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  • Letter
  • Open Access

Spin cat states in ferromagnetic insulators

Sanchar Sharma1, Victor A. S. V. Bittencourt1, Alexy D. Karenowska2, and Silvia Viola Kusminskiy1,3

  • 1Max Planck Institute for the Science of Light, 91058 Erlangen, Germany
  • 2Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
  • 3Department of Physics, University Erlangen-Nürnberg, 91058 Erlangen, Germany

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Phys. Rev. B 103, L100403 – Published 4 March, 2021

DOI: https://doi.org/10.1103/PhysRevB.103.L100403

Abstract

Generating nonclassical states in macroscopic systems is a long-standing challenge. A promising platform in the context of this quest are novel hybrid systems based on magnetic dielectrics, where photons can couple strongly and coherently to magnetic excitations, although a nonclassical state therein is yet to be observed. We propose a scheme to generate a magnetization cat state, i.e., a quantum superposition of two distinct magnetization directions, using a conventional setup of a macroscopic ferromagnet in a microwave cavity. Our scheme uses the ground state of an ellipsoid shaped magnet, which displays anisotropic quantum fluctuations akin to a squeezed vacuum. The magnetization collapses to a cat state by either a single photon or a parity measurement of the microwave cavity state. We find that a cat state with two components separated by ∼5ℏ is feasible and briefly discuss potential experimental setups that can achieve it.

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References (76)

