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Coherent microwave control of coupled electron-muon centers

Andrin Doll1,2,*, Chennan Wang1, Thomas Prokscha1, Jan Dreiser2, and Zaher Salman1,†

  • *Contact author: andrin.doll@psi.ch.
  • †Contact author: zaher.salman@psi.ch.
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Phys. Rev. Research 7, 033059 – Published 14 July, 2025

DOI: https://doi.org/10.1103/zgj6-sx4h

Abstract

Coherent control by means of tailored excitation is a key to versatile experimental schemes for spectroscopic investigation and technological utilization of quantum systems. Here we study a quantum system which consists of a coupled electron-muon spin state, i.e., muonium, a light isotope of hydrogen. We demonstrate the most fundamental coherent control techniques by microwave excitation of spin transitions, namely driven Rabi oscillations and Ramsey fringes upon free evolution. Unprecedented performance is achieved by the microwave hardware devised for these experiments, which enables coherent spin manipulation of individual, isolated, muonium centers. For muonium formed in SiO2 with strong electron-muon hyperfine interaction, a virtually undamped free precession signal is observed up to a 3.5µs time window. For muonium formed in Si with weak and anisotropic hyperfine interaction, a strong drive at the multi-quantum transition decouples the muonium center from its magnetic environment formed by the bath of Si29 nuclear spins at natural abundance. We expect that these capabilities will provide a powerful tool to investigate the effect of the environment on isolated coupled spins, uncover the details of coupled electron-muon systems in matter and validate quantum electrodynamics in the context of muonium spectroscopy.

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References (69)

