Skip to main content
SpringerLink
Log in

The C̆erenkov Effect Revisited: From Swimming Ducks to Zero Modes in Gravitational Analogues

  • Chapter
Analogue Gravity Phenomenology

Part of the book series: Lecture Notes in Physics ((LNP,volume 870))

Abstract

We present an interdisciplinary review of the generalized C̆erenkov emission of radiation from uniformly moving sources in the different contexts of classical electromagnetism, superfluid hydrodynamics, and classical hydrodynamics. The details of each specific physical systems enter our theory via the dispersion law of the excitations. A geometrical recipe to obtain the emission patterns in both real and wave-vector space from the geometrical shape of the dispersion law is discussed and applied to a number of cases of current experimental interest. Some consequences of these emission processes onto the stability of condensed-matter analogues of gravitational systems are finally illustrated.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The k=0 mode corresponds to a spatially constant modulation that does not transport energy nor momentum. As discussed in [29], many other interesting features of wave propagation can be graphically studied starting from iso-frequency surfaces analogous to the locus Σ.

  2. 2.

    The coefficients of the analytical form (6.20) can be understood from the Fourier transform of a delta function peaked on the conically-shaped locus Σ of Eq. (6.19).

  3. 3.

    It is interesting to note that in both these experiments the moving charge responsible for the C̆erenkov emission did not consist of a charged physical particle travelling through the medium, but rather consisted of a moving bullet of nonlinear optical polarization generated by a femtosecond optical pulse via the so-called inverse electro-optic effect.

  4. 4.

    Needless to say that the configuration of a moving superfluid hitting an impurity at rest is fully equivalent modulo a Galilean transformation to the case of a moving impurity crossing a superfluid at rest.

  5. 5.

    It is interesting to note that, as in the case of electromagnetic waves, accelerated objects emit surface waves independently from their speed [64].

References

  1. Whitham, G.B.: Linear and Nonlinear Waves. Wiley-Interscience, New York (1974)

    MATH  Google Scholar 

  2. Lighthill, J.: Waves in Fluids. Cambridge University Press, Cambridge (1979)

    Google Scholar 

  3. Mei, C.C., Stiassnie, M., Yue, D.K.P.: Theory and Applications of Ocean Surface Waves: Part I, Linear Aspects; Part II, Nonlinear Aspects. World Scientific, Singapore (2005)

    Google Scholar 

  4. Darrigol, O.: Worlds of Flow: A History of Hydrodynamics from the Bernoulli to Prandtl. Oxford University Press, Oxford (2005)

    Google Scholar 

  5. Darrigol, O.: Arch. Hist. Exact Sci. 58, 21–95 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. Sorensen, R.M.: Adv. Hydrosci. 9, 49–83 (1973)

    Google Scholar 

  7. Yih, C.-S., Zhu, S.: Q. Appl. Math. 47, 17–33 (1989)

    MathSciNet  MATH  Google Scholar 

  8. Yih, C.-S., Zhu, S.: Q. Appl. Math. 47, 35–44 (1989)

    MathSciNet  MATH  Google Scholar 

  9. Torsvik, T.: In: Quak, E., Soomere, T. (eds.) Applied Wave Mathematics. Springer, Berlin (2009)

    Google Scholar 

  10. Soomere, T.: In: Quak, E., Soomere, T. (eds.) Applied Wave Mathematics. Springer, Berlin (2009)

    Google Scholar 

  11. Raphaël, É., de Gennes, P.-G.: Phys. Rev. E 53, 3448 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  12. Le Merrer, M., Clanet, C., Quéré, D., Raphaël, É., Chevy, F.: Proc. Natl. Acad. Sci. USA 108, 15064 (2011)

    Article  ADS  Google Scholar 

  13. Jelley, J.V.: Cherenkov Radiation and Its Applications. Pergamon Press, London (1958)

    Google Scholar 

  14. Carusotto, I., Ciuti, C.: Phys. Rev. Lett. 93, 166401 (2004)

    Article  ADS  Google Scholar 

  15. Ciuti, C., Carusotto, I.: Phys. Status Solidi B 242, 2224 (2005)

    Article  ADS  Google Scholar 

  16. Amo, A., Lefrère, J., Pigeon, S., Adrados, C., Ciuti, C., Carusotto, I., Houdré, R., Giacobino, E., Bramati, A.: Nat. Phys. 5, 805 (2009)

    Article  Google Scholar 

  17. Cornell, E.: Talk at the KITP Conference on Quantum Gases (2004). http://online.itp.ucsb.edu/online/gases_c04/cornell/