  1. N. Ofek, A. Petrenko, R. Heeres, P. Reinhold, Z. Leghtas, B. Vlastakis, Y. Liu, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, Nature 536, 441 (2016).
  2. H. Jeong and M. S. Kim, Phys. Rev. A 65, 042305 (2002).
  3. T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, Phys. Rev. A 68, 042319 (2003).
  4. M. Mirrahimi, Z. Leghtas, V. V. Albert, S. Touzard, R. J. Schoelkopf, L. Jiang, and M. H. Devoret, New J. Phys. 16, 045014 (2014).
  5. W. J. Munro, K. Nemoto, G. J. Milburn, and S. L. Braunstein, Phys. Rev. A 66, 023819 (2002).
  6. T. C. Ralph, Phys. Rev. A 65, 042313 (2002).
  7. J. Huang, X. Qin, H. Zhong, Y. Ke, and C. Lee, Sci. Rep. 5, 17894 (2015).
  8. P. A. Knott, T. J. Proctor, A. J. Hayes, J. P. Cooling, and J. A. Dunningham, Phys. Rev. A 93, 033859 (2016).
  9. K. Huang, H. Le Jeannic, J. Ruaudel, V. B. Verma, M. D. Shaw, F. Marsili, S. W. Nam, E. Wu, H. Zeng, Y.-C. Jeong, R. Filip, O. Morin, and J. Laurat, Phys. Rev. Lett. 115, 023602 (2015).
  10. A. P. Lund, H. Jeong, T. C. Ralph, and M. S. Kim, Phys. Rev. A 70, 020101(R) (2004).
  11. J. Wenger, R. Tualle-Brouri, and P. Grangier, Phys. Rev. Lett. 92, 153601 (2004).
  12. B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, Science 342, 607 (2013).
  13. R. McConnell, H. Zhang, J. Hu, S. Ćuk, and V. Vuletić, Nature 519, 439 (2015).
  14. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
  15. S. Hong, R. Riedinger, I. Marinković, A. Wallucks, S. G. Hofer, R. A. Norte, M. Aspelmeyer, and S. Gröblacher, Science 358, 203 (2017).
  16. R. Riedinger, A. Wallucks, I. Marinković, C. Löschnauer, M. Aspelmeyer, S. Hong, and S. Gröblacher, Nature 556, 473 (2018).
  17. F. Tebbenjohanns, M. Frimmer, V. Jain, D. Windey, and L. Novotny, Phys. Rev. Lett. 124, 013603 (2020).
  18. U. Delić, M. Reisenbauer, K. Dare, D. Grass, V. Vuletić, N. Kiesel, and M. Aspelmeyer, Science 367, 892 (2020).
  19. I. Shomroni, L. Qiu, and T. J. Kippenberg, Phys. Rev. A 101, 033812 (2020).
  20. H. Zhan, G. Li, and H. Tan, Phys. Rev. A 101, 063834 (2020).
  21. D. Lachance-Quirion, Y. Tabuchi, A. Gloppe, K. Usami, and Y. Nakamura, Appl. Phys. Express 12, 070101 (2019).
  22. V. Cherepanov, I. Kolokolov, and V. L'vov, Phys. Rep. 229, 81 (1993).
  23. Ö. O. Soykal and M. E. Flatté, Phys. Rev. Lett. 104, 077202 (2010).
  24. X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang, Phys. Rev. Lett. 113, 156401 (2014).
  25. Y. Tabuchi, S. Ishino, T. Ishikawa, R. Yamazaki, K. Usami, and Y. Nakamura, Phys. Rev. Lett. 113, 083603 (2014).
  26. Y. Tabuchi, S. Ishino, A. Noguchi, T. Ishikawa, R. Yamazaki, K. Usami, and Y. Nakamura, C. R. Phys. 17, 729 (2016).
  27. J. A. Haigh, A. Nunnenkamp, A. J. Ramsay, and A. J. Ferguson, Phys. Rev. Lett. 117, 133602 (2016).
  28. A. Osada, R. Hisatomi, A. Noguchi, Y. Tabuchi, R. Yamazaki, K. Usami, M. Sadgrove, R. Yalla, M. Nomura, and Y. Nakamura, Phys. Rev. Lett. 116, 223601 (2016).
  29. X. Zhang, N. Zhu, C.-L. Zou, and H. X. Tang, Phys. Rev. Lett. 117, 123605 (2016).
  30. S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, Phys. Rev. A 94, 033821 (2016).
  31. X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang, Sci. Adv. 2, e1501286 (2016).
  32. C. Gonzalez-Ballestero, J. Gieseler, and O. Romero-Isart, Phys. Rev. Lett. 124, 093602 (2020).
  33. B. Heinrich, Y. Tserkovnyak, G. Woltersdorf, A. Brataas, R. Urban, and G. E. W. Bauer, Phys. Rev. Lett. 90, 187601 (2003).
  34. Y. Li, W. Cao, V. P. Amin, Z. Zhang, J. Gibbons, J. Sklenar, J. Pearson, P. M. Haney, M. D. Stiles, W. E. Bailey, V. Novosad, A. Hoffmann, and W. Zhang, Phys. Rev. Lett. 124, 117202 (2020).
  35. G. Woltersdorf, O. Mosendz, B. Heinrich, and C. H. Back, Phys. Rev. Lett. 99, 246603 (2007).
  36. R. Hisatomi, A. Osada, Y. Tabuchi, T. Ishikawa, A. Noguchi, R. Yamazaki, K. Usami, and Y. Nakamura, Phys. Rev. B 93, 174427 (2016).
  37. N. Zhu, X. Zhang, X. Han, C.-L. Zou, C. Zhong, C.-H. Wang, L. Jiang, and H. X. Tang, arXiv:2005.06429 [cond-mat.mes-hall].
  38. S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, Nature 443, 430 (2006).
  39. S. M. Rezende, Phys. Rev. B 79, 174411 (2009).