  1. C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017).
  2. A. D. Hillier, S. J. Blundell, I. McKenzie, I. Umegaki, L. Shu, J. A. Wright, T. Prokscha, F. Bert, K. Shimomura, A. Berlie, H. Alberto, and I. Watanabe, Muon spin spectroscopy, Nat. Rev. Methods Primers 2, 4 (2022).
  3. B. D. Patterson, Muonium states in semiconductors, Rev. Mod. Phys. 60, 69 (1988).
  4. I. McKenzie, The positive muon and µSR spectroscopy: Powerful tools for investigating the structure and dynamics of free radicals and spin probes in complex systems, Annu. Rep. Prog. Chem. Sect. C: Phys. Chem. 109, 65 (2013).
  5. A. Stoykov, R. Scheuermann, K. Sedlak, J. Rodriguez, U. Greuter, and A. Amato, High-field µSR instrument at PSI: Detector solutions, Phys. Proc. 30, 7 (2012).
  6. D. Favart, P. M. McIntyre, D. Y. Stowell, V. L. Telegdi, R. DeVoe, and R. A. Swanson, Precision measurement of the hyperfine interval of muonium by a novel technique: Ramsey resonance in zero field, Phys. Rev. Lett. 27, 1336 (1971).
  7. P. A. Thompson, P. Crane, T. Crane, J. J. Amato, V. W. Hughes, G. z. Putlitz, and J. E. Rothberg, Muonium. IV. Precision measurement of the muonium hyperfine-structure interval at weak and very weak magnetic fields, Phys. Rev. A 8, 86 (1973).
  8. D. E. Casperson et al., A new high precision measurement of the muonium hyperfine structure interval Δv1, Phys. Lett. B 59, 397 (1975).
  9. W. Liu et al., High precision measurements of the ground state hyperfine structure interval of muonium and of the muon magnetic moment, Phys. Rev. Lett. 82, 711 (1999).
  10. S. Nishimura et al., Rabi-oscillation spectroscopy of the hyperfine structure of muonium atoms, Phys. Rev. A 104, L020801 (2021).
  11. Mu-MASS Collaboration et al., Precision measurement of the lamb shift in muonium, Phys. Rev. Lett. 128, 011802 (2022).
  12. P. Strasser et al., Precision measurements of muonium and muonic helium hyperfine structure at J-PARC, Eur. Phys. J. D 79, 20 (2025).
  13. J. A. Brown, R. H. Heffner, M. Leon, S. A. Dodds, D. A. Vanderwater, and T. L. Estle, Detection of EPR transitions of muonium in quartz by muon-spin rotation, Phys. Rev. Lett. 43, 1751 (1979).
  14. K. W. Blazey, T. L. Estle, S. L. Rudaz, E. Holzschuh, W. Kündig, and B. D. Patterson, Double electron-muon resonance of anomalous muonium in silicon, Phys. Rev. B 34, 1422 (1986).
  15. J. S. Lord, S. F. J. Cox, H. V. Alberto, J. P. Duarte, and R. C. Vilão, Double-resonance determination of electron g-factors in muonium shallow-donor states, J. Phys.: Condens. Matter 16, S4707 (2004).
  16. Y. Morozumi, K. Nishiyama, and K. Nagamine, Muonium to diamagnetic muon conversion in KCl and NaCl revealed by time-differential muon spin resonance, Phys. Lett. A 118, 93 (1986).
  17. S. R. Kreitzman, RF resonance techniques for continuous muon beams, Hyperfine Interact. 65, 1055 (1991).
  18. R. Scheuermann, L. Schimmele, J. Schmidl, J. Major, D. Herlach, and C. A. Scott, Radio-frequency muon spin resonance (RFµSR) experiments on condensed matter, Appl. Magn. Reson. 13, 195 (1997).
  19. S. P. Cottrell, C. Johnson, S. F. J. Cox, and C. A. Scott, Radio-frequency techniques for muon charge state conversion measurements, Phys. B: Condens. Matter 326, 248 (2003).
  20. C. Johnson, S. P. Cottrell, K. Ghandi, and D. G. Fleming, Muon implantation in inert gases studied by radio frequency spectroscopy, J. Phys. B: At. Mol. Opt. Phys. 38, 119 (2005).
  21. I. McKenzie, R. Scheuermann, S. P. Cottrell, J. S. Lord, and I. M. Tucker, Hyperfine coupling constants of the cyclohexadienyl radical in benzene and dilute aqueous solution, J. Phys. Chem. B 117, 13614 (2013).
  22. D. G. Fleming, S. P. Cottrell, I. McKenzie, and K. Ghandi, Rate constants for the slow Mu + propane abstraction reaction at 300 K by diamagnetic RF resonance, Phys. Chem. Chem. Phys. 17, 19901 (2015).
