- Physical Review Journals
All JournalsPhysics Magazine

Physical Review A

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

Probing an electron-spin ensemble with squeezed microwave signals

P. Oehrl1,2, F. Fesquet1,2, K. E. Honasoge1,2, M. Handschuh1,2, A. Marx1, R. Gross1,2,3, K. G. Fedorov1,2,3, and H. Huebl1,2,3,*

  • *Contact author: hans.huebl@wmi.badw.de
PDF

Phys. Rev. A 114, 022603 – Published 4 August, 2026

DOI: https://doi.org/10.1103/f81b-px1l

Abstract

The efficient transfer of quantum states into a long-lived storage unit such as solid-state spin ensembles is widely recognized as a critical challenge with significant implications for quantum communication, sensing, and computing applications. Here, we experimentally investigate the interaction of propagating squeezed microwaves with an electron-spin-resonance transition in order to evaluate the use of spin ensembles as quantum memories for gigahertz signals. We generate continuous-variable microwave states with squeezing levels up to 5dB below the vacuum level and let this signal interrogate a spin ensemble, which is inductively coupled to a lumped-element superconducting microwave resonator with a cooperativity of C=0.3. By analyzing this signal using Wigner tomography and modeling our experimental results with a dedicated steady-state model based on the quantum input-output formalism, we extract a transfer efficiency of around 61% between the squeezed microwaves and the spin excitations, resulting in squeezing levels of the spin mode up to 0.5 dB below the vacuum level.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (62)

