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arxiv: 2512.22739 · v2 · submitted 2025-12-28 · 🪐 quant-ph

A method for robust spin relaxometry in the presence of imperfect state preparation

Ella P. Walsh , Sepehr Ahmadi , Alexander J. Healey , David A. Simpson , Liam T. Hall This is my paper

Pith reviewed 2026-05-16 20:03 UTC · model grok-4.3

classification 🪐 quant-ph
keywords spin relaxometryNV centersT1 relaxationimperfect polarizationquantum sensingnitrogen-vacancyparamagnetic sensingstate preparation
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The pith

A minimal fitting procedure corrects for imperfect spin polarization to give accurate T1 relaxation times in NV-center experiments.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops a fitting method for spin relaxometry with nitrogen-vacancy centers that handles cases where the initial spin state is not perfectly prepared. Standard analysis assumes perfect polarization and thus reports artificially short relaxation times when that assumption fails. The authors add a small number of parameters to the decay model to absorb the preparation errors. If successful, the method delivers reliable parameter estimates without extra hardware or perfect initialization. Researchers in condensed matter and medical sensing would benefit because it reduces systematic errors in field-free measurements.

Core claim

The authors claim that a minimal extension to the standard exponential fit, incorporating parameters for imperfect spin polarization, produces more accurate and robust estimates of relaxation times than conventional approaches, and that this framework supports efficient parallel computation of single-spin dynamics.

What carries the argument

a minimal fitting procedure that augments the T1 decay model with parameters for preparation errors

If this is right

  • More accurate T1 estimates in the presence of preparation imperfections
  • Reduced artifacts in paramagnetic sensing using NV centers
  • Framework for parallelizing studies of single-spin dynamics

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This approach might generalize to other quantum sensors where state initialization is imperfect.
  • It could enable more reliable measurements in nanodiamond-based sensing without additional calibration steps.
  • The parallelization framework suggests potential for scaling up to ensemble measurements or higher-throughput experiments.

Load-bearing premise

The assumption that a minimal set of additional parameters can fully capture the effects of imperfect spin polarization without introducing new systematic biases or requiring extensive validation data.

What would settle it

Experimental data from NV centers with independently verified perfect polarization should yield identical T1 values from both the new model and standard fits; significant deviation would falsify the robustness claim.

Figures

Figures reproduced from arXiv: 2512.22739 by Alexander J. Healey, David A. Simpson, Ella P. Walsh, Liam T. Hall, Sepehr Ahmadi.

Figure 1
Figure 1. Figure 1: FIG. 1. a) Widefield imaging of an ensemble of NV centers is captured with a camera. Laser power can be controlled by changing the linear [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. a) The two state system used to model relaxometry decays [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. a) The PL from the reference measurement of the bare [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

Spin relaxometry based on quantum spin systems has developed as a valuable tool in medical and condensed matter systems, offering the advantage of operating without the need for external DC or RF fields. Spin relaxometry with nitrogen-vacancy (NV) centers has been applied to paramagnetic sensing using both single crystal diamond and nanodiamond materials. However, these methods often suffer from artifacts and systematic uncertainties, particularly due to imperfect spin state preparation, leading to artificially fast T$_1$ relaxation times. Current analysis techniques fail to adequately account for these issues, limiting the precision of parameter estimation. In this work, we introduce a minimal fitting procedure that enables more robust parameter estimation in the presence of imperfect spin polarization. Our model improves upon existing approaches by offering more accurate fits and provides a framework for efficiently parallelizing single-spin dynamics studies.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript introduces a minimal fitting procedure for NV-center spin relaxometry that accounts for imperfect spin-state preparation, which is said to produce artificially fast T1 times in existing methods. The procedure is claimed to yield more accurate parameter estimates and to provide a framework for efficient parallelization of single-spin dynamics studies in paramagnetic sensing applications using both bulk and nanodiamond samples.

Significance. If the fitting procedure can be shown to be robust and free of new systematic biases, the work would offer a practical, low-overhead improvement to T1-based sensing in medical and condensed-matter contexts, where imperfect polarization is a common source of uncertainty.

major comments (1)
  1. [Abstract] Abstract: the central claim that the model 'improves upon existing approaches by offering more accurate fits' is stated without any equations, explicit parameter definitions, validation data, error analysis, or comparison to prior methods, leaving the load-bearing assertion unsupported by visible evidence.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review and recommendation of major revision. We address the single major comment below and have revised the manuscript to strengthen the abstract's presentation of our central claim.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the model 'improves upon existing approaches by offering more accurate fits' is stated without any equations, explicit parameter definitions, validation data, error analysis, or comparison to prior methods, leaving the load-bearing assertion unsupported by visible evidence.

    Authors: We agree that the abstract, as originally written, is too terse to stand alone on this point. The full manuscript defines the minimal fitting model explicitly in Section II (Eqs. 1–3), which incorporates the initial polarization factor P0 to account for imperfect state preparation; parameter definitions and the likelihood function appear in Section III; validation consists of Monte Carlo simulations, experimental NV-center data on both bulk and nanodiamond samples, bootstrap error estimates, and direct side-by-side comparison with standard single-exponential fitting in Section IV and Figures 2–4. To address the referee’s concern we have revised the abstract to include a one-sentence reference to the governing equation and to the quantitative improvement demonstrated in the validation section, thereby making the central claim traceable within the abstract itself. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The abstract introduces a minimal fitting procedure to correct for imperfect spin polarization in NV-center relaxometry, claiming more accurate fits without providing any equations, parameter definitions, or derivation steps. No load-bearing step reduces a claimed prediction to a quantity defined by its own fitted inputs, nor does the text invoke self-citations, uniqueness theorems, or ansatzes that collapse the central claim to its inputs by construction. The correction term is presented as independent, and the derivation remains self-contained against external benchmarks with no enumerated circularity patterns identifiable from the given text.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the fitting model is described at a high level without mathematical detail.

pith-pipeline@v0.9.0 · 5451 in / 927 out tokens · 22888 ms · 2026-05-16T20:03:27.144205+00:00 · methodology

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Reference graph

Works this paper leans on

41 extracted references · 41 canonical work pages

  1. [1]

    Figure 3e compares the relaxation rates measured for individual paramagnetic particles across the FOV for the two analysis methods. An averageΓ 1 value for each particle was calculated from a 10×10 pixel region centered on the particle (SI Figure 4), and error bars are indicative of the standard deviation over this region. We can see that the two- state f...

    work page

  2. [2]

    Balasubramanian, P

    G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V . Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, Ultralong spin coherence time in isotopically engineered diamond, Nature Materials8, 383 (2009)

    work page 2009

  3. [3]

    Mohan, C.-S

    N. Mohan, C.-S. Chen, H.-H. Hsieh, Y .-C. Wu, and H.- C. Chang, In Vivo Imaging and Toxicity Assessments of Fluorescent Nanodiamonds in Caenorhabditis elegans, Nano Letters10, 3692 (2010)

    work page 2010

  4. [4]

    L. T. Hall, P. Kehayias, D. A. Simpson, A. Jarmola, A. Stacey, D. Budker, and L. C. L. Hollenberg, Detection of nanoscale electron spin resonance spectra demonstrated using nitrogen- vacancy centre probes in diamond, Nature Communications7, 10211 (2016)

    work page 2016

  5. [5]

    E. S. Grant, L. T. Hall, L. C. L. Hollenberg, G. McColl, and D. A. Simpson, Nonmonotonic Superparamagnetic Behavior of the Ferritin Iron Core Revealed via Quantum Spin Relaxometry, ACS Nano17, 372 (2023)

    work page 2023

  6. [6]