  23. M. H. Dehn, Y. Cao, P.-X. Wang, S. P. Cottrell, M. J. MacLachlan, D. G. Fleming, and R. F. Kiefl, Direct observation of muonium reacting with uncapped gold nanoparticles in porous silica and nature of the final state, J. Chem. Phys. 152, 184706 (2020).
  24. S. R. Kreitzman, T. L. Estle, B. Hitti, J. W. Schneider, K. H. Chow, and R. L. Lichti, A microwave µSR spectrometer, Hyperfine Interact. 87, 1063 (1994).
  25. J. Lord, Microwave muon spin resonance experiments at ISIS, Phys. B: Condens. Matter 404, 999 (2009).
  26. T. Shiroka, C. Bucci, R. De Renzi, F. Galli, G. Guidi, G. H. Eaton, P. J. C. King, and C. A. Scott, Polarized muon spins in pulsed magnetic fields: A new method to study delayed muonium formation, Phys. Rev. Lett. 83, 4405 (1999).
  27. A. Amato, H. Luetkens, K. Sedlak, A. Stoykov, R. Scheuermann, M. Elender, A. Raselli, and D. Graf, The new versatile general purpose surface-muon instrument (GPS) based on silicon photomultipliers for µSR measurements on a continuous-wave beam, Rev. Sci. Instrum. 88, 093301 (2017).
  28. B. Johansson, S. Haraldson, L. Pettersson, and O. Beckman, A stripline resonator for ESR, Rev. Sci. Instrum. 45, 1445 (1974).
  29. A. Doll, Pulsed and continuous-wave magnetic resonance spectroscopy using a low-cost software-defined radio, AIP Adv. 9, 115110 (2019).
  30. T. Prokscha, K. H. Chow, H. Luetkens, E. Morenzoni, G. Nieuwenhuys, Z. Salman, R. Scheuermann, A. Suter, and H. P. Weber, Low-energy µSR investigations of photo-induced effects on a nm scale, Phys. Procedia 30, 219 (2012).
  31. F. James, M. Winkler et al., Minuit User's Guide, 23 (CERN, Geneva, 2004).
  32. A. Suter and B. M. Wojek, Musrfit: A free platform-independent framework for µSR data analysis, Phys. Proc. 30, 69 (2012).
  33. Y. Avni, Energy spectra of x-ray clusters of galaxies, Astrophys. J. 210, 642 (1976).
  34. S. Pribitzer, A. Doll, and G. Jeschke, SPIDYAN, a MATLAB library for simulating pulse EPR experiments with arbitrary waveform excitation, J. Magn. Reson. 263, 45 (2016).
  35. S. Boentgens, Spinop.m mathematica package (private communication).
  36. O. W. Sørensen, G. W. Eich, M. H. Levitt, G. Bodenhausen, and R. R. Ernst, Product operator formalism for the description of NMR pulse experiments, Prog. Nucl. Magn. Reson. Spectrosc. 16, 163 (1983).
  37. J. A. Brown, S. A. Dodds, T. L. Estle, R. H. Heffner, M. Leon, and D. A. Vanderwater, A precision determination of the hyperfine splitting of muonium in quartz, Solid State Commun. 33, 613 (1980).
  38. A. Schweiger and G. Jeschke, Principles of Pulse Electron Paramagnetic Resonance (Oxford University Press on Demand, Oxford, 2001).
  39. J. H. Brewer, Muonium in quartz, Hyperfine Interact. 8, 375 (1981).
  40. I. Solomon, Rotary spin echoes, Phys. Rev. Lett. 2, 301 (1959).
  41. N. F. Ramsey, A molecular beam resonance method with separated oscillating fields, Phys. Rev. 78, 695 (1950).
  42. J. Isoya, J. A. Weil, and P. H. Davis, EPR of atomic hydrogen H1 and H2 in α-quartz, J. Phys. Chem. Solids 44, 335 (1983).
  43. V. G. Baryshevskii, S. A. Kuten, and V. I. Rapoport, Quadrupole interactions of muonium in α-quartz, J. Phys. C: Solid State Phys. 16, 6651 (1983).
  44. S. G. Barsov, A. L. Getalov, V. A. Gordeev, S. P. Kruglov, L. A. Kuzmin, S. M. Mikirtychyants, G. V. Shcherbakov, V. G. Baryshevskii, S. A. Kuten, and V. I. Rapoport, Temperature dependence of the quadruple interaction and the diffusion of muonium atoms in α-quartz, Hyperfine Interact. 32, 631 (1986).
  45. M. H. Levitt, Composite pulses, Prog. Nucl. Magn. Reson. Spectrosc. 18, 61 (1986).
  46. N. J. Clayden, S. P. Cottrell, and I. McKenzie, Spin evolution in a radio frequency field studied through muon spin resonance, J. Magn. Reson. 214, 144 (2012).
