- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Phase-accumulating hyperfine strain sensing with rare-earth-ion phase memories

Mustafa Gündoğan*

  • *Contact author: mustafa.guendogan@physik.hu-berlin.de
PDF

Phys. Rev. B 114, 254103 – Published 3 November, 2026

DOI: https://doi.org/10.1103/w1j9-vdyt

Abstract

Long-lived hyperfine coherences in rare-earth-ion doped (REID) crystals provide controlled phase evolution windows for metrology. We use this resource to propose an experimental protocol for accessing strain shifts of ground state hyperfine transitions in non-Kramers REID materials, a quantity that is difficult to access directly with conventional spectroscopic methods. Starting from the crystal field Hamiltonian, we relate the response to strain-dependent effective quadrupole and Zeeman tensors, including changes in electronic wave functions, virtual electronic admixtures, and the bare nuclear quadrupole interaction. The protocol optically prepares a selected hyperfine class, uses a phase-controlled rf π/2 pulse to create the sensing coherence, and applies synchronized dynamical decoupling pulses during the phase evolution interval so that a coherent ac strain drive accumulates phase rather than averaging away. The accumulated phase is then retrieved by Raman heterodyne readout. The resulting framework provides a route to understanding strain-induced hyperfine shifts in non-Kramers REID systems.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (48)

