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Bose–Einstein condensation of paraxial light

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Abstract

Photons, due to the virtually vanishing photon–photon interaction, constitute to very good approximation an ideal Bose gas, but owing to the vanishing chemical potential a (free) photon gas does not show Bose–Einstein condensation. However, this is not necessarily true for a lower-dimensional photon gas. By means of a fluorescence induced thermalization process in an optical microcavity one can achieve a thermal photon gas with freely adjustable chemical potential. Experimentally, we have observed thermalization and subsequently Bose–Einstein condensation of the photon gas at room temperature. In this paper, we give a detailed description of the experiment, which is based on a dye-filled optical microcavity, acting as a white-wall box for photons. Thermalization is achieved in a photon number-conserving way by photon scattering off the dye molecules, and the cavity mirrors both provide an effective photon mass and a confining potential-key prerequisites for the Bose–Einstein condensation of photons. The experimental results are in good agreement with both a statistical and a simple rate equation model, describing the properties of the thermalized photon gas.

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References

  1. A. Einstein, Sitz.ber. Preuss. Akad. Wiss. Berl. Philos.-Hist. Kl. 1, 3 (1925)

    MathSciNet  Google Scholar 

  2. M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, E.A. Cornell, Science 269, 198 (1995)

    Article  ADS  Google Scholar 

  3. K.B. Davis, M.-O. Mewes, M.R. Andrews, N.J. van Druten, D.M. Durfee, D.M. Kurn, W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995)

    Article  ADS  Google Scholar 

  4. C.C. Bradley, C.A. Sackett, R.G. Hulet, Phys. Rev. Lett. 78, 985 (1997)

    Article  ADS  Google Scholar 

  5. S. Jochim, M. Bartenstein, A. Altmeyer, G. Hendl, S. Riedl, C. Chin, J. Hecker, R. Grimm, Science 302, 2101 (2003)

    Article  ADS  Google Scholar 

  6. M. Greiner, C. Regal, D. Jin, Nature 426, 537 (2003)

    Article  ADS  Google Scholar 

  7. A.J. Leggett, Rev. Mod. Phys. 73, 307 (2001)

    Article  ADS  Google Scholar 

  8. A.E. Siegman, Lasers (Univ. Science Books, Sausalito, 1986)

    Google Scholar 

  9. P.W. Milonni, J.H. Eberly, Lasers (Wiley, New York, 1988)

    Google Scholar 

  10. M.O. Scully, M.S. Zubairy, Quantum Optics, 1st edn. (Cambridge University Press, Cambridge, 1997)

    Google Scholar 

  11. M. Planck, Ann. Phys. 309, 553 (1901)

    Article  Google Scholar 

  12. S. Bose, Z. Phys. 26, 178 (1924)

    Article  ADS  Google Scholar 

  13. K. Huang, Statistical Mechanics (Wiley, New York, 1987)

    MATH  Google Scholar 

  14. W. Ketterle, D.S. Durfee, D.M. Stamper-Kurn, in Bose–Einstein Condensation in Atomic Gases, ed. by M. Inguscio, S. Stringari, C.K, Wieman Proceedings of the International School of Physics ‘Enrico Fermi’, Course CXL, (IOS Press, Amsterdam, 1999)

    Google Scholar 

  15. Y.B. Zel’dovich, E.V. Levich, Sov. Phys. JETP 28, 1287 (1969)

    ADS  Google Scholar 

  16. E. Müller, Physica A 139, 165 (1986)

    Article  MathSciNet  ADS  Google Scholar 

  17. R.Y. Chiao, Phys. Rev. A 60, 4114 (1999)

    Article  ADS  Google Scholar 

  18. R.Y. Chiao, Opt. Commun. 179, 157 (2000)

    Article  ADS  Google Scholar 

  19. M.W. Mitchell, C.I. Hancox, R.Y. Chiao, Phys. Rev. A 62, 043819 (2000)

    Article  ADS  Google Scholar 

  20. E.L. Bolda, R.Y. Chiao, W.H. Zurek, Phys. Rev. Lett. 86, 416 (2001)

    Article  ADS  Google Scholar 

  21. C.F. McCormick, R.Y. Chiao, J.M. Hickmann, Opt. Express 10, 581 (2002)

    ADS  Google Scholar 

  22. C.F. McCormick, Transverse effects in nonlinear optics: toward the photon superfluid. Ph.D. thesis, University of California, Berkeley (2003)

  23. P. Navez, Phys. Rev. A 68, 5 (2003)

    Google Scholar 

  24. R.Y. Chiao, T.H. Hansson, J.M. Leinaas, S. Viefers, Phys. Rev. A 69, 063816 (2004)

    Article  ADS  Google Scholar 

  25. J. Martinez, Anton. J. Opt. Soc. Am. B 23, 1644 (2006)

    Article  ADS  Google Scholar 

  26. B.T. Seaman, M.J. Holland, arXiv:0807.1356 (2008)

  27. C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, S. Rica, Phys. Rev. Lett. 95, 263901 (2005)

    Article  ADS  Google Scholar 

  28. C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008)

    Article  ADS  Google Scholar 

  29. P. Aschieri, J. Garnier, C. Michel, V. Doya, A. Picozzi, Phys. Rev. A 83, 033838 (2011)

    Article  ADS  Google Scholar 

  30. R. Weill, B. Levit, A. Bekker, B. Fischer, O. Gat, Opt. Express 18, 16520 (2010)

    Article  ADS  Google Scholar 

  31. J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J.M.J. Keeling, F.M. Marchetti, M.H. Szymańska, R. André, J.L. Staehli, V. Savona, P.B. Littlewood, B. Deveaud, L.S. Dang Nature 443, 409 (2006)