    Schäfer-Nolte, L

    E. Schäfer-Nolte, L. Schlipf, M. Ternes, F. Reinhard, K. Kern, and J. Wrachtrup, Tracking Temperature-Dependent Relaxation Times of Ferritin Nanomagnets with a Wideband Quantum Spectrometer, Physical Review Letters113, 217204 (2014)

    work page 2014

  7. [7]

    Pelliccione, B

    M. Pelliccione, B. A. Myers, L. M. A. Pascal, A. Das, and A. C. Bleszynski Jayich, Two-Dimensional Nanoscale Imaging of Gadolinium Spins via Scanning Probe Relaxometry with a Single Spin in Diamond, Physical Review Applied2, 054014 (2014)

    work page 2014

  8. [8]

    A. O. Sushkov, N. Chisholm, I. Lovchinsky, M. Kubo, P. K. Lo, S. D. Bennett, D. Hunger, A. Akimov, R. L. Walsworth, H. Park, and M. D. Lukin, All-Optical Sensing of a Single- Molecule Electron Spin, Nano Letters14, 6443 (2014)

    work page 2014

  9. [9]

    Rendler, J

    T. Rendler, J. Neburkova, O. Zemek, J. Kotek, A. Zappe, Z. Chu, P. Cigler, and J. Wrachtrup, Optical imaging of localized chemical events using programmable diamond quantum nanosensors, Nature Communications8, 14701 (2017)

    work page 2017

  10. [10]

    R. A. Shugayev, S. E. Crawford, J. P. Baltrus, N. A. Diemler, J. E. Ellis, K.-J. Kim, and P. C. Cvetic, Synthesis and Quantum Metrology of Metal–Organic Framework- Coated Nanodiamonds Containing Nitrogen Vacancy Centers, Chemistry of Materials33, 6365 (2021)

    work page 2021

  11. [11]

    Perona Martínez, A

    F. Perona Martínez, A. C. Nusantara, M. Chipaux, S. K. Padamati, and R. Schirhagl, Nanodiamond Relaxometry-Based Detection of Free-Radical Species When Produced in Chemical Reactions in Biologically Relevant Conditions, ACS Sensors5, 3862 (2020)

    work page 2020

  12. [12]

    J. M. Abendroth, K. Herb, E. Janitz, T. Zhu, L. A. Völker, and C. L. Degen, Single-Nitrogen–Vacancy NMR of Amine- Functionalized Diamond Surfaces, Nano Letters22, 7294 (2022)

    work page 2022

  13. [13]

    Müller, X

    C. Müller, X. Kong, J.-M. Cai, K. Melentijevi ´c, A. Stacey, M. Markham, D. Twitchen, J. Isoya, S. Pezzagna, J. Meijer, J. F. Du, M. B. Plenio, B. Naydenov, L. P. McGuinness, and F. Jelezko, Nuclear magnetic resonance spectroscopy with single spin sensitivity, Nature Communications5, 4703 (2014)

    work page 2014

  14. [14]

    R. W. de Gille, J. M. McCoey, L. T. Hall, J.-P. Tetienne, E. P. Malkemper, D. A. Keays, L. C. L. Hollenberg, and D. A. Simpson, Quantum magnetic imaging of iron organelles within the pigeon cochlea, Proceedings of the National Academy of Sciences118, e2112749118 (2021)

    work page 2021

  15. [15]

    D. P. Cistola and M. D. Robinson, Compact NMR relaxometry of human blood and blood components, TrAC Trends in Analytical Chemistry SI: Compact NMR,83, 53 (2016)

    work page 2016

  16. [16]

    Steinert, F

    S. Steinert, F. Ziem, L. T. Hall, A. Zappe, M. Schweikert, N. Götz, A. Aird, G. Balasubramanian, L. Hollenberg, and J. Wrachtrup, Magnetic spin imaging under ambient conditions with sub-cellular resolution, Nature Communications4, 1607 (2013)

    work page 2013

  17. [17]

