The European Physical Journal D

, Volume 56, Issue 3, pp 391–404 | Cite as

Density correlations and analog dynamical Casimir emission of Bogoliubov phonons in modulated atomic Bose-Einstein condensates

Cold Matter and Quantum Gases

Abstract

We present a theory of the density correlations that appear in an atomic Bose-Einstein condensate as a consequence of the emission of correlated pairs of Bogoliubov phonons by a time-dependent atom-atom scattering length. This effect can be considered as a condensed matter analog of the dynamical Casimir effect of quantum field theory. Different regimes as a function of the temporal shape of the modulation are identified and a simple physical picture of the phenomenon is discussed. Analytical expressions for the density correlation function are provided for the most significant limiting cases. This theory is able to explain some unexpected features recently observed in numerical studies of analog Hawking radiation from acoustic black holes.

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References

  1. 1.
    G.T. Moore, J. Math. Phys. 11, 2679 (1970)CrossRefADSGoogle Scholar
  2. 2.
    S.A. Fulling, P.C.W. Davies, Proc. R. Soc. London Ser. A 348, 393 (1976)MATHCrossRefMathSciNetADSGoogle Scholar
  3. 3.
    P.C.W. Davies, S.A. Fulling, Proc. R. Soc. London Ser. A 356, 237 (1977)CrossRefADSGoogle Scholar
  4. 4.
    M. Kardar, R. Golestanian, Rev. Mod. Phys. 71, 1233 (1999)CrossRefADSGoogle Scholar
  5. 5.
    M.-T. Jaekel, S. Reynaud, Phys. Rev. Lett. 77, 615 (1996)CrossRefADSGoogle Scholar
  6. 6.
    M.-T. Jaekel, S. Reynaud, Rep. Prog. Phys. 60, 863 (1997)CrossRefADSGoogle Scholar
  7. 7.
    A. Lambrecht, J. Opt. B: Quantum Semiclass. Opt. 7, S3 (2005)CrossRefADSGoogle Scholar
  8. 8.
    W.-J. Kim, J.H. Brownell, R. Onofrio, Phys. Rev. Lett. 96, 200402 (2006)CrossRefADSGoogle Scholar
  9. 9.
    E. Yablonovich, Phys. Rev. Lett. 62, 1742 (1989)CrossRefADSGoogle Scholar
  10. 10.
    Yu. E. Lozovik, V.G. Tsvetus, E.A. Vinogradov, JETP Lett. 61, 723 (1995)ADSGoogle Scholar
  11. 11.
    C.K. Law, Phys. Rev. A 49, 433 (1994)CrossRefADSGoogle Scholar
  12. 12.
    H. Saito, H. Hyuga, Phys. Rev. A 65, 053804 (2002)CrossRefADSGoogle Scholar
  13. 13.
    F.-X. Dezael, Ph.D. Thesis, Université Paris VI, 2007. Available online at: http://tel.archives-ouvertes.fr/tel-00165149/
  14. 14.
    C. Braggio, G. Bressi, G. Carugno, C. Del Noce, G. Galeazzi, A. Lombardi, A. Palmieri, G. Ruoso, D. Zanello, Europhys. Lett. 70, 754 (2005)CrossRefADSGoogle Scholar
  15. 15.
    W.-J. Kim, J.H. Brownell, R. Onofrio, Europhys. Lett. 78, 21002 (2007)CrossRefADSGoogle Scholar
  16. 16.
    C. Braggio, G. Bressi, G. Carugno, C. Del Noce, G. Galeazzi, A. Lombardi, A. Palmieri, G. Ruoso, D. Zanello, Europhys. Lett. 78, 21003 (2007)CrossRefADSGoogle Scholar
  17. 17.
    C. Ciuti, G. Bastard, I. Carusotto, Phys. Rev. B 72, 115303 (2005)CrossRefADSGoogle Scholar
  18. 18.
    C. Ciuti, I. Carusotto, Phys. Rev. A 74, 033811 (2006)CrossRefADSGoogle Scholar
  19. 19.
    S. De Liberato, C. Ciuti, I. Carusotto, Phys. Rev. Lett. 98, 103602 (2007)CrossRefADSGoogle Scholar