  1. R. M. Macfarlane, High-resolution laser spectroscopy of rare-earth doped insulators: A personal perspective, J. Lumin. 100, 1 (2002).
  2. P. Goldner, A. Ferrier, and O. Guillot-Noël, Rare earth-doped crystals for quantum information processing, in Handbook on the Physics and Chemistry of Rare Earths, edited by J.-C. G. Bünzli and V. K. Pecharsky (Elsevier, Amsterdam, 2015), Vol. 46, pp. 1–78.
  3. M. Lovrić, D. Suter, A. Ferrier, and P. Goldner, Faithful solid state optical memory with dynamically decoupled spin wave storage, Phys. Rev. Lett. 111, 020503 (2013).
  4. M. Gündoğan, P. M. Ledingham, K. Kutluer, M. Mazzera, and H. de Riedmatten, Solid state spin-wave quantum memory for time-bin qubits, Phys. Rev. Lett. 114, 230501 (2015).
  5. E. Fraval, M. J. Sellars, and J. J. Longdell, Method of extending hyperfine coherence times in Pr3+:Y2SiO5, Phys. Rev. Lett. 92, 077601 (2004).
  6. G. Heinze, C. Hubrich, and T. Halfmann, Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute, Phys. Rev. Lett. 111, 033601 (2013).
  7. M. Zhong, M. P. Hedges, R. L. Ahlefeldt, J. G. Bartholomew, S. E. Beavan, S. M. Wittig, J. J. Longdell, and M. J. Sellars, Optically addressable nuclear spins in a solid with a six-hour coherence time, Nature (London) 517, 177 (2015).
  8. Y. Ma, Y.-Z. Ma, Z.-Q. Zhou, C.-F. Li, and G.-C. Guo, One-hour coherent optical storage in an atomic frequency comb memory, Nat. Commun. 12, 2381 (2021).
  9. A. Ortu, A. Holzäpfel, J. Etesse, and M. Afzelius, Storage of photonic time-bin qubits for up to 20 ms in a rare-earth doped crystal, npj Quantum Inf. 8, 29 (2022).
  10. N. Galland, N. Lučić, B. Fang, S. Zhang, R. Le Targat, A. Ferrier, P. Goldner, S. Seidelin, and Y. Le Coq, Mechanical tunability of an ultranarrow spectral feature of a rare-earth-doped crystal via uniaxial stress, Phys. Rev. Appl. 13, 044022 (2020).
  11. S. Zhang, N. Galland, N. Lučić, R. Le Targat, A. Ferrier, P. Goldner, B. Fang, Y. Le Coq, and S. Seidelin, Inhomogeneous response of an ion ensemble from mechanical stress, Phys. Rev. Res. 2, 013306 (2020).
  12. R. M. Macfarlane, A. Arcangeli, A. Ferrier, and P. Goldner, Optical measurement of the effect of electric fields on the nuclear spin coherence of rare-earth ions in solids, Phys. Rev. Lett. 113, 157603 (2014).
  13. W. B. Mims, Phase memory in electron spin echoes, lattice relaxation effects in CaWO4: Er,Ce,Mn, Phys. Rev. 168, 370 (1968).
  14. T. W. Mossberg, Time-domain frequency-selective optical data storage, Opt. Lett. 7, 77 (1982).
  15. J. Mlynek, N. C. Wong, R. G. DeVoe, E. S. Kintzer, and R. G. Brewer, Raman heterodyne detection of nuclear magnetic resonance, Phys. Rev. Lett. 50, 993 (1983).
  16. N. C. Wong, E. S. Kintzer, J. Mlynek, R. G. DeVoe, and R. G. Brewer, Raman heterodyne detection of nuclear magnetic resonance, Phys. Rev. B 28, 4993 (1983).
  17. M. Mitsunaga, E. S. Kintzer, and R. G. Brewer, Raman heterodyne interference: Observations and analytic theory, Phys. Rev. B 31, 6947 (1985).
  18. K. Holliday, X.-F. He, P. T. H. Fisk, and N. B. Manson, Raman heterodyne detection of electron paramagnetic resonance, Opt. Lett. 15, 983 (1990).
  19. L. E. Erickson, Optical-pumping effects on Raman-heterodyne-detected multipulse RF nuclear-spin-echo decay, Phys. Rev. B 42, 3789 (1990).
  20. X. Fernandez-Gonzalvo, S. P. Horvath, Y.-H. Chen, and J. J. Longdell, Cavity-enhanced Raman heterodyne spectroscopy in Er3+:Y2SiO5 for microwave-to-optical signal conversion, Phys. Rev. A 100, 033807 (2019).
  21. G. G. G. King, P. S. Barnett, J. G. Bartholomew, A. Faraon, and J. J. Longdell, Probing strong coupling between a microwave cavity and a spin ensemble with Raman heterodyne spectroscopy, Phys. Rev. B 103, 214305 (2021).
  22. A. E. Rodríguez-Moldes, F. Appas, J. Hänni, J. V. Rakonjac, S. Grandi, and H. de Riedmatten, Long-lived telecom-heralded single-photon storage in an absorptive spin-rephased quantum memory, Phys. Rev. Lett. 137, 120803 (2026).
  23. S. Sevinçli, D. Rätzel, M. Krutzik, M. O. Oktel, and M. Gündoğan, Generation of squeezed optical states via stored classical pulses in a Bose gas, Phys. Rev. Res. 8, 033016 (2026).
  24. M. P. Hedges, J. J. Longdell, Y. Li, and M. J. Sellars, Efficient quantum memory for light, Nature (London) 465, 1052 (2010).
  25. K. W. H. Stevens, Matrix elements and operator equivalents connected with the magnetic properties of rare earth ions, Proc. Phys. Soc. A 65, 209 (1952).