  1. N. Gisin and R. Thew, Quantum communication, Nat. Photon. 1, 165 (2007).
  2. H. J. Kimble, The quantum internet, Nature (London) 453, 1023 (2008).
  3. M. K. Bhaskar, R. Riedinger, B. Machielse, D. S. Levonian, C. T. Nguyen, E. N. Knall, H. Park, D. Englund, M. Lončar, D. D. Sukachev, and M. Lukin, Experimental demonstration of memory-enhanced quantum communication, Nature (London) 580, 60 (2020).
  4. M. Teller, S. Plascencia, C. S. Jachimska, S. Grandi, and H. de Riedmatten, A solid-state temporally multiplexed quantum memory array at the single-photon level, npj Quantum Inf. 11, 92 (2025).
  5. W. Zhang, T. van Leent, K. Redeker, R. Garthoff, R. Schwonnek, F. Fertig, S. Eppelt, W. Rosenfeld, V. Scarani, C. C.-W. Lim, and H. Weinfurter, A device-independent quantum key distribution system for distant users, Nature (London) 607, 687 (2022).
  6. D. P. Nadlinger, P. Drmota, B. C. Nichol, G. Araneda, D. Main, R. Srinivas, D. M. Lucas, C. J. Ballance, K. Ivanov, E.-Z. Tan, R. Sekatski, R. L. Urbanke, R. Renner, N. Sangouard, and J.-D. Bancal, Experimental quantum key distribution certified by Bell's theorem, Nature (London) 607, 682 (2022).
  7. Y.-F. Pu, S. Zhang, Y.-K. Wu, N. Jiang, W. Chang, C. Li, and L.-M. Duan, Experimental demonstration of memory-enhanced scaling for entanglement connection of quantum repeater segments, Nat. Photon. 15, 374 (2021).
  8. S. Wiesner, Conjugate coding, SIGACT News 15, 78 (1983).
  9. F. Pastawski, N. Y. Yao, L. Jiang, M. D. Lukin, and J. I. Cirac, Unforgeable noise-tolerant quantum tokens, Proc. Natl. Acad. Sci. USA 109, 16079 (2012).
  10. K. Jiráková, K. Bartkiewicz, A. Černoch, and K. Lemr, Experimentally attacking quantum money schemes based on quantum retrieval games, Sci. Rep. 9, 16318 (2019).
  11. H. P. Specht, C. Nölleke, A. Reiserer, M. Uphoff, E. Figueroa, S. Ritter, and G. Rempe, A single-atom quantum memory, Nature (London) 473, 190 (2011).
  12. J.-S. Tang, Z.-Q. Zhou, Y.-T. Wang, Y.-L. Li, X. Liu, Y.-L. Hua, Y. Zou, S. Wang, D.-Y. He, G. Chen, Y.-N. Sun, Y. Yu, M.-F. Li, G.-W. Zha, H.-Q. Ni, Z.-C. Niu, C.-F. Li, and G.-C. Guo, Storage of multiple single-photon pulses emitted from a quantum dot in a solid-state quantum memory, Nat. Commun. 6, 8652 (2015).
  13. A. Wallucks, I. Marinković, B. Hensen, R. Stockill, and S. Gröblacher, A quantum memory at telecom wavelengths, Nat. Phys. 16, 772 (2020).
  14. N. Bar-Gill, L. M. Pham, A. Jarmola, D. Budker, and R. L. Walsworth, Solid-state electronic spin coherence time approaching one second, Nat. Commun. 4, 1743 (2013).
  15. 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).
  16. A. Ghirri, C. Bonizzoni, F. Troiani, N. Buccheri, L. Beverina, A. Cassinese, and M. Affronte, Coherently coupling distinct spin ensembles through a high-Tc superconducting resonator, Phys. Rev. A 93, 063855 (2016).
  17. A. Strinić, P. Oehrl, A. Marx, P. A. Bushev, H. Huebl, R. Gross, and N. Kukharchyk, Broadband electron paramagnetic resonance spectroscopy of Er167:LiYF47 at millikelvin temperatures, Phys. Rev. B 111, 214430 (2025).
  18. N. Timoney, I. Usmani, P. Jobez, M. Afzelius, and N. Gisin, Single-photon-level optical storage in a solid-state spin-wave memory, Phys. Rev. A 88, 022324 (2013).
  19. C. Grezes, B. Julsgaard, Y. Kubo, W. L. Ma, M. Stern, A. Bienfait, K. Nakamura, J. Isoya, S. Onoda, T. Ohshima, V. Jacques, D. Vion, D. Esteve, R. B. Liu, K. Mølmer, and P. Bertet, Storage and retrieval of microwave fields at the single-photon level in a spin ensemble, Phys. Rev. A 92, 020301(R) (2015).
  20. J. O'Sullivan, O. W. Kennedy, K. Debnath, J. Alexander, C. W. Zollitsch, M. Šimėnas, A. Hashim, C. N. Thomas, S. Withington, I. Siddiqi, K. Mølmer, and J. J. L. Morton, Random-access quantum memory using chirped pulse phase encoding, Phys. Rev. X 12, 041014 (2022).
  21. C. Eichler, A. J. Sigillito, S. A. Lyon, and J. R. Petta, Electron spin resonance at the level of 104 spins using low impedance superconducting resonators, Phys. Rev. Lett. 118, 037701 (2017).