    Kaufmann, D

    S. Kaufmann, D. A. Simpson, L. T. Hall, V . Perunicic, P. Senn, S. Steinert, L. P. McGuinness, B. C. Johnson, T. Ohshima, F. Caruso, J. Wrachtrup, R. E. Scholten, P. Mulvaney, and L. Hollenberg, Detection of atomic spin labels in a lipid bilayer using a single-spin nanodiamond probe, Proceedings of the National Academy of Sciences110, 10894 (2013)

    work page 2013

  18. [18]

    Schmid-Lorch, T

    D. Schmid-Lorch, T. Häberle, F. Reinhard, A. Zappe, M. Slota, L. Bogani, A. Finkler, and J. Wrachtrup, Relaxometry and Dephasing Imaging of Superparamagnetic Magnetite Nanoparticles Using a Single Qubit, Nano Letters15, 4942 9 (2015)

    work page 2015

  19. [19]

    Maletinsky, S

    P. Maletinsky, S. Hong, M. S. Grinolds, B. Hausmann, M. D. Lukin, R. L. Walsworth, M. Loncar, and A. Yacoby, A robust scanning diamond sensor for nanoscale imaging with single nitrogen-vacancy centres, Nature Nanotechnology7, 320 (2012)

    work page 2012

  20. [20]

    Wrachtrup and A

    J. Wrachtrup and A. Finkler, Single spin magnetic resonance, Journal of Magnetic Resonance269, 225 (2016)

    work page 2016

  21. [21]

    Bluvstein, Z

    D. Bluvstein, Z. Zhang, and A. C. B. Jayich, Identifying and Mitigating Charge Instabilities in Shallow Diamond Nitrogen- Vacancy Centers, Physical Review Letters122, 076101 (2019)

    work page 2019

  22. [22]

    Z. Guo, Y . Huang, M. Cai, C. Li, M. Shen, M. Wang, P. Yu, Y . Wang, F. Shi, P. Wang, and J. Du, Wide-field Fourier magnetic imaging with electron spins in diamond, npj Quantum Information10, 1 (2024)

    work page 2024

  23. [23]

    Pfender, N

    M. Pfender, N. Aslam, G. Waldherr, P. Neumann, and J. Wrachtrup, Single-spin stochastic optical reconstruction microscopy, Proceedings of the National Academy of Sciences 111, 14669 (2014)

    work page 2014

  24. [24]

    D. J. McCloskey, N. Dontschuk, D. A. Broadway, A. Nadarajah, A. Stacey, J.-P. Tetienne, L. C. L. Hollenberg, S. Prawer, and D. A. Simpson, Enhanced Widefield Quantum Sensing with Nitrogen-Vacancy Ensembles Using Diamond Nanopillar Arrays, ACS Applied Materials & Interfaces12, 13421 (2020)

    work page 2020

  25. [25]

    S. A. Momenzadeh, R. J. Stöhr, F. F. de Oliveira, A. Brunner, A. Denisenko, S. Yang, F. Reinhard, and J. Wrachtrup, Nanoengineered Diamond Waveguide as a Robust Bright Platform for Nanomagnetometry Using Shallow Nitrogen Vacancy Centers, Nano Letters15, 165 (2015)

    work page 2015

  26. [26]

    C. J. Widmann, C. Giese, M. Wolfer, D. Brink, N. Heidrich, and C. E. Nebel, Fabrication and characterization of single crystalline diamond nanopillars with NV-centers, Diamond and Related Materials Advances in Diamond Thin Films and Novel Nanocarbon Materials,54, 2 (2015)

    work page 2015

  27. [27]

    E. Neu, P. Appel, M. Ganzhorn, J. Miguel-Sánchez, M. Lesik, V . Mille, V . Jacques, A. Tallaire, J. Achard, and P. Maletinsky, Photonic nano-structures on (111)-oriented diamond, Applied Physics Letters104, 153108 (2014)

    work page 2014

  28. [28]

    T. M. Babinec, B. J. M. Hausmann, M. Khan, Y . Zhang, J. R. Maze, P. R. Hemmer, and M. Lon ˇcar, A diamond nanowire single-photon source, Nature Nanotechnology5, 195 (2010)

    work page 2010

  29. [29]