  18. Carusotto, I., Hu, S.X., Collins, L.A., Smerzi, A.: Phys. Rev. Lett. 97, 260403 (2006)

    Article  ADS  Google Scholar 

  19. Afanasiev, G., Kartavenko, V.G., Magar, E.N.: Physica B 269, 95 (1999)

    Article  ADS  Google Scholar 

  20. Stevens, T.E., Wahlstrand, J.K., Kuhl, J., Merlin, R.: Science 291, 627 (2001)

    Article  ADS  Google Scholar 

  21. Carusotto, I., Artoni, M., La Rocca, G.C., Bassani, F.: Phys. Rev. Lett. 87, 064801 (2001)

    Article  ADS  Google Scholar 

  22. Luo, C., Ibanescu, M., Johnson, S.G., Joannopoulos, J.D.: Science 299, 368 (2003)

    Article  ADS  Google Scholar 

  23. Xi, S., Chen, H., Jiang, T., Ran, L., Huangfu, J., Wu, B.-I., Kong, J.A., Chen, M.: Phys. Rev. Lett. 103, 194801 (2009)

    Article  ADS  Google Scholar 

  24. Pitaevskii, L., Stringari, S.: Bose-Einstein Condensation. Oxford University Press, Oxford (2003)

    MATH  Google Scholar 

  25. Pines, D., Nozieres, P.: The Theory of Quantum Liquids, vols. 1 and 2. Addison-Wesley, Redwood City (1966)

    Google Scholar 

  26. Leggett, A.J.: Rev. Mod. Phys. 71, S318 (1999)

    Article  Google Scholar 

  27. Landau, L.D., Lifshitz, E.M., Pitaevskii, L.P.: Statistical Physics, vol. 2. Pergamon, Oxford (1980)

    Google Scholar 

  28. Mayoral, C., Recati, A., Fabbri, A., Parentani, R., Balbinot, R., Carusotto, I.: New J. Phys. 13, 025007 (2011)

    Article  ADS  Google Scholar 

  29. Lock, E.H.: Phys. Usp. 51, 375–393 (2008)

    Article  ADS  Google Scholar 

  30. Pomeau, Y., Rica, S.: Phys. Rev. Lett. 71, 247 (1993)

    Article  ADS  Google Scholar 

  31. Astrakharchik, G.E., Pitaevskii, L.P.: Phys. Rev. A 70, 013608 (2004)

    Article  ADS  Google Scholar 

  32. Vavilov, S.: Dokl. Akad. Nauk SSSR 2, 457 (1934)

    Google Scholar 

  33. Cherenkov, P.A.: Dokl. Akad. Nauk SSSR 2, 451 (1934)

    Google Scholar 

  34. Frank, I., Tamm, I.: Dokl. Akad. Nauk SSSR 14, 107 (1937)

    Google Scholar 

  35. Auston, D.H., Cheung, K.P., Valdmanis, J.A., Kleinman, D.A.: Phys. Rev. Lett. 53, 1555 (1984)

    Article  ADS  Google Scholar 

  36. Tamm, I.: J. Phys. (Mosc.) 1, 439 (1939)

    MATH  Google Scholar 

  37. Frank, I.M.: Nucl. Instrum. Methods Phys. Res., Sect. A 248, 7 (1986)

    Article  ADS  Google Scholar 

  38. Hau, L.V., Harris, S.E., Dutton, Z., Behroozi, C.H.: Nature 397, 594 (1999)

    Article  ADS  Google Scholar 

  39. Kash, M.M., et al.: Phys. Rev. Lett. 82, 5229 (1999)

    Article  ADS  Google Scholar 

  40. Inouye, S., et al.: Phys. Rev. Lett. 85, 4225 (2000)

    Article  ADS  Google Scholar 

  41. Budker, D., Kimball, D.F., Rochester, S.M., Yashchuk, V.V.: Phys. Rev. Lett. 83, 1767 (1999)

    Article  ADS  Google Scholar 

  42. Frisch, T., Pomeau, Y., Rica, S.: Phys. Rev. Lett. 69, 1644 (1992)

    Article  ADS  Google Scholar 

  43. Neely, T., Samson, E., Bradley, A., Davis, M., Anderson, B.: Phys. Rev. Lett. 104, 160401 (2010)

    Article  ADS  Google Scholar 

  44. Amo, A., Pigeon, S., Sanvitto, D., Sala, V.G., Hivet, R., Carusotto, I., Pisanello, F., Lemenager, G., Houdre, R., Giacobino, E., Ciuti, C., Bramati, A.: Science 332, 1167 (2011)