  20. 20.
    I. Carusotto, M. Antezza, F. Bariani, S. De Liberato, C. Ciuti, Phys. Rev. A 77, 063621 (2008)CrossRefADSGoogle Scholar
  21. 21.
    A.V. Dodonov, L.C. Celeri, F. Pascoal, M.D. Lukin, S.F. Yelin, arXiv:0806.4035Google Scholar
  22. 22.
    S. De Liberato, D. Gerace, I. Carusotto, C. Ciuti, arXiv:0906.2706Google Scholar
  23. 23.
    M.O. Scully, V.V. Kocharovsky, A. Belyanin, E. Fry, F. Capasso, Phys. Rev. Lett. 91, 243004 (2003)CrossRefADSGoogle Scholar
  24. 24.
    A. Belyanin, V.V. Kocharovsky, F. Capasso, E. Fry, M.S. Zubairy, M.O. Scully, Phys. Rev. A 74, 023807 (2006)CrossRefADSGoogle Scholar
  25. 25.
    B.L. Hu, A. Roura, Phys. Rev. Lett. 93, 129301 (2004)CrossRefADSGoogle Scholar
  26. 26.
    M.O. Scully, V.V. Kocharovsky, A. Belyanin, E. Fry, F. Capasso, Phys. Rev. Lett. 93, 129302 (2004)CrossRefADSGoogle Scholar
  27. 27.
    G. Günter, A.A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorba, S. De Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, R. Huber, Nature 458, 178 (2009)CrossRefADSGoogle Scholar
  28. 28.
    M. Sandberg, C.M. Wilson, F. Persson, T. Bauch, G. Johansson, V. Shumeiko, T. Duty, P. Delsing, Appl. Phys. Lett. 92, 203501 (2008)CrossRefADSGoogle Scholar
  29. 29.
    P. Delsing, seminars at the Solid State Quantum Information Workshop (Pisa, 2008) and at ETH (Zurich, 2009)Google Scholar
  30. 30.
    W.G. Unruh, Phys. Rev. Lett. 46, 1351 (1981)CrossRefADSGoogle Scholar
  31. 31.
    Artificial Black Holes, edited by M. Novello, M. Visser, G. Volovik (World Scientific, River Edge, 2002)Google Scholar
  32. 32.
    P.O. Fedichev, U.R. Fischer, Phys. Rev. Lett. 91, 240407 (2003)CrossRefMathSciNetADSGoogle Scholar
  33. 33.
    P. Jain, S. Weinfurtner, M. Visser, C.W. Gardiner, Phys. Rev. A 76, 033616 (2007)CrossRefADSGoogle Scholar
  34. 34.
    T.A. Jacobson, G.E. Volovik, Phys. Rev. D 58, 064021 (1998)CrossRefADSGoogle Scholar
  35. 35.
    L.J. Garay, J.R. Anglin, J.I. Cirac, P. Zoller, Phys. Rev. Lett. 85, 4643 (2000)CrossRefADSGoogle Scholar
  36. 36.
    C. Barceló, S. Liberati, M. Visser, Int. J. Mod. Phys. A 18, 3735 (2003)MATHCrossRefADSGoogle Scholar
  37. 37.
    C. Barceló, S. Liberati, M. Visser, Phys. Rev. A 68, 053613 (2003)CrossRefADSGoogle Scholar
  38. 38.
    S. Giovanazzi, C. Farrell, T. Kiss, U. Leonhardt, Phys. Rev. A 70, 063602 (2004)CrossRefADSGoogle Scholar
  39. 39.
    C. Barceló, S. Liberati, M. Visser, Living Rev. Rel. 8, 12 (2005)Google Scholar
  40. 40.
    R. Schützhold, Phys. Rev. Lett. 97, 190405 (2006)CrossRefADSGoogle Scholar
  41. 41.
    S. Wuester, C.M. Savage, Phys. Rev. A 76, 013608 (2007)CrossRefADSGoogle Scholar
  42. 42.
    P.O. Fedichev, U.R. Fischer, Phys. Rev. A 69, 033602 (2004)CrossRefADSGoogle Scholar
  43. 43.
    M. Uhlmann, Y. Xu, R. Schützhold, New J. Phys. 7, 248 (2005)CrossRefADSGoogle Scholar
  44. 44.
    R. Balbinot, A. Fabbri, S. Fagnocchi, A. Recati, I. Carusotto, Phys. Rev. A 78, 021603 (2008)CrossRefADSGoogle Scholar
  45. 45.
    I. Carusotto, S. Fagnocchi, A. Recati, R. Balbinot, A. Fabbri, New J. Phys. 10, 103001 (2008)CrossRefADSGoogle Scholar
