Research ArticlePHYSICS

Robust optical polarization of nuclear spin baths using Hamiltonian engineering of nitrogen-vacancy center quantum dynamics

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Science Advances  31 Aug 2018:
Vol. 4, no. 8, eaat8978
DOI: 10.1126/sciadv.aat8978
  • Fig. 1 Theoretical framework overview.

    Polarization of a bath of nuclear spins (gray) by an electron spin (yellow): The initially unpolarized bath and the polarized electron spin (upper left) evolve according to an engineered Hamiltonian that describes a flip-flop interaction, and the electron spin is periodically reinitialized. After several repetitions, the nuclear spin bath is polarized (lower right). Illustration of effective Hamiltonian engineering (gray box): A combination of standard symmetric and asymmetric DD sequences with the effective Hamiltonians HSzIx/y can be modified to a flip-flop Hamiltonian HSxIx + SyIy by introducing basis changes with π/2 pulses.

  • Fig. 2 PulsePol sequence and simulations of robustness.

    PulsePol sequence (A) and robustness compared to nuclear orientation via electron spin locking (NOVEL). (B) The polarization transfer to a single nuclear spin for NOVEL (upper graph) under perfect conditions (black line). A Δ = (2π)0.5-MHz detuning error (dashed blue line) and 2% Rabi frequency error (dashed-dotted green line) drastically reduce polarization transfer. For PulsePol (lower graph) under perfect conditions (black line), the transfer is 28% slower, as predicted by the effective Hamiltonian of Eq. 2 (red crosses). Detuning errors Δ = 0.1Ω0 = (2π)5 MHz (dashed blue line) and Rabi frequency errors δΩ = 0.1Ω0 = (2π)5 MHz (dashed-dotted green line) have a very small effect. (C) Considering a system of one electron spin and five nuclear spins, for the same parameters ωI = (2π)2 MHz and Ω0 = (2π)50 MHz, polarization transfer versus Δ and δΩ/Ω0 for the PulsePol sequence, with a comparison to a NOVEL sequence for its relevant detuning values |Δ| < (2π)2 MHz in the inset. The graphs result from averaging more than 100 realizations of the locations of the five closest nuclear spins to the NV center electron spin on a carbon lattice, and for PulsePol, a resonance shift of 2.5% and corresponding phase errors were used (see the Supplementary Materials).

  • Fig. 3 Experimental implementation via optically polarized NV centers in diamond.

    (A) Probing robustness to detuning on a single NV by detuning the MW frequency from the NV |ms = 0〉 ↔ |ms = − 1〉 transition. (B) PROPI sequence used for detecting polarization efficiency of PulsePol. (C) PROPI readout for different detunings Δ for PulsePol (red) and NOVEL (blue). The lines are the smoothed simulation result of a comparable nuclear spin bath with no free parameters. For more details, see text. Polarization buildup by consecutive polarization transfers for NOVEL, PulsePol, and ISE (D) for Δ = 0 MHz, where all sequences, (E) Δ = (2π)20 MHz, where only PulsePol and very slow ISE are able to transfer polarization.

  • Fig. 4 Hyperpolarization applications with NV centers in diamonds.

    (A) Illustration of shallow NV polarization setup, where NV centers implanted ~3-nm-deep polarize-diffusing molecules in a solution outside of the diamond and (B) nanodiamonds with randomly oriented NV centers, where the polarization of 13C spins (orange) allows for the usage as MRI contrast agents. (C) Polarization transfer from near-surface NV centers to a bath of 1200 nuclear spin bath, using the same Rabi and Larmor frequency and sequence as in Fig. 2C averaged over NV centers with transition frequencies drawn from a Gaussian distribution with a (2π)20-MHz width. The simulation uses matrix product states (39) and a diffusion coefficient of D = 1.4/2.8 × 10−12m2/s (blue dotted/red dashed curve), resulting in different correlation times and efficiencies. The inset shows that the NV linewidth is well within the working range of the PulsePol protocol [Ω = (2π)50MHz]. More details of the simulation are included in the Supplementary Materials. (D) On the basis of the resilience to detunings |Δ| < (2π)30MHz for a Rabi frequency of Ω = (2π)50MHz, more than 11% of the NV orientations in nanodiamonds (azimuthal angle between 90° ± 6.5°, as shown on the sphere) contribute to polarization transfer.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/8/eaat8978/DC1

    Supplementary Text

    Section S1. Hamiltonian of the system

    Section S2. Effective Hamiltonian of PulsePol

    Section S3. Error robustness

    Section S4. Finite pulses

    Section S5. Composite pulses

    Section S6. Effect of phase errors

    Section S7. Hamiltonian with NV centers in nanodiamonds

    Section S8. Depolarization behavior

    Section S9. Simulation parameters for shallow NV centers

    Fig. S1. MW pulse sequence for pulsed polarization transfer.

    Fig. S2. Error resistance of PulsePol by using composite pulses.

    Fig. S3. Effect of phase errors.

    Fig. S4. Error resistance of PulsePol versus the resonance shift.

    Fig. S5. Comparison between simulation results and experimental data of polarization buildup and depolarization.

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • Section S1. Hamiltonian of the system
    • Section S2. Effective Hamiltonian of PulsePol
    • Section S3. Error robustness
    • Section S4. Finite pulses
    • Section S5. Composite pulses
    • Section S6. Effect of phase errors
    • Section S7. Hamiltonian with NV centers in nanodiamonds
    • Section S8. Depolarization behavior
    • Section S9. Simulation parameters for shallow NV centers
    • Fig. S1. MW pulse sequence for pulsed polarization transfer.
    • Fig. S2. Error resistance of PulsePol by using composite pulses.
    • Fig. S3. Effect of phase errors.
    • Fig. S4. Error resistance of PulsePol versus the resonance shift.
    • Fig. S5. Comparison between simulation results and experimental data of polarization buildup and depolarization.

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