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Optically pumped spin polarization as a probe of many-body thermalization

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Science Advances  01 May 2020:
Vol. 6, no. 18, eaaz6986
DOI: 10.1126/sciadv.aaz6986
  • Fig. 1 Low-field dynamic polarization and manipulation of 13C spins in diamond.

    (A) Electron-nuclear spin set. Polarization flows from hyperfine-coupled carbons to bulk carbons. (B) Schematics of the NV/P1 energy diagrams as a function of the magnetic field. Cross-relaxation between the NV and P1 is most favorable when the energy differences are matched (vertical arrows); this condition depends on the angle θ between the magnetic field B and the NV symmetry axis. (C) DNP and detection protocol. We illuminate the sample with 532-nm laser light for a time tOP at a variable field B, followed by sample shuttling to the bore of a 9.0-T magnet for high-field 13C NMR detection. (D) NMR signal amplitude of hyperpolarized 13C as a function of B. In a typical experiment, the magnetic field during DNP is set at B( + ) or at B( − ), so as to produce the largest positive or negative 13C polarization, respectively. a.u., arbitrary units. (E) Indirect observation of low-field 13C NMR through variable-frequency RF excitation; for simplicity, the drawing omits the sample shuttling step. (F) Experimental results from applying the protocol in (E) for different RF powers. In (D) to (F), the optical pumping time is tOP = 10 s and the laser power is 1 W focused to a ~200-μm-diameter focal spot; in (F), the RF-pulse duration is tRF = 250 ms, the magnetic field is B( + ) = 52.3 mT, and its angle θ with the NV axis amounts to ~6°.

  • Fig. 2 13C spin diffusion spectroscopy via signal amplification of low-abundance nuclei.

    (A) Schematics of the spin diffusion process. Starting with the cross-relaxation of an NV-P1 pair and a strongly hyperfine-coupled 13C spin (green circles), polarization flows from less abundant, unobservable nuclei to more abundant, bulk carbons. RF excitation at a predefined (but variable) frequency equilibrates the populations of a select nuclear spin subset (horizontal red band), hence disrupting the polarization flow. (B) Experimental protocol. 13C NMR detection is carried out at 9.0 T, following sample shuttling (not shown). (C) 13C NMR signal amplitude as a function of the RF upon application of the protocol in (B) in a vicinity of the 13C Larmor frequency at B( + ) = 52.3 mT. The faint solid trace reproduces the spectrum in Fig. 1F at 0 dBm. (D) Same as in (C) but for an extended RF range. Here, the magnetic field is B( + ) = 52.3 mT (B( − ) = 52.7 mT) in the upper (lower) half plot (green and red circles, respectively). The dashed green square on the left indicates the region of the spectrum presented in (C). Solid lines are guides to the eye; faint horizontal traces indicate signal levels in the absence of RF. (E) 13C NMR signal amplitude as a function of the applied magnetic field in the presence of RF excitation either resonant (39.6 MHz) or nonresonant (30.0 MHz) with the dip in (D). Solid lines are guides to the eye. In (C) to (E), the RF power is –8 dBm, and tOP = tRF = 5 s.

  • Fig. 3 Electron spin–mediated many-body nuclear spin diffusion under NV-P1 cross-relaxation.

    (A) Histograms of hyperfine resonance frequencies above 1 MHz for 13C nuclei near individual P1s and NVs (upper and lower plots, respectively). For reference, the faint green and red bands reproduce the level of RF absorption observed in Fig. 2D. (B) The impact of RF excitation on DNP efficiency can be cast in terms of a polarization sink of width δνb defined by the excited bandwidth. For a given RF power, the sink efficiency reflects on the spin network connectivity: (i) Full contrast arises when all polarization transfer pathways (solid lines) rely on a single nuclear spin site (grey circle) featuring a characteristic hyperfine shift. (ii) For a typical frequency change δνd between consecutive nuclear spin nodes and assuming δνd > δνb, the sink efficiency diminishes as the number of alternative pathways increases. (iii) Full contrast reappears when δνd ≲ δνb. (C) (Top) Model spin chain comprising two carbons hyperfine-coupled to two P1s subject to a dipolar interaction ℐd. (Bottom) Calculated eigenenergies for eigenstates ∣i⟩, i = 1 … 8 within the subspace where the electron spins are antiparallel; for these calculations, ‖A1‖ = 2π × 6 MHz and ‖A2‖ = 2π × 10 MHz. (D) 13C polarization in the presence of RF for the spin system in (C) for different ℐd; both 13C spins are assumed to be initially polarized. (E) Network of 22 13C spins in a Cayley tree configuration; green, yellow, and orange lines indicate Jeff equal to 100, 10, and 1 kHz, respectively. (F) Computed 13C magnetization in each ring as a function of time starting from a configuration where only the central spin is polarized.

  • Fig. 4 Probing paramagnetic center–assisted nuclear spin diffusion.

    (A) Experimental protocol. We apply a train of short, equidistant RF pulses during the fixed illumination time tOP = 5 s and monitor the 13C DNP signal as we increase the number of pulses l. (B) (Top) 13C NMR signal amplitude S(τ) as a function of the interpulse time τ ≈ tOP/l at a representative RF. The RF pulse duration is τRF = 1 ms at a power of −8 dBm; the solid line is a fit to a stretched exponential (see the main text). (Bottom) Probability distribution for the diffusion rate μ; the vertical dotted and dashed lines indicate the characteristic diffusion rate 1/τd and distribution median μ¯. The shadowed half corresponds to transport processes with rates faster than τd1. (C) We model the observed response as a classical flow of magnetization through a chain of m boxes, each containing Ni spins with hyperfine resonance frequencies within box-selective bandwidths Δνi. The arrow indicates increasing hyperfine coupling ‖A‖, and γi, i + 1 denotes the polarization transfer rate between neighboring boxes. (D) Numerical simulations of the model in (C) for chains of length m = 40 and with uniform (but variable) spin transfer rate γ. We attain a sigmoidal response, whose inflection point at τd grows with the inverse of the spin diffusion rate γ. The magnetization contrast δMm reflects on the RF impact, here set to act on a fraction of the spins in the 20th box of the chain. (E) Effective spin diffusion constant Deff=rC2τd1 at different RF frequencies νRF as determined from data plots similar to those in (C); DC is the spin diffusion for carbon in pure diamond. The broad green band reproduces the RF absorption from Fig. 2D and has been included as a reference. All experiments are carried out at a fixed magnetic field B( + ) = 52.3 mT.

Supplementary Materials

  • Supplementary Materials

    Optically pumped spin polarization as a probe of many-body thermalization

    Daniela Pagliero, Pablo R. Zangara, Jacob Henshaw, Ashok Ajoy, Rodolfo H. Acosta, Jeffrey A. Reimer, Alexander Pines, Carlos A. Meriles

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