  47. A. Doll and G. Jeschke, Wideband frequency-swept excitation in pulsed EPR spectroscopy, J. Magn. Reson. 280, 46 (2017).
  48. B. D. Patterson, A. Hintermann, W. Kündig, P. F. Meier, F. Waldner, H. Graf, E. Recknagel, A. Weidinger, and T. Wichert, Anomalous muonium in silicon, Phys. Rev. Lett. 40, 1347 (1978).
  49. R. F. Kiefl, M. Celio, T. L. Estle, S. R. Kreitzman, G. M. Luke, T. M. Riseman, and E. J. Ansaldo, Si29 hyperfine structure of anomalous muonium in silicon: Proof of the bond-centered model, Phys. Rev. Lett. 60, 224 (1988).
  50. G. Jeschke, Generation and transfer of coherence in electron-nuclear spin systems by non-ideal microwave pulses, Mol. Phys. 88, 355 (1996).
  51. Y. V. Gorelkinskii and N. N. Nevinnyi, Electron paramagnetic resonance of hydrogen in silicon, Phys. B: Condens. Matter 170, 155 (1991).
  52. C. G. Van de Walle, Structural identification of hydrogen and muonium centers in silicon: First-principles calculations of hyperfine parameters, Phys. Rev. Lett. 64, 669 (1990).
  53. A. R. Porter, M. D. Towler, and R. J. Needs, Muonium as a hydrogen analogue in silicon and germanium: Quantum effects and hyperfine parameters, Phys. Rev. B 60, 13534 (1999).
  54. T. L. Estle and D. A. Vanderwater, Theory of double electron-muon resonance, Phys. Rev. B 27, 3962 (1983).
  55. B. Herzog and E. L. Hahn, Transient nuclear induction and double nuclear resonance in solids, Phys. Rev. 103, 148 (1956).
  56. R. de Sousa and S. Das Sarma, Theory of nuclear-induced spectral diffusion: Spin decoherence of phosphorus donors in Si and GaAs quantum dots, Phys. Rev. B 68, 115322 (2003).
  57. W. M. Witzel, M. S. Carroll, Ł. Cywiński, and S. Das Sarma, Quantum decoherence of the central spin in a sparse system of dipolar coupled spins, Phys. Rev. B 86, 035452 (2012).
  58. J. M. Wilkinson and S. J. Blundell, Information and decoherence in a muon-fluorine coupled system, Phys. Rev. Lett. 125, 087201 (2020).
  59. T. G. Castner, Direct measurement of the valley-orbit splitting of shallow donors in silicon, Phys. Rev. Lett. 8, 13 (1962).
  60. C. Bucci, R. De Renzi, G. Guidi, P. Podini, R. Tedeschi, and L. O. Norlin, Low temperature spectrum and relaxation of muonium in silicon, Hyperfine Interact. 8, 385 (1981).
  61. W. E. Blumberg, Nuclear spin-lattice relaxation caused by paramagnetic impurities, Phys. Rev. 119, 79 (1960).
  62. G. Khutsishvili, Spin diffusion and magnetic relaxation of nuclei, Sov. Phys. JETP 15, 909 (1962).
  63. R. Hanson, V. V. Dobrovitski, A. E. Feiguin, O. Gywat, and D. D. Awschalom, Coherent dynamics of a single spin interacting with an adjustable spin bath, Science 320, 352 (2008).
  64. V. V. Dobrovitski, A. E. Feiguin, R. Hanson, and D. D. Awschalom, Decay of Rabi oscillations by dipolar-coupled dynamical spin environments, Phys. Rev. Lett. 102, 237601 (2009).
  65. A. Doll, Data and code for microwave-excited muonium manuscript (2025), doi: 10.5281/zenodo.15090279.
  66. P. R. Shrestha, N. Abhyankar, M. A. Anders, K. P. Cheung, R. Gougelet, J. T. Ryan, V. Szalai, and J. P. Campbell, Nonresonant transmission line probe for sensitive interferometric electron spin resonance detection, Anal. Chem. 91, 11108 (2019).
  67. S. Ritt and P.-A. Amaudruz, Midas—Maximum integrated data acquisition system, https://midas.triumf.ca.
  68. W. M. Witzel and S. Das Sarma, Multiple-pulse coherence enhancement of solid state spin qubits, Phys. Rev. Lett. 98, 077601 (2007).
  69. W. Yang and R.-B. Liu, Quantum many-body theory of qubit decoherence in a finite-size spin bath, Phys. Rev. B 78, 085315 (2008).

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Phys. Rev. Research 7, 033059– Published 14 July, 2025
  • Received 7 April 2025
  • Accepted 26 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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