  26. M. T. Hutchings, Point-charge calculations of energy levels of magnetic ions in crystalline electric fields, in Solid State Physics, edited by F. Seitz and D. Turnbull (Academic Press, New York, 1964), Vol. 16, pp. 227–273.
  27. M. A. Teplov, Magnetic resonance on Pr141 nuclei in a Pr2(SO4)3·H2O single crystal, Sov. Phys. JETP 26, 872 (1968).
  28. J. J. Longdell, M. J. Sellars, and N. B. Manson, Hyperfine interaction in ground and excited states of praseodymium-doped yttrium orthosilicate, Phys. Rev. B 66, 035101 (2002).
  29. J. J. Longdell, A. L. Alexander, and M. J. Sellars, Characterization of the hyperfine interaction in europium-doped yttrium orthosilicate and europium chloride hexahydrate, Phys. Rev. B 74, 195101 (2006).
  30. O. Guillot-Noël, P. Goldner, F. Beaudoux, Y. Le Du, J. Lejay, A. Amari, A. Walther, L. Rippe, and S. Kröll, Hyperfine structure and hyperfine coherent properties of praseodymium in single-crystalline La2(Wo4)3 by hole-burning and photon-echo techniques, Phys. Rev. B 79, 155119 (2009).
  31. Ł. Cywiński, R. M. Lutchyn, C. P. Nave, and S. Das Sarma, How to enhance dephasing time in superconducting qubits, Phys. Rev. B 77, 174509 (2008).
  32. C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017).
  33. G. de Lange, D. Ristè, V. V. Dobrovitski, and R. Hanson, Single-spin magnetometry with multipulse sensing sequences, Phys. Rev. Lett. 106, 080802 (2011).
  34. A. M. Souza, G. A. Álvarez, and D. Suter, Robust dynamical decoupling for quantum computing and quantum memory, Phys. Rev. Lett. 106, 240501 (2011).
  35. See Supplemental Material at http://link.aps.org/supplemental/10.1103/w1j9-vdyt for Videos 1 and 2 showing the individual pseudospins and collective Bloch vector during the strain-induced phase evolution for the synchronized and 5% detuned dynamical decoupling sequences.
  36. K. Anai, Y. Enomoto, H. Omura, K. Nagano, K. Izumi, M. Endo, and S. Takeda, Quantum-enhanced optical phase-insensitive heterodyne detection beyond 3-dB noise penalty of image band, Opt. Express 32, 19372 (2024).
  37. M. Gündoğan, A. Ahmadi, and M. Krutzik, Memory-assisted squeezed light velocimetry under realistic loss and incoherent noise, AVS Quantum Sci. 8, 034405 (2026).
  38. G. Heinze, C. Hubrich, and T. Halfmann, Coherence time extension in Pr3+:Y2SiO5 by self-optimized magnetic fields and dynamical decoupling, Phys. Rev. A 89, 053825 (2014).
  39. A. L. Alexander, J. J. Longdell, and M. J. Sellars, Measurement of the ground-state hyperfine coherence time of Eu3+151:Y2SiO5, J. Opt. Soc. Am. B 24, 2479 (2007).
  40. J. M. Kindem, J. G. Bartholomew, P. J. T. Woodburn, T. Zhong, I. Craiciu, R. L. Cone, C. W. Thiel, and A. Faraon, Characterization of Yb3+171:YVO4 for photonic quantum technologies, Phys. Rev. B 98, 024404 (2018).
  41. P. Ovartchaiyapong, K. W. Lee, B. A. Myers, and A. C. B. Jayich, Dynamic strain-mediated coupling of a single diamond spin to a mechanical resonator, Nat. Commun. 5, 4429 (2014).
  42. J. Teissier, A. Barfuss, P. Appel, E. Neu, and P. Maletinsky, Strain coupling of a nitrogen-vacancy center spin to a diamond mechanical oscillator, Phys. Rev. Lett. 113, 020503 (2014).
  43. K. Mølmer, Y. Le Coq, and S. Seidelin, Dispersive coupling between light and a rare-earth-ion–doped mechanical resonator, Phys. Rev. A 94, 053804 (2016).
  44. R. Ohta, L. Herpin, V. 1. Bastidas, T. Tawara, H. Yamaguchi, and H. Okamoto, Rare-earth-mediated opto-mechanical system in the reversed dissipation regime, Phys. Rev. Lett. 126, 047404 (2021).
  45. A. Louchet-Chauvet, P. Verlot, J.-P. Poizat, and T. Chanelière, Piezo-orbital backaction force in a rare-earth-doped crystal, Phys. Rev. Appl. 20, 054004 (2023).
  46. P.-O. Löwdin, A note on the quantum-mechanical perturbation theory, J. Chem. Phys. 19, 1396 (1951).
  47. J. R. Schrieffer and P. A. Wolff, Relation between the Anderson and Kondo Hamiltonians, Phys. Rev. 149, 491 (1966).
  48. T. Ishikawa, A. Yoshizawa, Y. Mawatari, H. Watanabe, and S. Kashiwaya, Influence of dynamical decoupling sequences with finite-width pulses on quantum sensing for AC magnetometry, Phys. Rev. Appl. 10, 054059 (2018).

Outline

Information

Phys. Rev. B 114, 254103– Published 3 November, 2026
  • Received 11 May 2026
  • Revised 25 September 2026
  • Accepted 1 October 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation