Electron Induced Nanoscale Nuclear Spin Relaxation Probed by Hyperpolarization Injection

William Beatrez, Arjun Pillai, Otto Janes, Dieter Suter, and Ashok Ajoy

Phys. Rev. Lett. 131, 010802 – Published 7 July 2023

Abstract

We report on experiments that quantify the role of a central electronic spin as a relaxation source for nuclear spins in its nanoscale environment. Our strategy exploits hyperpolarization injection from the electron as a means to controllably probe an increasing number of nuclear spins in the bath and subsequently interrogate them with high fidelity. Our experiments are focused on a model system of a nitrogen vacancy center electronic spin surrounded by several hundred ${}^{13}C$ nuclear spins. We observe that the ${}^{13}C$ transverse spin relaxation times vary significantly with the extent of hyperpolarization injection, allowing the ability to measure the influence of electron-mediated relaxation extending over several nanometers. These results suggest interesting new means to spatially discriminate nuclear spins in a nanoscale environment and have direct relevance to dynamic nuclear polarization and quantum sensors and memories constructed from hyperpolarized nuclei.

Received 14 July 2022
Accepted 7 June 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.010802

Physics Subject Headings (PhySH)

Quantum control Quantum metrology Quantum sensing

Nuclear magnetic resonance

Quantum Information, Science & Technology

Authors & Affiliations

William Beatrez¹, Arjun Pillai ¹, Otto Janes¹, Dieter Suter ², and Ashok Ajoy ^1,3,4,*

¹Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
²Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
³Lawrence Berkeley National Laboratory, Chemical Sciences Division, Berkeley, California 94720, USA
⁴CIFAR Azrieli Global Scholars Program, 661 University Ave, Toronto, ON M5G 1M1, Canada

^*ashokaj@berkeley.edu

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Vol. 131, Iss. 1 — 7 July 2023

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Images

Figure 1
System and protocol. (a)–(c) System consists of central NV electron (red) and ${}^{13}C$ nuclei (green) and P1 centers (blue) at distance $r$ . Dashed lines are internuclear dipolar couplings. Profile denotes $1 / r^{6}$ NV-mediated relaxation effect. (a),(c) NV acts as polarization source and relaxation sink, respectively, during different experimental regimes. (d) Experiment schematic: (I) $NV \to {}^{13}C$ hyperpolarization for period $τ$ at 36 mT, (II) transport to high field, and (III) ${}^{13}C$ readout for time $t$ at 7 T. (e) Hyperpolarization (I) involves microwave chirps [20, 21]. (f) Measurement (III) comprises a train of spin-locking $ϑ$ pulses with interrogation in $t_{acq}$ interpulse intervals [22]. Note: Time $τ$ describes hyperpolarization time and time $t$ describes readout time.
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Figure 2
Effect of increasing hyperpolarization time $τ$ . (a) Spin-lock decays for different hyperpolarization times $τ$ corresponding to color bar [regime I in Fig. 1]. Single-shot data [obtained with $t_{acq} = 32 μ s$ and $ϑ \approx π / 2$ in Fig. 1] is boxcar averaged over 97 ms and normalized after truncation at $t = 9.7 ms$ . Dashed line represents $1 / e$ intercept. Inset (i): Enlarged representative 1 s segment [gray window in (a)]. Dashed line is a fitted piecewise monoexponential. (b) Instantaneous lifetime $T_{2}$ measured along decay curve, extracted from slopes as in the inset of (a). Color bar [see (a)] represents $τ$ . Dashed line shows exemplary segment ending at 16 s [gray window in (a)]. (c) Instantaneous $T_{2}$ plotted against $τ$ . Points show $T_{2}$ lifetimes from (b) for exemplary 1 s segments ending at labeled $t$ values. Lines are spline fits.
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Figure 3
Quantifying instantaneous decay rates. (a) Full data in Fig. 2 plotted on a log scale with respect to $\sqrt{t}$ for different $τ$ (color bar). Traces extending to $t = 144 s$ have $\sim 10^{6}$ points. Upper axis shows time $t$ . Six equally sized (in $\sqrt{t}$ ) segments [labeled (i)–(vi)] are selected. (b) Enlargement of segment (i) (sampled every $\approx 5 ms$ ) for representative marked $τ$ values [same color bar as (a)]. Dashed lines are at equally spaced $\sqrt{t}$ values to guide the eye. (c) Extracted time constants $T_{2}^{'}$ from slopes of the corresponding segments in (a). Segment (i) shows a steep increase in $T_{2}^{'}$ with $τ$ ; subsequent segments show progressively flatter profiles (gray arrow). Crossover of early and late segments occurs at $τ \approx 32 s$ (dashed line). (d) Variations in short and long time decay behavior with $τ$ . At long $t$ , decay closely follows $α = 1 / 2$ [dashed lines, extracted from segment (vi)], while short times $t$ show a transition from convex to concave behavior at $τ \approx 32 s$ [similar to Fig. 3]. Upper axis represents time $t$ .
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Figure 4
Simulations of polarization evolution in time and space. (a) Spatial polarization buildup with $τ$ (color bar) plotting polarization $P (r, τ)$ in a shell at distance $r$ from the central NV center [during regime I in Fig. 1]. (b) Polarization distribution during readout period $t$ (color bar) in regime III of Fig. 1. Here, we set the initial condition to be the $τ = 120 s$ polarization distribution in (a). (c) Simulated NMR signals following (a) and (b) for different hyperpolarization times $τ$ similar to Fig. 2. Data reveal $T_{2}^{'}$ increase with $τ$ , in agreement with the experimental data in Fig. 2 [see (a) for color bar]. (d) Stretched exponential decay dynamics. Analogous to Fig. 3, data from (c) are plotted on a logarithmic scale with respect to $\sqrt{t}$ . Stretched exponential behavior qualitatively matches data in Fig. 3. Segments labeled (i)–(vi) are used to extract $T_{2}^{'}$ decay constants. (e) Extracted $T_{2}^{'}$ decay constants for representative segments (i)–(vi) show qualitative agreement with Fig. 3. Here, dark lines are simulation and light lines are experimental data. Dashed line marks crossover at $τ \sim 32 s$ .
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