- Open Access
Probing many-body phenomena with atomically thin nuclear spin layers in diamond
Phys. Rev. Research 8, 023304 – Published 16 June, 2026
DOI: https://doi.org/10.1103/6z22-4z36
Abstract
Quantum simulation aims to recreate complex many-body phenomena in controlled environments, offering insights into dynamics that are otherwise difficult to model. Existing platforms, however, are often complex and costly to scale, typically requiring ultrapure vacuum or low temperatures. Here, we introduce a platform based on a thin, strongly interacting nuclear spin layer in diamond that allows controlled exploration of many-body dynamics at room temperature. Nearby nitrogen-vacancy centers enable polarization, readout, and, combined with radio-frequency fields, coherent control of the nuclear spins. We demonstrate strong, tunable interactions among the nuclear spins and use the system to probe discrete time-crystalline order across varying interaction ranges. By combining ease of use with operation at ambient temperatures, our work opens new opportunities for investigating strongly correlated many-body effects.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (63)
- E. Schrödinger, Quantum mechanics 100 years on: An unfinished revolution, Nature (London) 637, 251 (2025).
- C. Viermann, M. Sparn, N. Liebster, M. Hans, E. Kath, Á. Parra-López, M. Tolosa-Simeón, N. Sánchez-Kuntz, T. Haas, H. Strobel, et al., Quantum field simulator for dynamics in curved spacetime, Nature (London) 611, 260 (2022).
- M. D. Maceda and C. Sabín, Digital quantum simulation of cosmological particle creation with IBM quantum computers, Sci. Rep. 15, 3476 (2025).
- P. Richerme, M. C. Revelle, C. G. Yale, D. Lobser, A. D. Burch, S. M. Clark, D. Saha, M. A. Lopez-Ruiz, A. Dwivedi, J. M. Smith, et al., Quantum computation of hydrogen bond dynamics and vibrational spectra, J. Phys. Chem. Lett. 14, 7256 (2023).
- T. Navickas, R. J. MacDonell, C. H. Valahu, V. C. Olaya-Agudelo, F. Scuccimarra, M. J. Millican, V. G. Matsos, H. L. Nourse, A. D. Rao, M. J. Biercuk, et al., Experimental quantum simulation of chemical dynamics, J. Am. Chem. Soc. 147, 23566 (2025).
- M. C. Banuls, R. Blatt, J. Catani, A. Celi, J. I. Cirac, M. Dalmonte, L. Fallani, K. Jansen, M. Lewenstein, S. Montangero, et al., Simulating lattice gauge theories within quantum technologies, Eur. Phys. J. D 74, 165 (2020).
- G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kalinowski, R. Samajdar, et al., Probing topological spin liquids on a programmable quantum simulator, Science 374, 1242 (2021).
- J. Randall, C. Bradley, F. Van Der Gronden, A. Galicia, M. Abobeih, M. Markham, D. Twitchen, F. Machado, N. Yao, and T. Taminiau, Many-body–localized discrete time crystal with a programmable spin-based quantum simulator, Science 374, 1474 (2021).
- X. Mi, M. Ippoliti, C. Quintana, A. Greene, Z. Chen, J. Gross, F. Arute, K. Arya, J. Atalaya, R. Babbush, et al., Time-crystalline eigenstate order on a quantum processor, Nature (London) 601, 531 (2022).
- S. Choi, J. Choi, R. Landig, G. Kucsko, H. Zhou, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, V. Khemani, et al., Observation of discrete time-crystalline order in a disordered dipolar many-body system, Nature (London) 543, 221 (2017).
- M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, and L. C. Hollenberg, The nitrogen-vacancy colour centre in diamond, Phys. Rep. 528, 1 (2013).
- H. Gao, L. S. Martin, L. B. Hughes, N. T. Leitao, P. Put, H. Zhou, N. U. Koyluoglu, S. A. Meynell, A. C. B. Jayich, H. Park, et al., Signal amplification in a solid-state sensor through asymmetric many-body echo, Nature (London) 646, 68 (2025).