    D. A. Simpson, J.-P. Tetienne, J. M. McCoey, K. Ganesan, L. T. Hall, S. Petrou, R. E. Scholten, and L. C. L. Hollenberg, Magneto-optical imaging of thin magnetic films using spins in diamond, Scientific Reports6, 22797 (2016)

    work page 2016

  30. [30]

    J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, High-sensitivity diamond magnetometer with nanoscale resolution, Nature Physics4, 810 (2008)

    work page 2008

  31. [31]

    C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Reviews of Modern Physics89, 035002 (2017)

    work page 2017

  32. [32]

    J. D. A. Wood, D. A. Broadway, L. T. Hall, A. Stacey, D. A. Simpson, J.-P. Tetienne, and L. C. L. Hollenberg, Wide-band nanoscale magnetic resonance spectroscopy using quantum relaxation of a single spin in diamond, Physical Review B94, 155402 (2016)

    work page 2016

  33. [33]

    D. C. Johnston, Stretched exponential relaxation arising from a continuous sum of exponential decays, Physical Review B74, 184430 (2006)

    work page 2006

  34. [34]

    Tetienne, R

    J.-P. Tetienne, R. W. de Gille, D. A. Broadway, T. Teraji, S. E. Lillie, J. M. McCoey, N. Dontschuk, L. T. Hall, A. Stacey, D. A. Simpson, and L. C. L. Hollenberg, Spin properties of dense near-surface ensembles of nitrogen-vacancy centers in diamond, Physical Review B97, 085402 (2018)

    work page 2018

  35. [35]

    Pezzagna, B

    S. Pezzagna, B. Naydenov, F. Jelezko, J. Wrachtrup, and J. Meijer, Creation efficiency of nitrogen-vacancy centres in diamond, New Journal of Physics12, 065017 (2010)

    work page 2010

  36. [36]

    Jarmola, V

    A. Jarmola, V . M. Acosta, K. Jensen, S. Chemerisov, and D. Budker, Temperature- and Magnetic-Field-Dependent Longitudinal Spin Relaxation in Nitrogen-Vacancy Ensembles in Diamond, Physical Review Letters108, 197601 (2012)

    work page 2012

  37. [37]

    D. A. Redman, S. Brown, R. H. Sands, and S. C. Rand, Spin dynamics and electronic states of N-V centers in diamond by EPR and four-wave-mixing spectroscopy, Physical Review Letters67, 3420 (1991)

    work page 1991

  38. [38]

    M. B. Walker, A T5 spin–lattice relaxation rate for non-Kramers ions, Canadian Journal of Physics46, 1347 (1968)

    work page 1968

  39. [39]

    B. T. Flinn, V . Radu, M. W. Fay, A. J. Tyler, J. Pitcairn, M. J. Cliffe, B. L. Weare, C. T. Stoppiello, M. L. Mather, and A. N. Khlobystov, Nitrogen vacancy defects in single-particle nanodiamonds sense paramagnetic transition metal spin noise from nanoparticles on a transmission electron microscopy grid, Nanoscale Advances5, 6423 (2023)

    work page 2023

  40. [40]

    B. A. Myers, A. Das, M. C. Dartiailh, K. Ohno, D. D. Awschalom, and A. C. Bleszynski Jayich, Probing Surface Noise with Depth-Calibrated Spins in Diamond, Physical Review Letters113, 027602 (2014)

    work page 2014

  41. [41]

    Robledo, H

    L. Robledo, H. Bernien, T. Van Der Sar, and R. Hanson, Spin dynamics in the optical cycle of single nitrogen-vacancy centres in diamond, New Journal of Physics13, 025013 (2011). 10 FIG. SI 1. a) Probability of occupying|0⟩can be seen to converge as N increases. b), c) Population of initial state plotted as a function of time through the sequence in Figure...

    work page 2011