    Article  ADS  Google Scholar 

  45. Nardin, G., Grosso, G., Léger, Y., Pietka, B., Morier-Genoud, F., Deveaud-Plédran, B.: Nat. Phys. 7, 635 (2011)

    Article  Google Scholar 

  46. Sanvitto, D., Pigeon, S., Amo, A., Ballarini, D., De Giorgi, M., Carusotto, I., Hivet, R., Pisanello, F., Sala, V.G., Soares-Guimaraes, P.S., Houdr, R., Giacobino, E., Ciuti, C., Bramati, A., Gigli, G.: Nat. Photonics 5, 610 (2011)

    Article  ADS  Google Scholar 

  47. Roberts, D.C., Pomeau, Y.: Phys. Rev. Lett. 95, 145303 (2005)

    Article  ADS  Google Scholar 

  48. Rayfield, G.W.: Phys. Rev. Lett. 16, 934 (1966)

    Article  ADS  Google Scholar 

  49. Phillips, A., McClintock, P.V.E.: Phys. Rev. Lett. 33, 1468 (1974)

    Article  ADS  Google Scholar 

  50. Ketterle, W., Inouye, S.: Lecture notes from Summer School on Bose-Einstein condensates and atom lasers, Cargs̀e, France (2000). Available as preprint arXiv:cond-mat/0101424

  51. Leboeuf, P., Pavloff, N.: Phys. Rev. A 64, 033602 (2001)

    Article  ADS  Google Scholar 

  52. Pavloff, N.: Phys. Rev. A 66, 013610 (2002)

    Article  ADS  Google Scholar 

  53. Gladush, Yu.G., El, G.A., Gammal, A., Kamchatnov, A.M.: Phys. Rev. A 75, 033619 (2007)

    Article  ADS  Google Scholar 

  54. Freixanet, T., Sermage, B., Bloch, J., Marzin, J.Y., Planel, R.: Phys. Rev. B 60, R8509 (1999)

    Article  ADS  Google Scholar 

  55. Houdré, R., Weisbuch, C., Stanley, R.P., Oesterle, U., Ilegems, M.: Phys. Rev. B 61, 13333R (2000)

    Article  ADS  Google Scholar 

  56. Langbein, W., Hvam, J.M.: Phys. Rev. Lett. 88, 047401 (2002)

    Article  ADS  Google Scholar 

  57. Bazaliy, Y.B., Jones, B.A., Zhang, S.C.: Phys. Rev. B 57, R3213 (1998)

    Article  ADS  Google Scholar 

  58. Fernández-Rossier, J., Braun, M., Núñez, A.S., MacDonald, A.H.: Phys. Rev. B 69, 174412 (2004)

    Article  ADS  Google Scholar 

  59. Vlaminck, V., Bailleul, M.: Science 322, 410 (2008)

    Article  ADS  Google Scholar 

  60. Cohen-Tannoudji, C., Diu, D., Laloë, F.: Quantum Mechanics. Wiley, New York (1978)

    Google Scholar 

  61. Jannes, G., Piquet, R., Maïssa, P., Mathis, C., Rousseaux, G.: Phys. Rev. E 83, 056312 (2011)

    Article  ADS  Google Scholar 

  62. Russell, J.S.: Report on waves. British Association for the Advancement of Science, Annual Report (1844). Figure reproduced from [4, 5]

    Google Scholar 

  63. Thomson, W. (Lord Kelvin): On ship waves. Lecture delivered at the “Conversazione” in the Science and Art Museum, Edinburgh, on 3 August 1887. Published in: Institution of Mechanical Engineers, Minutes of proceedings, 409–434 (1887). Figure reproduced from [4, 5]

    Google Scholar 

  64. Chepelianskii, A., Chevy, F., Raphaël, É.: Phys. Rev. Lett. 100, 074504 (2008)

    Article  ADS  Google Scholar 

  65. Bush, J.W.M., Hu, D.L.: Annu. Rev. Fluid Mech. 38, 339 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  66. Voise, J., Casas, J.: J. R. Soc. Interface 7, 343 (2010)