  22. A. Bienfait, P. Campagne-Ibarcq, A. H. Kiilerich, X. Zhou, S. Probst, J. J. Pla, T. Schenkel, D. Vion, D. Esteve, J. J. L. Morton, K. Moelmer, and P. Bertet, Magnetic resonance with squeezed microwaves, Phys. Rev. X 7, 041011 (2017).
  23. L. Zhong, E. P. Menzel, R. Di Candia, P. Eder, M. Ihmig, A. Baust, M. Haeberlein, E. Hoffmann, K. Inomata, T. Yamamoto, Y. Nakamura, E. Solano, F. Deppe, A. Marx, and R. Gross, Squeezing with a flux-driven Josephson parametric amplifier, New J. Phys. 15, 125013 (2013).
  24. S. Pogorzalek, K. G. Fedorov, L. Zhong, J. Goetz, F. Wulschner, M. Fischer, P. Eder, E. Xie, K. Inomata, T. Yamamoto, Y. Nakamura, A. Marx, F. Deppe, and R. Gross, Hysteretic flux response and nondegenerate gain of flux-driven Josephson parametric amplifiers, Phys. Rev. Appl. 8, 024012 (2017).
  25. M. Renger, S. Pogorzalek, Q. Chen, Y. Nojiri, K. Inomata, Y. Nakamura, M. Partanen, A. Marx, R. Gross, F. Deppe, and K. G. Fedorov, Beyond the standard quantum limit for parametric amplification of broadband signals, npj Quantum Inf. 7, 160 (2021).
  26. K. E. Honasoge, M. Handschuh, W. K. Yam, S. Gandorfer, D. Bazulin, N. Bruckmoser, L. Koch, A. Marx, R. Gross, and K. G. Fedorov, Fabrication of low-loss Josephson parametric devices, Phys. Rev. B 111, 214508 (2025).
  27. E. P. Menzel, F. Deppe, M. Mariantoni, M. A. Araque Caballero, A. Baust, T. Niemczyk, E. Hoffmann, A. Marx, E. Solano, and R. Gross, Dual-path state reconstruction scheme for propagating quantum microwaves and detector noise tomography, Phys. Rev. Lett. 105, 100401 (2010).
  28. M. Mariantoni, E. P. Menzel, F. Deppe, M. A. Araque Caballero, A. Baust, T. Niemczyk, E. Hoffmann, E. Solano, A. Marx, and R. Gross, Planck spectroscopy and quantum noise of microwave beam splitters, Phys. Rev. Lett. 105, 133601 (2010).
  29. S. Gandorfer, M. Renger, W. K. Yam, F. Fesquet, A. Marx, R. Gross, and K. G. Fedorov, Two-dimensional Planck spectroscopy for microwave photon calibration, Phys. Rev. Appl. 23, 024064 (2025).
  30. K. G. Fedorov, S. Pogorzalek, U. Las Heras, M. Sanz, P. Yard, P. Eder, M. Fischer, J. Goetz, E. Xie, K. Inomata, Y. Nakamura, R. Di Candia, E. Solano, A. Marx, F. Deppe, and R. Gross, Finite-time quantum entanglement in propagating squeezed microwaves, Sci. Rep. 8, 6416 (2018).
  31. S. Weichselbaumer, M. Zens, C. W. Zollitsch, M. S. Brandt, S. Rotter, R. Gross, and H. Huebl, Echo trains in pulsed electron spin resonance of a strongly coupled spin ensemble, Phys. Rev. Lett. 125, 137701 (2020).
  32. J. Gordon and K. Bowers, Microwave spin echoes from donor electrons in silicon, Phys. Rev. Lett. 1, 368 (1958).
  33. G. Feher, Electron spin resonance experiments on donors in silicon. I. Electronic structure of donors by the electron nuclear double resonance technique, Phys. Rev. 114, 1219 (1959).
  34. J. H. Wesenberg, A. Ardavan, G. A. D. Briggs, J. J. L. Morton, R. J. Schoelkopf, D. I. Schuster, and K. Mølmer, Quantum computing with an electron spin ensemble, Phys. Rev. Lett. 103, 070502 (2009).
  35. I. Chiorescu, N. Groll, S. Bertaina, T. Mori, and S. Miyashita, Magnetic strong coupling in a spin-photon system and transition to classical regime, Phys. Rev. B 82, 024413 (2010).
  36. I. Diniz, S. Portolan, R. Ferreira, J. M. Gérard, P. Bertet, and A. Auffeves, Strongly coupling a cavity to inhomogeneous ensembles of emitters: Potential for long-lived solid-state quantum memories, Phys. Rev. A 84, 063810 (2011).
  37. F. Fesquet, Demonstration of microwave single-shot quantum key distribution, Ph.D. thesis, Technische Universität München, 2025, https://www.wmi.badw.de/fileadmin/WMI/Publications/Fesquet_Florian_Doktorarbeit_2025.pdf.
  38. C. W. Gardiner and M. J. Collett, Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation, Phys. Rev. A 31, 3761 (1985).
  39. D. A. Steck, Quantum and Atom Optics (2023).
  40. K. Sandner, H. Ritsch, R. Amsüss, C. Koller, T. Nöbauer, S. Putz, J. Schmiedmayer, and J. Majer, Strong magnetic coupling of an inhomogeneous nitrogen-vacancy ensemble to a cavity, Phys. Rev. A 85, 053806 (2012).
  41. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