- W. Wu, E. J. Davis, L. B. Hughes, B. Ye, Z. Wang, D. Kufel, T. Ono, S. A. Meynell, M. Block, C. Liu, et al., Spin squeezing in an ensemble of nitrogen-vacancy centers in diamond, Nature (London) 646, 7480 (2025).
- J. Cai, A. Retzker, F. Jelezko, and M. B. Plenio, A large-scale quantum simulator on a diamond surface at room temperature, Nat. Phys. 9, 168 (2013).
- I. Lovchinsky, J. Sanchez-Yamagishi, E. Urbach, S. Choi, S. Fang, T. Andersen, K. Watanabe, T. Taniguchi, A. Bylinskii, E. Kaxiras, et al., Magnetic resonance spectroscopy of an atomically thin material using a single-spin qubit, Science 355, 503 (2017).
- T. Unden, N. Tomek, T. Weggler, F. Frank, P. London, J. Zopes, C. Degen, N. Raatz, J. Meijer, H. Watanabe, et al., Coherent control of solid state nuclear spin nano-ensembles, npj Quantum Inf. 4, 39 (2018).
- C. Findler, J. Lang, C. Osterkamp, M. Nesládek, and F. Jelezko, Indirect overgrowth as a synthesis route for superior diamond nano sensors, Sci. Rep. 10, 22404 (2020).
- N. Y. Yao, A. C. Potter, I.-D. Potirniche, and A. Vishwanath, Discrete time crystals: Rigidity, criticality, and realizations, Phys. Rev. Lett. 118, 030401 (2017).
- F. Silva, X. Bonnin, J. Scharpf, and A. Pasquarelli, Microwave analysis of PACVD diamond deposition reactor based on electromagnetic modelling, Diamond Relat. Mater. 19, 397 (2010).
- C. Osterkamp, Engineering colour centres in tailored diamond, Ph.D. thesis, Universität Ulm, 2021.
- J. Lang, Atomic engineering of defects in diamond: A platform for quantum technologies, Ph.D. thesis, Universität Ulm, 2023.
- J. Casanova, Z.-Y. Wang, J. F. Haase, and M. B. Plenio, Robust dynamical decoupling sequences for individual-nuclear-spin addressing, Phys. Rev. A 92, 042304 (2015).
- T. H. Taminiau, J. J. T. Wagenaar, T. Van der Sar, F. Jelezko, V. V. Dobrovitski, and R. Hanson, Detection and control of individual nuclear spins using a weakly coupled electron spin, Phys. Rev. Lett. 109, 137602 (2012).
- M. Loretz, J. M. Boss, T. Rosskopf, H. J. Mamin, D. Rugar, and C. L. Degen, Spurious harmonic response of multipulse quantum sensing sequences, Phys. Rev. X 5, 021009 (2015).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/6z22-4z36 for details on the experimental setup, numerical simulations of distance estimation, polarization dynamics, and time-crystalline order, as well as additional information on nuclear coherence experiments, which includes Refs. [42, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63].
- P. Schätzle, R. Ghassemizadeh, D. F. Urban, T. Wellens, P. Knittel, F. Reiter, J. Jeske, and W. Hahn, Spin coherence in strongly coupled spin baths in quasi-two-dimensional layers, Phys. Rev. B 110, L220302 (2024).
- S. Nadarajah, A generalized normal distribution, J. Appl. Stat. 32, 685 (2005).
- M. Posselt and J. Biersack, Computer simulation of ion implantation into crystalline targets, Nucl. Instrum. Methods Phys. Res., Sect. B 64, 706 (1992).
- P. London, J. Scheuer, J.-M. Cai, I. Schwarz, A. Retzker, M. B. Plenio, M. Katagiri, T. Teraji, S. Koizumi, J. Isoya, R. Fischer, L. P. McGuinness, B. Naydenov, and F. Jelezko, Detecting and polarizing nuclear spins with double resonance on a single electron spin, Phys. Rev. Lett. 111, 067601 (2013).
- A. Henstra, P. Dirksen, J. Schmidt, and W. T. Wenckebach, Nuclear spin orientation via electron spin locking (novel), J. Magn. Reson. (1969) 77, 389 (1988).
- S. R. Hartmann and E. L. Hahn, Nuclear double resonance in the rotating frame, Phys. Rev. 128, 2042 (1962).
- O. T. Whaites, C. I. Ioannou, B. J. Pingault, G. L. van de Stolpe, T. H. Taminiau, and T. S. Monteiro, Hyperpolarization of nuclear spins: Polarization blockade, Phys. Rev. Res. 5, 043291 (2023).
- K. Sasaki and E. Abe, Suppression of pulsed dynamic nuclear polarization by many-body spin dynamics, Phys. Rev. Lett. 132, 106904 (2024).
- A. W. Overhauser, Polarization of nuclei in metals, Phys. Rev. 92, 411 (1953).
- A. Ajoy, B. Safvati, R. Nazaryan, J. Oon, B. Han, P. Raghavan, R. Nirodi, A. Aguilar, K. Liu, X. Cai, et al., Hyperpolarized relaxometry based nuclear 1 noise spectroscopy in diamond, Nat. Commun. 10, 5160 (2019).
- E. L. Hahn, Spin echoes, Phys. Rev. 80, 580 (1950).
- J. Choi, H. Zhou, H. S. Knowles, R. Landig, S. Choi, and M. D. Lukin, Robust dynamic Hamiltonian engineering of many-body spin systems, Phys. Rev. X 10, 031002 (2020).
- J. S. Waugh, L. M. Huber, and U. Haeberlen, Approach to high-resolution NMR in solids, Phys. Rev. Lett. 20, 180 (1968).
- F. Wilczek, Quantum time crystals, Phys. Rev. Lett. 109, 160401 (2012).
- M. P. Zaletel, M. Lukin, C. Monroe, C. Nayak, F. Wilczek, and N. Y. Yao, Colloquium: Quantum and classical discrete time crystals, Rev. Mod. Phys. 95, 031001 (2023).
- W. W. Ho, S. Choi, M. D. Lukin, and D. A. Abanin, Critical time crystals in dipolar systems, Phys. Rev. Lett. 119, 010602 (2017).
- W. Beatrez, O. Janes, A. Akkiraju, A. Pillai, A. Oddo, P. Reshetikhin, E. Druga, M. McAllister, M. Elo, B. Gilbert, D. Suter, and A. Ajoy, Floquet prethermalization with lifetime exceeding 90 s in a bulk hyperpolarized solid, Phys. Rev. Lett. 127, 170603 (2021).
- P. Peng, C. Yin, X. Huang, C. Ramanathan, and P. Cappellaro, Floquet prethermalization in dipolar spin chains, Nat. Phys. 17, 444 (2021).
- H. Mamin, C. T. Rettner, M. Sherwood, L. Gao, and D. Rugar, High field-gradient dysprosium tips for magnetic resonance force microscopy, Appl. Phys. Lett. 100, 013102 (2012).
- A. L. Burin, Localization in a random XY model with long-range interactions: Intermediate case between single-particle and many-body problems, Phys. Rev. B 92, 104428 (2015).
- J. Casanova, Z.-Y. Wang, and M. B. Plenio, Arbitrary nuclear-spin gates in diamond mediated by a nitrogen-vacancy-center electron spin, Phys. Rev. A 96, 032314 (2017).
- C. E. Bradley, J. Randall, M. H. Abobeih, R. C. Berrevoets, M. J. Degen, M. A. Bakker, M. Markham, D. J. Twitchen, and T. H. Taminiau, A ten-qubit solid-state spin register with quantum memory up to one minute, Phys. Rev. X 9, 031045 (2019).
- T. Joas, F. Ferlemann, R. Sailer, P. J. Vetter, J. Zhang, R. S. Said, T. Teraji, S. Onoda, T. Calarco, G. Genov, and M.M. Muller, and F. Jelezko, High-fidelity electron spin gates for scaling diamond quantum registers, Phys. Rev. X 15, 021069 (2025).
- L. M. Pham, S. J. DeVience, F. Casola, I. Lovchinsky, A. O. Sushkov, E. Bersin, J. Lee, E. Urbach, P. Cappellaro, H. Park, et al., NMR technique for determining the depth of shallow nitrogen-vacancy centers in diamond, Phys. Rev. B 93, 045425 (2016).
- C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017).
- A. Gali, M. Fyta, and E. Kaxiras, Ab initio supercell calculations on nitrogen-vacancy center in diamond: Electronic structure and hyperfine tensors, Phys. Rev. B 77, 155206 (2008).
- R. Blinder, Y. Mindarava, T. H. Tran, A. Momenzadeh, S. Yang, P. Siyushev, H. Sumiya, K. Tamasaku, T. Osaka, N. Morishita, et al., Reducing inhomogeneous broadening of spin and optical transitions of nitrogen-vacancy centers in high-pressure, high-temperature diamond, Commun. Mater. 5, 224 (2024).
- Y. Mindarava, R. Blinder, V. A. Davydov, M. Zaghrioui, V. N. Agafonov, C. Autret, P. Balasubramanian, R. Gonzalez Brouwer, and F. Jelezko, “Core–shell” diamond nanoparticles with centers and a highly isotopically enriched shell as a promising hyperpolarization agent, J. Phys. Chem. C 125, 27647 (2021).
- T. Hom, W. Kiszenik, and B. Post, Accurate lattice constants from multiple reflection measurements. II. Lattice constants of germanium silicon, and diamond, J. Appl. Crystallogr. 8, 457 (1975).
- J. R. Maze, A. Dréau, V. Waselowski, H. Duarte, J.-F. Roch, and V. Jacques, Free induction decay of single spins in diamond, New J. Phys. 14, 103041 (2012).
- A. Karabanov, D. Wiśniewski, I. Lesanovsky, and W. Köckenberger, Dynamic nuclear polarization as kinetically constrained diffusion, Phys. Rev. Lett. 115, 020404 (2015).
- M. Fishman, S. White, and E. M. Stoudenmire, The ITensor software library for tensor network calculations, SciPost Phys. Codebases 4 (2022).
- M. Pfender, N. Aslam, H. Sumiya, S. Onoda, P. Neumann, J. Isoya, C. A. Meriles, and J. Wrachtrup, Nonvolatile nuclear spin memory enables sensor-unlimited nanoscale spectroscopy of small spin clusters, Nat. Commun. 8, 834 (2017).
- U. Haeberlen, High Resolution NMR in Solids: Selective Averaging, Advances in Magnetic Resonance Supplement 1 (Academic Press, New York, 1976).
- N. Grimm, K. Senkalla, P. J. Vetter, J. Frey, P. Gundlapalli, T. Calarco, G. Genov, M. M. Müller, and F. Jelezko, Coherent control of a long-lived nuclear memory spin in a germanium-vacancy multi-qubit node, Phys. Rev. Lett. 134, 043603 (2025).
- M. Degen, S. Loenen, H. Bartling, C. Bradley, A. Meinsma, M. Markham, D. Twitchen, and T. Taminiau, Entanglement of dark electron-nuclear spin defects in diamond, Nat. Commun. 12, 3470 (2021).
- A. Ajoy, R. Nirodi, A. Sarkar, P. Reshetikhin, E. Druga, A. Akkiraju, M. McAllister, G. Maineri, S. Le, A. Lin, et al., Dynamical decoupling in interacting systems: Applications to signal-enhanced hyperpolarized readout, arXiv:2008.08323.
- C. Findler, R. Blinder, K. Schüle, P. Balasubramanian, C. Osterkamp, and F. Jelezko, Detecting nitrogen-vacancy-hydrogen centers on the nanoscale using nitrogen-vacancy centers in diamond, Phys. Rev. Mater. 8, 026203 (2024).