  40. D. Lachance-Quirion, Y. Tabuchi, S. Ishino, A. Noguchi, T. Ishikawa, R. Yamazaki, and Y. Nakamura, Sci. Adv. 3, e1603150 (2017).
  41. D. Lachance-Quirion, S. P. Wolski, Y. Tabuchi, S. Kono, K. Usami, and Y. Nakamura, Science 367, 425 (2020).
  42. V. A. S. V. Bittencourt, V. Feulner, and S. V. Kusminskiy, Phys. Rev. A 100, 013810 (2019).
  43. M. Elyasi, Y. M. Blanter, and G. E. W. Bauer, Phys. Rev. B 101, 054402 (2020).
  44. J. Li, S.-Y. Zhu, and G. S. Agarwal, Phys. Rev. Lett. 121, 203601 (2018).
  45. J. Li and S. Gröblacher, Quantum Sci. Technol. 6, 024005 (2021).
  46. A. Kamra and W. Belzig, Phys. Rev. Lett. 116, 146601 (2016).
  47. A. Kamra, W. Belzig, and A. Brataas, Appl. Phys. Lett. 117, 090501 (2020).
  48. M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D.-G. Welsch, Phys. Rev. A 55, 3184 (1997).
  49. A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, Science 312, 83 (2006).
  50. B. R. Johnson, M. D. Reed, A. A. Houck, D. I. Schuster, L. S. Bishop, E. Ginossar, J. M. Gambetta, L. DiCarlo, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, Nat. Phys. 6, 663 (2010).
  51. G. Nogues, A. Rauschenbeutel, S. Osnaghi, M. Brune, J. M. Raimond, and S. Haroche, Nature 400, 239 (1999).
  52. L. Sun, A. Petrenko, Z. Leghtas, B. Vlastakis, G. Kirchmair, K. M. Sliwa, A. Narla, M. Hatridge, S. Shankar, J. Blumoff, L. Frunzio, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, Nature 511, 444 (2014).
  53. D. D. Stancil and A. Prabhakar, Spin Waves: Theory and Applications (Springer, New York, 2009).
  54. J. A. Osborn, Phys. Rev. 67, 351 (1945).
  55. T. Holstein and H. Primakoff, Phys. Rev. 58, 1098 (1940).
  56. D. Walls and G. Milburn, Quantum Optics (Springer, Berlin, 2008).
  57. R. J. Glauber, Phys. Rev. 131, 2766 (1963).
  58. J. Bourhill, N. Kostylev, M. Goryachev, D. L. Creedon, and M. E. Tobar, Phys. Rev. B 93, 144420 (2016).
  59. C. A. Potts and J. P. Davis, Appl. Phys. Lett. 116, 263503 (2020).
  60. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.103.L100403 for detailed derivations of the ground state of the system and the heralded magnetization state after a single photon or a parity measurement which includes Refs. [56, 71, 72, 73, 74, 75, 76].
  61. We note that the cat size seems to be nonzero when R≈0, but this is merely an artifact of the definition which is irrelevant for rcat∼5.
  62. R. Jozsa, J. Mod. Opt. 41, 2315 (1994).
  63. A. Uhlmann, Rep. Math. Phys. 9, 273 (1976).
  64. P. Andrich, C. F. de las Casas, X. Liu, H. L. Bretscher, J. R. Berman, F. J. Heremans, P. F. Nealey, and D. D. Awschalom, npj Quantum Inf. 3, 28 (2017).
  65. D. I. Schuster, A. A. Houck, J. A. Schreier, A. Wallraff, J. M. Gambetta, A. Blais, L. Frunzio, J. Majer, B. Johnson, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Nature 445, 515 (2007).
  66. S. Klingler, H. Maier-Flaig, C. Dubs, O. Surzhenko, R. Gross, H. Huebl, S. T. B. Goennenwein, and M. Weiler, Appl. Phys. Lett. 110, 092409 (2017).
  67. M. Yanagisawa, Phys. Rev. Lett. 103, 203601 (2009).
  68. K. Jacobs, L. Tian, and J. Finn, Phys. Rev. Lett. 102, 057208 (2009).
  69. K. Jacobs, J. Finn, and S. Vinjanampathy, Phys. Rev. A 83, 041801(R) (2011).
  70. J. Zhang, Y. xi Liu, R.-B. Wu, K. Jacobs, and F. Nori, Phys. Rep. 679, 1 (2017).
  71. J. Dereziński, J. Math. Phys. 58, 121101 (2017).
  72. J. Colpa, Physica A 93, 327 (1978).
  73. S. L. Braunstein, Phys. Rev. A 71, 055801 (2005).
  74. C. Navarrete-Benlloch, An Introduction to the Formalism of Quantum Information with Continuous Variables (Morgan & Claypool, London, 2015), pp. 2053–2571.
  75. A. Royer, Phys. Rev. A 15, 449 (1977).
  76. W. P. Schleich, Quantum Optics in Phase Space (John Wiley & Sons, New York, 2005), Chap. 3, pp. 67–98.

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Phys. Rev. B 103, L100403– Published 4 March, 2021
  • Received 17 September 2020
  • Revised 4 December 2020
  • Accepted 10 February 2021
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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. Open access publication funded by the Max Planck Society.

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