  46. 46.
    K. Staliunas, S. Longhi, G.J. de Valcárcel, Phys. Rev. Lett. 89, 210406 (2002)CrossRefADSGoogle Scholar
  47. 47.
    A. Iucci, M.A. Cazalilla, A.F. Ho, T. Giamarchi, Phys. Rev. A 73, 041608 (2006)CrossRefADSGoogle Scholar
  48. 48.
    C. Kollath, A. Iucci, T. Giamarchi, W. Hofstetter, U. Schollwöck, Phys. Rev. Lett. 97, 050402 (2006)CrossRefADSGoogle Scholar
  49. 49.
    L. Goren, E. Mariani, A. Stern, Phys. Rev. A 75, 063612 (2007)CrossRefADSGoogle Scholar
  50. 50.
    S.D. Huber, E. Altman, H.P. Büchler, G. Blatter, Phys. Rev. B 75, 085106 (2007)CrossRefADSGoogle Scholar
  51. 51.
    M. Krämer, C. Tozzo, F. Dalfovo, Phys. Rev. A 71, R061602 (2005)CrossRefADSGoogle Scholar
  52. 52.
    P. Calabrese, J. Cardy, Phys. Rev. Lett. 96, 136801 (2006)CrossRefADSGoogle Scholar
  53. 53.
    P. Calabrese, J. Cardy, J. Stat. Mech. P06008 (2007)Google Scholar
  54. 54.
    S. Sotiriadis, P. Calabrese, J. Cardy, arXiv:0903.0895Google Scholar
  55. 55.
    M.A. Cazalilla, Phys. Rev. Lett. 97, 156403 (2006)CrossRefADSGoogle Scholar
  56. 56.
    V. Gritsev, E. Demler, M. Lukin, A. Polkovnikov, Phys. Rev. Lett. 99, 200404 (2007)CrossRefADSGoogle Scholar
  57. 57.
    A. Imambekov, I.E. Mazets, D.S. Petrov, V. Gritsev, S. Manz, S. Hofferberth, T. Schumm, E. Demler, J. Schmiedmayer, Phys. Rev. A 80, 033604 (2009)CrossRefGoogle Scholar
  58. 58.
    T. Stöferle, H. Moritz, C. Schori, M. Köhl, T. Esslinger, Phys. Rev. Lett. 92, 130403 (2004)CrossRefADSGoogle Scholar
  59. 59.
    T. Stöferle, H. Moritz, C. Schori, M. Köhl, T. Esslinger, Phys. Rev. A 70, 011601(R) (2004)ADSGoogle Scholar
  60. 60.
    C. Schori, T. Stöferle, H. Moritz, M. Köhl, T. Esslinger, Phys. Rev. Lett. 93, 240402 (2004)CrossRefADSGoogle Scholar
  61. 61.
    P. Engels, C. Atherton, M.A. Hoefer, Phys. Rev. Lett. 98, 095301 (2007)CrossRefADSGoogle Scholar
  62. 62.
    L. Pitaevskii, S. Stringari, Bose-Einstein condensation (Clarendon Press, Oxford, 2003)MATHGoogle Scholar
  63. 63.
    I. Bloch, J. Dalibard, W. Zwerger, Many-Body Physics with Ultracold Gases, Rev. Mod. Phys. 80, 885 (2008)CrossRefADSGoogle Scholar
  64. 64.
    A. Öttl, S. Ritter, M. Köhl, T. Esslinger, Phys. Rev. Lett. 95, 090404 (2005)CrossRefGoogle Scholar
  65. 65.
    M. Greiner, C.A. Regal, J.T. Stewart, D.S. Jin, Phys. Rev. Lett. 94, 110401 (2005)CrossRefADSGoogle Scholar
  66. 66.
    S. Fölling, F. Gerbier, A. Widera, O. Mandel, T. Gericke, I. Bloch, Nature 434, 481 (2005)CrossRefADSGoogle Scholar
  67. 67.
    T. Rom et al., Nature 444, 733 (2006)CrossRefADSGoogle Scholar
  68. 68.
    A. Perrin, H. Chang, V. Krachmalnicoff, M. Schellekens, D. Boiron, A. Aspect, C.I. Westbrook, Phys. Rev. Lett. 99, 150405 (2007)CrossRefADSGoogle Scholar
  69. 69.
    T. Jeltes, J.M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, C.I. Westbrook, Nature 445, 402 (2007)CrossRefADSGoogle Scholar
  70. 70.
    S. Hofferberth, I. Lesanovsky, T. Schumm, A. Imambekov, V. Gritsev, E. Demler, J. Schmiedmayer, Nature Phys. 4, 489 (2008)CrossRefADSGoogle Scholar
  71. 71.