    Article  ADS  Google Scholar 

  32. R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, Science 316, 1007 (2007)

    Article  ADS  Google Scholar 

  33. J. Kasprzak, M. Richard, A. Baas, B. Deveaud, R. André, J.-P. Poizat, L.S. Dang, Phys. Rev. Lett. 100, 1 (2008)

    Article  Google Scholar 

  34. J. Kasprzak, D.D. Solnyshkov, R. Andre, L.S. Dang, G. Malpuech, Phys. Rev. Lett. 101, 146404 (2008)

    Article  ADS  Google Scholar 

  35. K.G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, L.S. Dang, B. Deveaud-Plédran, Nat. Phys. 4, 706 (2008)

    Article  Google Scholar 

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

    Article  Google Scholar 

  37. J. Klaers, F. Vewinger, M. Weitz, Nat. Phys. 6, 512 (2010)

    Article  Google Scholar 

  38. J. Klaers, J. Schmitt, F. Vewinger, M. Weitz, Nature 468, 545 (2010)

    Article  ADS  Google Scholar 

  39. E.H. Kennard, Phys. Rev. 11, 29 (1918)

    Article  ADS  Google Scholar 

  40. E.H. Kennard, Phys. Rev. 29, 466 (1927)

    Article  ADS  Google Scholar 

  41. B.I. Stepanov, Dokl. Akad. Nauk SSSR 112, 839 (1957)

    Google Scholar 

  42. L.P. Kazachenko, B.I. Stepanov, Opt. Spektrosk. 2, 339 (1957)

    Google Scholar 

  43. J. Klaers, Bose–Einstein-Kondensation von paraxialem Licht. Ph.D. thesis, University of Bonn (2011)

  44. H. Kogelnik, T. Li, Appl. Opt. 5, 1550 (1966)

    Article  ADS  Google Scholar 

  45. V. Bagnato, D. Kleppner, Phys. Rev. A 44, 7439 (1991)

    Article  ADS  Google Scholar 

  46. D.S. Petrov, D.M. Gangardt, G.V. Shlyapnikov, J. Phys.-Paris IV 116, 5 (2004)

    Google Scholar 

  47. W.J. Mullin, J. Low Temp. Phys. 106, 615 (1997)

    Article  ADS  Google Scholar 

  48. W.J. Mullin, J. Low Temp. Phys. 110, 167 (1998)

    Article  Google Scholar 

  49. H. Yokoyama, S.D. Brorson, J. Appl. Phys. 66, 4801 (1989)

    Article  ADS  Google Scholar 

  50. E. De Angelis, F. De Martini, P. Mataloni, J. Opt. B, Quantum Semiclass. Opt. 2, 149 (2000)

    Article  ADS  Google Scholar 

  51. K.H. Drexhage, in Progress in Optics, ed. by E. Wolf (North-Holland, Amsterdam, 1974)

    Google Scholar 

  52. R. Hulet, E. Hilfer, D. Kleppner, Phys. Rev. Lett. 55, 2137 (1985)

    Article  ADS  Google Scholar 

  53. W. Jhe, A. Anderson, E. Hinds, D. Meschede, L. Moi, S. Haroche, Phys. Rev. Lett. 58, 666 (1987)

    Article  ADS  Google Scholar 

  54. F. De Martini, G. Innocenti, G.R. Jacobovitz, P. Mataloni, Phys. Rev. Lett. 59, 2955 (1987)

    Article  ADS  Google Scholar 

  55. F. De Martini, M. Marrocco, P. Mataloni, L. Crescentini, R. Loudon, Phys. Rev. A 43, 2480 (1991)

    Article  ADS  Google Scholar 

  56. P. Milonni, J. Mod. Opt. 9, 119 (2007)

    Google Scholar 

  57. R. Loudon, M.J. Adams, IEE Proc. Optoelectron. 1, 289 (2007)

    Google Scholar 

  58. D. Meschede, Phys. Rep. 211, 201 (1992)

    Article  ADS  Google Scholar 

  59. H. Walther, B.T.H. Varcoe, B.G. Englert, T. Becker, Rep. Prog. Phys. 69, 1325 (2006)

    Article  ADS  Google Scholar 

  60. I. Fujiwara, D. Ter Haar, H. Wergeland, J. Stat. Phys. 2, 329 (1970)

    Article  ADS  Google Scholar 

  61. R.M. Ziff, G.E. Uhlenbeck, M. Kac, Phys. Rep. 32, 169 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  62. Vi.V. Kocharovsky, Vl.V. Kocharovsky, M. Holthaus, C.H. Raymond Ooi, A.A. Svidzinsky, W. Ketterle, M.O. Scully, Adv. At. Mol. Opt. Phys. 53, 291 (2006)

