- 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

Spectroscopic footprints of quantum friction in nonreciprocal and chiral media

O. J. Franca1,*, Fabian Spallek1, Steffen M. Giesen2, Robert Berger2, Kilian Singer1, Stefan Aull1, and Stefan Yoshi Buhmann1,†

  • *Contact author: uk081688@uni-kassel.de
  • †Contact author: stefan.buhmann@uni-kassel.de
PDF

Phys. Rev. A 112, 012803 – Published 7 July, 2025

DOI: https://doi.org/10.1103/jhnk-tpcf

Abstract

We investigate how the quantum friction experienced by a polarizable atom moving with constant velocity parallel to a planar interface is modified when the latter consists of chiral or nonreciprocal media, with special focus on topological insulators. Macroscopic quantum electrodynamics is used to obtain the velocity-dependent Casimir-Polder frequency shift and decay rate. These results are a generalization to matter with time-reversal symmetry breaking. Our findings are illustrated by examining the nonretarded and retarded limits for five examples: a perfectly conducting mirror, a perfectly reflecting nonreciprocal mirror, a three-dimensional topological insulator, a perfectly reflecting chiral mirror, and an isotropic chiral medium. Different asymptotic power laws are found for all these materials. Interestingly, two bridges exist between chirality and nonreciprocity through the frequency shift, which arise as a consequence of the magnetoelectric coupling. Specifically, the position-dependent Casimir-Polder frequency shift for the nonreciprocal case depends on a geometric magnetic field associated with photoionization of chiral molecules, while the Casimir-Polder frequency shift depending on the velocity for the chiral case has the optical rotatory strength as the atomic response, and those for the nonreciprocal case depend on an analog of the optical rotatory strength.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (105)