    V. Guarrera, N. Fabbri, L. Fallani, C. Fort, K.M.R. van der Stam, M. Inguscio, Phys. Rev. Lett. 100, 250403 (2008)CrossRefADSGoogle Scholar
  72. 72.
    R. Durrer, The Cosmic Microwave Background (Cambridge University Press, 2008)Google Scholar
  73. 73.
    G. Hinshaw et al., Astrophys. J. Suppl. 180, 225 (2009)CrossRefADSGoogle Scholar
  74. 74.
    V.F. Mukhanov, H.A. Feldman, R.H. Brandenberger, Phys. Rep. 215, 203 (1992)CrossRefMathSciNetADSGoogle Scholar
  75. 75.
    S. Bashinsky, E. Bertschinger, Phys. Rev. Lett. 87, 081301 (2001)CrossRefADSGoogle Scholar
  76. 76.
    D. Campo, R. Parentani, Phys. Rev. D 70, 105020 (2004)CrossRefADSGoogle Scholar
  77. 77.
    C. Chin, R. Grimm, P. Julienne, E. Tiesinga, arXiv:0812.1496Google Scholar
  78. 78.
    T. Kinoshita, T. Wenger, D.S. Weiss, Science 305, 1125 (2004)CrossRefADSGoogle Scholar
  79. 79.
    B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling, I. Cirac, G.V. Shlyapnikov, T.W. Hänsch, I. Bloch, Nature 429, 277 (2004)CrossRefADSGoogle Scholar
  80. 80.
    Y. Castin, in Coherent atomic matter waves, Lecture Notes of Les Houches Summer School, edited by R. Kaiser, C. Westbrook, F. David (EDP Sciences and Springer-Verlag, 2001), pp. 1–136Google Scholar
  81. 81.
    L. Kofman, A. Linde, A.A. Starobinsky, Phys. Rev. D 56, 3258 (1997)CrossRefADSGoogle Scholar
  82. 82.
    J.P. Zibin, R. Brandenberger, D. Scott, Phys. Rev. D 63, 043511 (2001)CrossRefADSGoogle Scholar
  83. 83.
    Y. Nambu, Y. Araki, Class. Quan. Grav. 23, 511 (2006)MATHCrossRefMathSciNetADSGoogle Scholar
  84. 84.
    M.R. Matthews D.S. Hall, D.S. Jin, J.R. Ensher, C.E. Wieman, E.A. Cornell, F. Dalfovo, C. Minniti, S. Stringari, Phys. Rev. Lett. 81, 243 (1998)CrossRefADSGoogle Scholar
  85. 85.
    E.A. Donley, N.R. Claussen, S.L. Cornish, J.L. Roberts, E.A. Cornell, C.E. Wieman, Nature 412, 295 (2001)CrossRefADSGoogle Scholar
  86. 86.
    A. Polkovnikov, V. Gritsev, Nature Phys. 4, 477 (2008)CrossRefADSGoogle Scholar
  87. 87.
    T. Kiss, J. Janszky, P. Adam, Phys. Rev. A 49, 4935 (1994)CrossRefADSGoogle Scholar
  88. 88.
    M. Naraschewski, R.J. Glauber, Phys. Rev. A 59, 4595 (1999)CrossRefADSGoogle Scholar
  89. 89.
    S. Dettmer, D. Hellweg, P. Ryytty, J.J. Arlt, W. Ertmer, K. Sengstock, D.S. Petrov, G.V. Shlyapnikov, H. Kreutzmann, L. Santos, M. Lewenstein, Phys. Rev. Lett. 87, 160406 (2001)CrossRefADSGoogle Scholar
  90. 90.
    E. Cornell, talk at the Towards the observation of Hawking radiation in condensed matter systems workshop (Valencia, Spain, 2009), see the webpage http://www.uv.es/workshopEHR

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • I. Carusotto
    • 1
  • R. Balbinot
    • 2
  • A. Fabbri
    • 3
  • A. Recati
    • 1
    • 4
  1. 1.CNR-INFM BEC Center and Dipartimento di Fisica, Università di TrentoPovo, TrentoItaly
  2. 2.Dipartimento di Fisica dell’Università di Bologna and INFN sezione di BolognaBolognaItaly
  3. 3.Departamento de Fisica Teorica and IFICUniversidad de Valencia-CSICBurjassotSpain
  4. 4.Physik-DepartmentTechnische Universität MünchenGarchingGermany

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