Engineering spin coherence in core-shell diamond nanocrystals

Abstract

Fluorescent diamond nanocrystals can host spin qubit sensors capable of probing the physical properties of biological systems with nanoscale spatial resolution. Sub-100 nm diamond nanosensors can readily be delivered into intact cells and even living organisms. However, applications beyond current proof-of-principle experiments require a substantial increase in sensitivity, which is limited by surface induced charge instability and electron-spin dephasing. In this work, we utilize engineered core-shell structures to achieve a drastic increase in qubit coherence times (T₂) from 1.1 to 35 μs in bare nanodiamonds to upward of 52 to 87 μs. We use electron-paramagnetic-resonance results to present a band bending model and connect silica encapsulation to the removal of deleterious mid-gap surface states that are negatively affecting the qubit's spin properties. Combined with a 1.9-fold increase in particle luminescence these advances correspond to up to two-order-of-magnitude reduction in integration time. Probing qubit dynamics at a single particle level further reveals that the noise characteristics fundamentally change from a bath with spins that rearrange their spatial configuration during the course of an experiment to a more dilute static bath. The observed results shed light on the underlying mechanisms governing fluorescence and spin properties in diamond nanocrystals and offer an effective noise mitigation strategy based on engineered core-shell structures.

Keywords: core-shell; nanodiamonds; quantum engineering; quantum sensing; qubit coherence.

Fig. 1.

Optical properties of bare and core-shell particles. (A) False-colored TEM of Bare (Top) and core-shell (Bottom) particles. Blue corresponds to the diamond core and green to the silica shell (for raw TEM images and size distributions see SI Appendix, Fig. S3). The aggregation of core-shell particles is an artifact of drying the solution on the TEM grid (SI Appendix). (B) CLEM measurements of fluorescence of core-shell (green circles) and bare (blue circles) particles as a function of their diamond core radius. Solid lines represent a fit to y = ar³, where r is the core radius and a is a fit parameter. Inset: representative TEM of a bare (i) and a core-shell (ii) particle, marked in red on the main panel. Although these particles exhibit similar fluorescent intensity, the diamond core radius of the core-shell particle is smaller. (C) Normalized spectrum (Top) obtained from an ensemble of core-shell (green) and bare (blue) particles. Dashed black lines represent deconvolution to NV⁰ (Left) and NV^– (Right) (black lines are extracted from figure 1 in ref. 31). Subtraction (lower panel) of the core-shell spectrum from bare spectrum showing a shift from NV⁰ to NV^– in core-shell particles. Spectral decomposition reveals that for bare diamond, 24% of the emission originates from NV^– and for core-shell structures, 29% originates from NV^–.

Fig. 2.

EPR of paramagnetic defects in bare and core-shell particles. (A) Continuous wave X-band EPR (g = 2.0031 ± 0.00005) for bare (blue) and core-shell (green) diamond nanocrystals with ~70 nm core size. (B) Spectral deconvolution of the EPR signal into contributions from X (g = 2.0032), H1 (g = 2.0028), and P1-spins (g = 2.0026), normalized to a sample mass of 1 mg. All measurements were performed at room temperature. See methods and SI5 for details about EPR spectrum modeling. (C) Band energy diagram for both oxygen-terminated (Left) and SiO2-coated (Right) diamonds with corresponding affinities (χ). The model shows the corresponding spatial dependence of the Fermi level (Ef), conduction band minimum (Ec), valence band maximum (Ev), and substitutional nitrogen (P1; orange). The diamond–silica heterojunction exhibits a type 1 band alignment with an upward band bending of diamond energy levels. A conduction band offset (CBO) of 1.3 eV and a valence band offset (VBO) of 2.6 eV promote confinement of charges to the diamond, as supported by the higher fluorescence of core-shell particles. The energies and occupation of X-spins levels are also illustrated as a Gaussian near Ef, positioned within the ~1.95 eV gap between the NV center ground (NV⁻) and excited (NV⁻) gestates. (D) Schematic depiction of a bare (Top) and a core-shell (Bottom) structured diamond nanocrystal with an NV-qubit (orange) in the diamond host blue. Surface spins are indicated in yellow.

Fig. 3.

Relaxation and coherence of individually resolvable diamond nanocrystals. (A) Single quantum relaxation measurements of bare (blue; n = 24) and core-shell (green; n = 23) particles presented as a box and whiskers plot (Left) and a histogram (Right). The Inset shows double quantum relaxation times of the same particles (double quantum relaxations were measured at ~6.7 G). (B) Maximally obtained T₂ times under CPMG dynamical decoupling of randomly selected twelve bare and eight core-shell particles presented as a function of the number of pulses applied (Left) and as a histogram (Right). Note, for some of the investigated bare diamonds T₂ does not increase with N (blue points with low N number of pulses), while for all core-shell structured particles, we observed a T₂ for N > 1,000 (SI Appendix, Fig. S9 and Section S9). Solid lines are fits to a power law as described in the main text. The Inset shows a representative coherence time trace data for one bare and one core-shell particle with N = 1,472. (C) Correlation of core size with T₁ (Upper) and max T₂ (Lower) for four bare and four core-shell particles. (D) Representative CLEM images of bare (Upper) and core-shell (Lower) particles for the data shown in C. Insets are larger magnifications of individual particles. (Scale bar, 100 nm.) See SI Appendix, Fig. S4 for TEM images of additional particles from each group. See Dataset S2 for full dataset.

Fig. 4.

Probing spin bath properties using spectral decomposition and stretching factor spectroscopy. (A) Spectral decomposition of CPMG data from bare (blue) and core-shell (green) particles. Gray dotted lines show fits to 1/f ^a considering DQ data (SI Appendix, Fig. S10). Solid lines show fits for 1/f^a plus a single (for bare) or a double (for core-shell) Lorentzian, with the addition of white noise (SI Appendix, Fig. S10 for exact fitting details). (B) Four representatives bare (Left) and core-shell (Right) echo stretching factors. Gray dashed lines are exponential fits for the random walk regime (the cutoff is marked by the black dashed line). Core-shell particles also show ballistic regime fits to n = 3. (C) Distribution of echo stretching factors for bare (blue) and core-shell (green). Data points with n ≤ 0.75 (blue box) can be explained by configurational averaging, while data points with n ≈ 1 (green box) correspond to fixed spins’ positions (see SI Appendix, Section S11 for more details).