  1. H. B. G. Casimir, Proc. K. Ned. Akad. Wet. Amsterdam 51, 793 (1948).
  2. P. W. Milonni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics (Academic, New York, 2013).
  3. D Dalvit, P. Milonni, D. Roberts, and F. da Rosa, Casimir Physics, Lecture Notes in Physics (Springer, 2011), Vol. 834, pp. 1–22.
  4. L. M. Woods, D. A. R. Dalvit, A. Tkatchenko, P. Rodriguez-Lopez, A. W. Rodriguez, and R. Podgornik, Rev. Mod. Phys. 88, 045003 (2016).
  5. H. B. G. Casimir and D. Polder, Phys. Rev. 73, 360 (1948).
  6. J. B. Pendry, J. Phys.: Condens. Matter 9, 10301 (1997).
  7. A. I. Volokitin and B. N. J. Persson, Rev. Mod. Phys. 79, 1291 (2007).
  8. J. B. Pendry, New J. Phys. 12, 033028 (2010).
  9. M. G. Silveirinha, New J. Phys. 16, 063011 (2014).
  10. M. B. Farias, W. J. M. Kort-Kamp, and D. A. R. Dalvit, Phys. Rev. B 97, 161407(R) (2018).
  11. S. Scheel and S. Y. Buhmann, Phys. Rev. A 80, 042902 (2009).
  12. F. Intravaia, R. O. Behunin, and D. A. R. Dalvit, Phys. Rev. A 89, 050101(R) (2014).
  13. F. Intravaia, R. O. Behunin, C. Henkel, K. Busch, and D. A. R. Dalvit, Phys. Rev. Lett. 117, 100402 (2016).
  14. R. Zhao, A. Manjavacas, F. J. Garcia de Abajo, and J. B. Pendry, Phys. Rev. Lett. 109, 123604 (2012).
  15. A. I. Volotkin, JETP Lett. 104, 504 (2016); M. B. Farias, C. D. Fosco, F. C. Lombardo, and F. D. Mazzitelli, Phys. Rev. D 95, 065012 (2017).
  16. V. Frolov and V. Ginzburg, Phys. Lett. A 116, 423 (1986).
  17. M. V. Nezlin, Sov. Phys. Usp. 19, 946 (1976).
  18. V. L. Ginzburg, Phys. Usp. 39, 973 (1996).
  19. M. F. Maghrebi, R. Golestanian, and M. Kardar, Phys. Rev. A 88, 042509 (2013).
  20. F. Intravaia, V. E. Mkrtchian, S. Y. Buhmann, S. Scheel, D. A. R. Dalvit, and C. Henkel, J. Phys.: Condens. Matter 27, 214020 (2015).
  21. G. Dedkov and A. Kyasov, Phys. Solid State 44, 1809 (2002).
  22. G. Barton, New J. Phys. 12, 113045 (2010).
  23. M. G. Silveirinha and S. I. Maslovski, Phys. Rev. A 86, 042118 (2012); G. Pieplow and C. Henkel, New J. Phys. 15, 023027 (2013); U. D. Jentschura, G. Lach, M. De Kieviet, and K. Pachucki, Phys. Rev. Lett. 114, 043001 (2015); A. I. Volokitin, Phys. Rev. A 96, 012520 (2017); F. C. Lombardo and P. I. Villar, J. Phys.: Conf. Ser. 880, 012035 (2017); P. Rodriguez-Lopez and E. Martín-Martínez, Phys. Rev. A 98, 032507 (2018).
  24. J. Klatt, R. Bennett, and S. Y. Buhmann, Phys. Rev. A 94, 063803 (2016).
  25. F. Intravaia, R. O. Behunin, C. Henkel, K. Busch, and D. A. R. Dalvit, Phys. Rev. A 94, 042114 (2016).
  26. F. Intravaia, M. Oelschläger, D. Reiche, D. A. R. Dalvit, and K. Busch, Phys. Rev. Lett. 123, 120401 (2019).
  27. M. B. Pogrebinskii, Fiz. Tekh. Poluprovodn. (S.-Peterburg) 11, 637 (1977) [Sov. Phys. Semi-cond. 11, 372 (1977)]; P. J. Price, Physica 117–118, 750 (1983); A. I. Volokitin and B. N. J. Persson, Phys. Rev. Lett. 106, 094502 (2011).
  28. T. J. Gramila, J. P. Eisenstein, A. H. MacDonald, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. 66, 1216 (1991); R. V. Gorbachev, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. Tudorovskiy, T. V. Grigorieva, A. H. MacDonald, K. Watanabe, T. Taniguchi, and L. P. Ponamarenko, Nat. Phys. 8, 896 (2012).
  29. S. Y. Buhmann, Dispersion Forces I: Macroscopic Quantum Electrodynamics and Ground-State Casimir, Casimir–Polder and van der Waals Forces, Springer Tracts in Modern Physics (Springer, Berlin, 2012), Vol. 247.
  30. S. Y. Buhmann, L. Knöll, D.-G. Welsch, and H. T. Dung, Phys. Rev. A 70, 052117 (2004).
  31. S. Scheel and S. Y. Buhmann, Acta Phys. Slovaca 58, 675 (2008).
  32. S. Y. Buhmann, Dispersion Forces II: Many-Body Effects, Excited Atoms, Finite Temperature and Quantum Friction, Springer Tracts in Modern Physics (Springer, Berlin, 2012), Vol. 248.
  33. J. Klatt, C. M. Kropf, and S. Y. Buhmann, Phys. Rev. Lett. 126, 210401 (2021).
  34. N. Kavokine, M.-L. Bocquet, and L. Bocquet, Nature (London) 602, 84 (2022).
  35. M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
  36. X. L. Qi and S. C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).