  42. S. Probst, F. Song, P. A. Bushev, A. V. Ustinov, and M. Weides, Efficient and robust analysis of complex scattering data under noise in microwave resonators, Rev. Sci. Instrum. 86, 024706 (2015).
  43. S. L. Braunstein and P. van Loock, Quantum information with continuous variables, Rev. Mod. Phys. 77, 513 (2005).
  44. M. Müller, T. Luschmann, A. Faltermeier, S. Weichselbaumer, L. Koch, G. B. P. Huber, H. W. Schumacher, N. Ubbelohde, D. Reifert, T. Scheller, F. Deppe, A. Marx, S. Filipp, M. Althammer, R. Gross, and H. Huebl, Magnetic field robust high quality factor NbTiN superconducting microwave resonators, Mater. Quantum Technol. 2, 015002 (2022).
  45. D. F. Walls and G. J. Milburn, Quantum Optics, 1st ed. (Springer, Berlin, Heidelberg, 1994).
  46. F. Damanet, A. J. Daley, and J. Keeling, Atom-only descriptions of the driven-dissipative Dicke model, Phys. Rev. A 99, 033845 (2019).
  47. S. Giaccari, G. Dellea, M. G. Genoni, and G. Bertaina, Higher-order adiabatic elimination in atom-cavity systems and its impact on spin-squeezing generation, Quantum Sci. Technol. 11, 035019 (2026).
  48. M. Afzelius, N. Sangouard, G. Johansson, M. Staudt, and C. Wilson, Proposal for a coherent quantum memory for propagating microwave photons, New J. Phys. 15, 065008 (2013).
  49. B. Julsgaard, C. Grezes, P. Bertet, and K. Mølmer, Quantum memory for microwave photons in an inhomogeneously broadened spin ensemble, Phys. Rev. Lett. 110, 250503 (2013).
  50. L. Greggio, T. Lorriaux, A. Petrescu, M. Mirrahimi, and A. Bienfait, Optimal absorption and emission of itinerant fields into a spin-ensemble memory, Phys. Rev. (2026), doi: 10.1103/6xjr-tflh.
  51. J. Z. Bernád, M. Schilling, Y. Wen, M. M. Müller, T. Calarco, P. Bertet, and F. Motzoi, Analytical solutions for optimal photon absorption into inhomogeneous spin memories, J. Phys. B 58, 035501 (2025).
  52. F. Fesquet, F. Kronowetter, M. Renger, W. K. Yam, S. Gandorfer, K. Inomata, Y. Nakamura, A. Marx, R. Gross, and K. G. Fedorov, Demonstration of microwave single-shot quantum key distribution, Nat. Commun. 15, 7544 (2024).
  53. P. Oehrl and H. Huebl, Probing an electron spin ensemble with squeezed microwave signals, [Dataset], Zenodo, 2026, https://doi.org/10.5281/zenodo.21260844.
  54. A. Schweiger and G. Jeschke, Principles of Pulse Electron Paramagnetic Resonance (Oxford University Press, Oxford, 2001).
  55. S. Weichselbaumer, P. Natzkin, C. W. Zollitsch, M. Weiler, R. Gross, and H. Huebl, Quantitative modeling of superconducting planar resonators for electron spin resonance, Phys. Rev. Appl. 12, 024021 (2019).
  56. C. W. Zollitsch, K. Mueller, D. P. Franke, S. T. B. Goennenwein, M. S. Brandt, R. Gross, and H. Huebl, High cooperativity coupling between a phosphorus donor spin ensemble and a superconducting microwave resonator, Appl. Phys. Lett. 107, 142105 (2015).
  57. E. L. Hahn, Spin echoes, Phys. Rev. 80, 580 (1950).
  58. A. M. Tyryshkin, S. A. Lyon, A. V. Astashkin, and A. M. Raitsimring, Electron spin relaxation times of phosphorus donors in silicon, Phys. Rev. B 68, 193207 (2003).
  59. C. Eichler, D. Bozyigit, C. Lang, M. Baur, L. Steffen, J. M. Fink, S. Filipp, and A. Wallraff, Observation of two-mode squeezing in the microwave frequency domain, Phys. Rev. Lett. 107, 113601 (2011).
  60. S. Boutin, D. M. Toyli, A. V. Venkatramani, A. W. Eddins, I. Siddiqi, and A. Blais, Effect of higher-order nonlinearities on amplification and squeezing in Josephson parametric amplifiers, Phys. Rev. Appl. 8, 054030 (2017).
  61. K. G. Fedorov, L. Zhong, S. Pogorzalek, P. Eder, M. Fischer, J. Goetz, E. Xie, F. Wulschner, K. Inomata, T. Yamamoto, Y. Nakamura, R. Di Candia, U. L. Heras, M. Sanz, E. Solano, E. P. Menzel, F. Deppe, A. Marx, and R. Gross, Displacement of propagating squeezed microwave states, Phys. Rev. Lett. 117, 020502 (2016).
  62. J. Wang, H. M. Wiseman, and G. J. Milburn, Dynamical creation of entanglement by homodyne-mediated feedback, Phys. Rev. A 71, 042309 (2005).

Outline

Information

Phys. Rev. A 114, 022603– Published 4 August, 2026
  • Received 28 December 2025
  • Accepted 7 July 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