. S3. Illustration of phase noise on and off the clock transition.

    fig. S4. T2 coherence time scaling with number of π pulses.

    fig. S5. Temperature dependence of the 1s:A ⇔ 1s:Γ7 optical transitions’ linewidth.

    Reference (64)

  • Supplementary Materials

    This PDF file includes:

    • Hyperfine constant
    • T1 decoherence
    • T2 decoherence
    • fig. S1. Linewidth measurements using hole burning.
    • fig. S2. Impact of room temperature blackbody radiation on T1 lifetimes.
    • fig. S3. Illustration of phase noise on and off the clock transition.
    • fig. S4. T2 coherence time scaling with number of π pulses.
    • fig. S5. Temperature dependence of the 1s:A ⇔ 1s:Γ7 optical transitions’ linewidth.
    • Reference (64)

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