  37. L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 98, 106803 (2007); L. Fu and C. L. Kane, Phys. Rev. B 76, 045302 (2007).
  38. J. E. Moore and L. Balents, Phys. Rev. B 75, 121306(R) (2007); R. Roy, ibid. 79, 195322 (2009).
  39. C.-Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y. Ou, P. Wei, L.-L. Wang, Z.-Q. Ji, Y. Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S.-C. Zhang, K. He, Y. Wang et al., Science 340, 167 (2013); X. Kou, S.-T. Guo, Y. Fan, L. Pan, M. Lang, Y. Jiang, Q. Shao, T. Nie, K. Murata, J. Tang, Y. Wang, L. He, T.-K. Lee, W.-L. Lee, and K. L. Wang, Phys. Rev. Lett. 113, 137201 (2014); J. G. Checkelsky, R. Yoshimi, A. Tsukazaki, K. S. Takahashi, Y. Kozuka, J. Falson, M. Kawasaki, and Y. Tokura, Nat. Phys. 10, 731 (2014); C. Z. Chang, W. Zhao, D. Y. Kim, H. Zhang, B. A. Assaf, D. Heiman, S.-C. Zhang, C- Liu, M. H. W. Chan, and J. S. Moodera, Nat. Mater. 14, 473 (2015).
  40. M. Mogi, M. Kawamura, R. Yoshimi, A. Tsukazaki, Y. Kozuka, N. Shirakawa, K. S. Takahashi, M. Kawasaki, and Y. Tokura, Nat. Mater. 16, 516 (2017).
  41. L. Wu, M. Salehi, N. Koirala, J. Moon, S. Oh, and N. P. Armitage, Science 354, 1124 (2016).
  42. V. Dziom, A. Shuvaev, A. Pimenov, G. V. Astakhov, C. Ames, K. Bendias, J. Böttcher, G. Tkachov, E. M. Hankiewicz, C. Brüne, H. Buhmann, and L. W. Molenkamp, Nat. Commun. 8, 15197 (2017).
  43. X. L. Qi, T. L. Hughes, and S. C. Zhang, Phys. Rev. B 78, 195424 (2008).
  44. K. N. Okada, Y. Takahashi, M. Mogi, R. Yoshimi, A. Tsukazaki, K. S. Takahashi, N. Ogawa, M. Kawasaki, and Y. Tokura, Nat. Commun. 7, 12245 (2016).
  45. O. J. Franca, L. F. Urrutia, and O. Rodríguez-Tzompantzi, Phys. Rev. D 99, 116020 (2019).
  46. O. J. Franca and S. Y. Buhmann, Phys. Rev. B 105, 155120 (2022).
  47. O. J. Franca and L. F. Urrutia, Rev. Mex. Fis. 68, 060701 (2022).
  48. O. J. Franca and S. Y. Buhmann, Phys. Rev. B 110, 195150 (2024).
  49. X. L. Qi, R. D. Li, J. D. Zang, and S. C. Zhang, Science 323, 1184 (2009).
  50. J. D. Castaño-Yepes, O. J. Franca, C. F. Ramirez-Gutierrez, and J. C. del Valle, Physica E 123, 114202 (2020).
  51. D. Xiao, J. Jiang, J.-H. Shin, W. Wang, F. Wang, Y.-F. Zhao, C. Liu, W. Wu, M. H.-W. Chan, N. Samarth, and C.-Z. Chang, Phys. Rev. Lett. 120, 056801 (2018); M. Mogi, M. Kawamura, A. Tsukazaki, R. Yoshimi, K. S. Takahashi, M. Kawasaki, and Y. Tokura, Sci. Adv. 3, eaao1669 (2017); N. Varnava and D. Vanderbilt, Phys. Rev. B 98, 245117 (2018).
  52. S. Y. Buhmann, D. T. Butcher, and S. Scheel, New J. Phys. 14, 083034 (2012).
  53. S. Fuchs, J. A. Crosse, and S. Y. Buhmann, Phys. Rev. A 95, 023805 (2017).
  54. L. Onsager, Phys. Rev. 37, 405 (1931).
  55. H. A. Lorentz, Koninklijke Nederlandse Akademie van Wetenschappen te Amsterdam 4, 176 (1896).
  56. S. Y. Buhmann, S. M. Giesen, M. Diekmann, R. Berger, S. Aull, P. Zahariev, M. Debatin, and K. Singer, New J. Phys. 23, 083040 (2021).
  57. E. U. Condon, Rev. Mod. Phys. 9, 432 (1937).
  58. P. Král, I. Thanopulos, M. Shapiro, and D. Cohen, Phys. Rev. Lett. 90, 033001 (2003).
  59. D. Vardanega, F. Picaud, and C. Giradet, Surf. Sci. 601, 3818 (2007).
  60. J. Trost and K. Hornberger, Phys. Rev. Lett. 103, 023202 (2009).
  61. D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics: An Introduction to Radiation Molecule Interactions (Academic, New York, 1984).
  62. D. T. Butcher, S. Y. Buhmann, and S. Scheel, New J. Phys. 14, 113013 (2012).
  63. P. Barcellona, H. Safari, A. Salam, and S. Y. Buhmann, Phys. Rev. Lett. 118, 193401 (2017).
  64. F. Suzuki, T. Momose, and S. Y. Buhmann, Phys. Rev. A 99, 012513 (2019).
  65. P. Curie, J. Phys. Theor. Appl. 3, 393 (1894).
  66. J. A. Crosse, S. Fuchs, and S. Y. Buhmann, Phys. Rev. A 92, 063831 (2015).
  67. S. Y. Buhmann, V. N. Marachevsky, and S. Scheel, Phys. Rev. A 98, 022510 (2018).
  68. D. Ayuso, A. F. Ordonez, and O. Smirnova, Phys. Chem. Chem. Phys. 24, 26962 (2022).
  69. A. F. Ordonez and O. Smirnova, Phys. Rev. A 99, 043416 (2019).