    Google Scholar 

  63. J.R. Lakowicz, Principles of Fluorescence Spectroscopy (Kluwer Academic, New York, 1999)

    Google Scholar 

  64. D.A. Sawicki, R.S. Knox, Phys. Rev. A 54, 4837 (1996)

    Article  ADS  Google Scholar 

  65. J. Klaers, J. Schmitt, T. Damm, F. Vewinger, M. Weitz, (2011, in preparation)

  66. F. De Martini, G. Jacobovitz, Phys. Rev. Lett. 60, 1711 (1988)

    Article  ADS  Google Scholar 

  67. H. Yokoyama, K. Nishi, T. Anan, Y. Nambu, S.D. Brorson, E.P. Ippen, M. Suzuki, Opt. Quantum Electron. 24, 245 (1992)

    Article  Google Scholar 

  68. Y. Yamamoto, S. Machida, G. Björk, Opt. Quantum Electron. 24, 215 (1992)

    Article  Google Scholar 

  69. D. Magde, R. Wong, P.G. Seybold, J. Photochem. Photobiol. A, Chem. 75, 327 (2002)

    Article  Google Scholar 

  70. L.R. Wilson, B.S. Richards, Appl. Opt. 48, 212 (2009)

    Article  ADS  Google Scholar 

  71. A. Penzkofer, Y. Lu, Chem. Phys. 103, 399 (1986)

    Article  ADS  Google Scholar 

  72. A. Penzkofer, W. Leupacher, J. Lumin. 37, 61 (1987)

    Article  Google Scholar 

  73. M. Fischer, J. Georges, Chem. Phys. Lett. 260, 115 (1996)

    Article  ADS  Google Scholar 

  74. S. Noda, K. Tomoda, N. Yamamoto, A. Chutinan, Science 289, 604 (2000)

    Article  ADS  Google Scholar 

  75. A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, H.M. Van Driel, Nature 405, 437 (2000)

    Article  ADS  Google Scholar 

  76. R. Pappalardo, H. Samelson, A. Lempicki, IEEE J. Quantum Electron. 6, 716 (1970)

    Article  ADS  Google Scholar 

  77. N. Tammuz, R.P. Smith, R.L.D. Campbell, S. Beattie, S. Moulder, J. Dalibard, Z. Hadzibabic, Phys. Rev. Lett. 106, 230401 (2011)

    Article  ADS  Google Scholar 

  78. F. De Martini, F. Cairo, P. Mataloni, F. Verzegnassi, Phys. Rev. A 46, 4220 (1992)

    Article  ADS  Google Scholar 

  79. E. Ippen, C. Shank, A. Dienes, IEEE J. Quantum Electron. 7, 178 (1971)

    Article  ADS  Google Scholar 

  80. O.G. Peterson, S.A. Tuccio, B.B. Snavely, Appl. Phys. Lett. 17, 245 (1970)

    Article  ADS  Google Scholar 

  81. M. Kasha, Discuss. Faraday Soc. 9, 14 (1950)

    Article  Google Scholar 

  82. M.E. Lusty, M.H. Dunn, Appl. Phys. B, Lasers Opt. 44, 193 (1987)

    Article  ADS  Google Scholar 

  83. A. Nag, D. Goswami, J. Photochem. Photobiol. A, Chem. 206, 188 (2009)

    Article  Google Scholar 

  84. Z. Hadzibabic, J. Dalibard, in Nano Optics and Atomics: Transport of Light and Matter Waves. Proceedings of the International School of Physics Enrico Fermi, vol. CLXXIII (IOS Press, Amsterdam, 2011)

    Google Scholar 

  85. Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, J. Dalibard, Nature 441, 1111 (2006)

    Article  ADS  Google Scholar 

  86. P. Clade, C. Ryu, A. Ramanathan, K. Helmerson, W.D. Phillips, Phys. Rev. Lett. 102, 170401 (2009)

    Article  ADS  Google Scholar 

  87. R. Hanbury Brown, R.Q. Twiss, Nature 178, 1046 (1956)

    Article  ADS  Google Scholar 

  88. E.M. Purcell, Nature 178, 1449 (1956)

    Article  ADS  Google Scholar 

  89. W. van Sark, K.W. Barnham, L.H. Slooff, A.J. Chatten, A. Búchtemann, A. Meyer, S.J. McCormack, R. Koole, D.J. Farrell, R. Bose, E.E. Bende, A.R. Burgers, T. Budel, J. Quilitz, M. Kennedy, T. Meyer, S.H. Wadman, G.P. van Klink, G. van Koten, A. Meijerink, D. Vanmaekelbergh, Opt. Express 16, 21773 (2008)

    Article  ADS  Google Scholar 

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Klaers, J., Schmitt, J., Damm, T. et al. Bose–Einstein condensation of paraxial light. Appl. Phys. B 105, 17 (2011). https://doi.org/10.1007/s00340-011-4734-6

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