    Article  Google Scholar 

  67. Chen, X.-N., Sharma, S.-D.: J. Fluid Mech. 335, 305–321 (1997)

    Article  ADS  MATH  Google Scholar 

  68. Chen, X.-N., Sharma, S.-D., Stuntz, N.: J. Fluid Mech. 478, 111–124 (2003)

    Article  ADS  MATH  Google Scholar 

  69. Chen, X.-N., Sharma, S.-D., Stuntz, N.: J. Ship Res. 47, 1–10 (2003)

    Google Scholar 

  70. Belgiorno, F., Cacciatori, S.L., Ortenzi, G., Sala, V.G., Faccio, D.: Phys. Rev. Lett. 104, 140403 (2010)

    Article  ADS  Google Scholar 

  71. Rubino, E., McLenaghan, J., Kehr, S.C., Belgiorno, F., Townsend, D., Rohr, S., Kuklewicz, C.E., Leonhardt, U., König, F., Faccio, D.: Preprint. arXiv:1201.2689

  72. Balbinot, R., Fabbri, A., Fagnocchi, S., Recati, A., Carusotto, I.: Phys. Rev. A 78, 021603 (2008)

    Article  ADS  Google Scholar 

  73. Carusotto, I., Fagnocchi, S., Recati, A., Balbinot, R., Fabbri, A.: New J. Phys. 10, 103001 (2008)

    Article  ADS  Google Scholar 

  74. Recati, A., Pavloff, N., Carusotto, I.: Phys. Rev. A 80, 043603 (2009)

    Article  ADS  Google Scholar 

  75. Macher, J., Parentani, R.: Phys. Rev. A 80, 043601 (2009)

    Article  ADS  Google Scholar 

  76. Macher, J., Parentani, R.: Phys. Rev. D 79, 124008 (2009)

    Article  ADS  Google Scholar 

  77. Kamchatnov, A.M., Pavloff, N.: Preprint. arXiv:1111.5134

  78. Rousseaux, G., Mathis, C., Maïssa, P., Philbin, T.G., Leonhardt, U.: New J. Phys. 10, 053015 (2008)

    Article  ADS  Google Scholar 

  79. Rousseaux, G., Maïssa, P., Mathis, C., Coullet, P., Philbin, T.G., Leonhardt, U.: New J. Phys. 12, 095018 (2010)

    Article  ADS  Google Scholar 

  80. Weinfurtner, S., Tedford, E.W., Prentice, M.C.J., Unruh, W.G., Lawrence, G.A.: Phys. Rev. Lett. 106, 021302 (2010)

    Article  ADS  Google Scholar 

  81. Unruh, W.G.: Philos. Trans. R. Soc. Lond. 366, 2905–2913 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Acknowledgements

I.C. is grateful to G. C. La Rocca and M. Artoni for triggering his interest in the rich physics of the C̆erenkov effect, to C. Ciuti, M. Wouters, A. Amo, A. Bramati, E. Giacobino, and A. Smerzi for a long-lasting collaboration on (among other) the Bogoliubov-C̆erenkov emission in atomic and polaritonic superfluids, and to R. Balbinot, A. Fabbri, C. Mayoral, R. Parentani, and A. Recati for fruitful collaboration on analogue models. I.C. acknowledges financial support from ERC through the QGBE grant. G.R. is grateful to Conseil Général 06 and région PACA (HYDRO Project) for financial support.

Author information

Authors and Affiliations

  1. INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123, Povo, Italy

    Iacopo Carusotto

  2. Laboratoire J.-A. Dieudonné, UMR CNRS-UNS 6621, Université de Nice-Sophia Antipolis, Parc Valrose, 06108, Nice Cedex 02, France

    Germain Rousseaux

Authors
  1. Iacopo Carusotto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Germain Rousseaux
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Iacopo Carusotto .

Editor information

Editors and Affiliations

  1. School of Engineering and Physical Science, Heriot-Watt University, Edinburgh, United Kingdom

    Daniele Faccio

  2. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Francesco Belgiorno

  3. Dipartimento di Fisica e Matematica, Universita’ dell’Insubria, Como, Italy

    Sergio Cacciatori

  4. Dipartimento di Fisica e Matematica, Universita’ dell’Insubria, Como, Italy

    Vittorio Gorini

  5. Int. School for Adv. Studies (SISSA), Trieste, Italy

    Stefano Liberati

  6. Dipartimento di Fisica e Matematica, Universita’ dell’Insubria, Como, Italy

    Ugo Moschella

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Carusotto, I., Rousseaux, G. (2013). The C̆erenkov Effect Revisited: From Swimming Ducks to Zero Modes in Gravitational Analogues. In: Faccio, D., Belgiorno, F., Cacciatori, S., Gorini, V., Liberati, S., Moschella, U. (eds) Analogue Gravity Phenomenology. Lecture Notes in Physics, vol 870. Springer, Cham. https://doi.org/10.1007/978-3-319-00266-8_6

Download citation

Publish with us

Policies and ethics

Search

Navigation