  70. M. Morgenstern, C. Pauly, J. Kellner, M. Liebmann, M. Pratzer, G. Bihlmayer, M. Eschbach, L. Plucinski, S. Otto, B. Rasche, M. Ruck, M. Richter, S. Just, F. Lüpke, and B. Voigtländer, Phys. Status Solidi B 258, 2000060 (2021).
  71. R. Noguchi, T. Takahashi, K. Kuroda, M. Ochi, T. Shirasawa, M. Sakano, C. Bareille, M. Nakayama, M. D. Watson, K. Yaji, A. Harasawa, H. Iwasawa, P. Dudin, T. K. Kim, M. Hoesch, V. Kandyba, A. Giampietri, A. Barinov, S. Shin, R. Arita et al., Nature (London) 566, 518 (2019).
  72. I. H. Grinberg, M. Lin, W. A. Benalcazar, T. L. Hughes, and G. Bahl, Phys. Rev. Appl. 14, 064042 (2020).
  73. A. Martín-Ruiz, M. Cambiaso, and L. F. Urrutia, Phys. Rev. D 92, 125015 (2015).
  74. A. Martín-Ruiz, M. Cambiaso, and L. F. Urrutia, Europhys. Lett. 113, 60005 (2016).
  75. T. H. O'Dell, The Electrodynamics of Magneto-Electric Media (North-Holland, Amsterdam, 1970).
  76. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, Course of Theoretical Physics Vol. 8 (Pergamon, Oxford, 1984).
  77. F. W. Hehl, Y. N. Obukhov, J.-P. Rivera, and H. Schmid, Relativistic analysis of magnetoelectric crystals: Extracting a new 4-dimensional P odd and T odd pseudoscalar from Cr2O3 data, Phys. Lett. A 372, 1141 (2008).
  78. S. S. Batsanov, E. D. Ruchkin, and I. A. Poroshina, Refractive Indices of Solids, Springer Briefs in Applied Sciences and Technology (Springer, Singapore, 2016).
  79. J.-P. Rivera, Eur. Phys. J. B 71, 299 (2009).
  80. S. M. Ali, T. M. Habashy, and J. A. Kong, J. Opt. Soc. Am. A 9, 413 (1992).
  81. C. Caloz and A. Sihvola, arXiv:1903.09087.
  82. A. Lakhtakia, V. K. Varadan, and V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media, Lecture Notes in Physics (Springer-Verlag, 1989).
  83. I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Biisotropic Media (Artech House, London, 1994).
  84. L. D. Barron, Chem. Phys. Lett. 123, 423 (1986).
  85. L. D. Barron, J. Am. Chem. Soc. 108, 5539 (1986).
  86. L. D. Barron (private communication).
  87. L. A. Kerber, O. Kreuz, T. Ring, H. Braun, R. Berger, and D. M. Reich, arXiv:2405.12893.
  88. F. Pulm, J. Schramm, J. Hormes, S. Grimme, and S. D. Peyerimhoff, Chem. Phys. 224, 143 (1997).
  89. A. Brown, C. Kemp, and S. Mason, Mol. Phys. 20, 787 (1971).
  90. A. Brown, C. M. Kemp, and S. F. Mason, J. Chem. Soc. A A, 751 (1971).
  91. W. S. Brickell, A. Brown, C. M. Kemp, and S. F. Mason, J. Chem. Soc. A A, 756 (1971).
  92. B. A. Stickler, M. Diekmann, R. Berger, and D. Wang, Phys. Rev. X 11, 031056 (2021).
  93. C. I. Sukenik, M. G. Boshier, D. Cho, V. Sandoghdar, and E. A. Hinds, Phys. Rev. Lett. 70, 560 (1993).
  94. K. Voronin, A. S. Taradin, M. V. Gorkunov, and D. G. Baranov, ACS Photonics 9, 2652 (2022).
  95. Silpa B. S., Shovan Kanti Barik, S. Chaudhuri, and S. Roy, Opt. Continuum 1, 1176 (2022).
  96. F. Suzuki, S. A. Shah, D. A. R. Dalvit, and M. Arndt, Phys. Rev. Res. 6, 023145 (2024).
  97. J. Zou and S. D. Hogan, Phys. Rev. A 107, 062820 (2023).
  98. J. Keller, T. Burgermeister, D. Kalincev, J. Kiethe, and T. Mehlstäubler, J. Phys.: Conf. Ser. 723, 012027 (2016).
  99. A. Arias, G. Lochead, T. M. Wintermantel, S. Helmrich, and S. Whitlock, Phys. Rev. Lett. 122, 053601 (2019).
  100. P. Sikivie, Rev. Mod. Phys. 93, 015004 (2021).
  101. D. M. Nenno, C. A. C. Garcia, J. Gooth, C. Felser, and P. Narang, Nat. Rev. Phys. 2, 682 (2020).
  102. D. J. E. Marsh, K. C. Fong, E. W. Lentz, L. Šmejkal, and M. N. Ali, Phys. Rev. Lett. 123, 121601 (2019).
  103. J. Schütte-Engel, D. J. E. Marsh, A. J. Millar, A. Sekine, F. Chadha-Day, S. Hoof, M. N. Ali, K. C. Fong, E. Hardy, and L. Šmejkal, J. Cosmol. Astropart. Phys. 08 (2021) 066.
  104. H. S. Røising, B. Fraser, S. M. Griffin, S. Bandyopadhyay, A. Mahabir, S.-W. Cheong, and A. V. Balatsky, Phys. Rev. Res. 3, 033236 (2021).
  105. C. S. Rapp, J. C. Franz, S. Y. Buhmann, and O. J. Franca, arXiv:2406.10038.

Outline

Information

Phys. Rev. A 112, 012803– Published 7 July, 2025
  • Received 23 December 2024
  • Accepted 6 June 2025
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