Advertisement

Normal mode splitting in quantum degenerate Fermi gas in nano-cavity

  • Kamran Ullah
  • Farhan Saif
Regular Article
  • 43 Downloads

Abstract

We report the normal mode splitting in the fermionic displacement spectrum as a single mode light field interacts with a mechanical mode of ultra-cold quantum degenerate Fermi gas trapped inside a Fabry–Pérot cavity in the strong coupling regime. We explain the normal mode splitting in the outgoing field of the cavity field and in the field quadratures as well. As a function of system parameters, such as coupling strength between fermionic mode and field mode, number of fermionic atoms, cavity decay rate and fluctuations associated with the fermionic mode we explain the phenomenon of normal mode splitting. The low-lying fermions ensemble displays a collective density oscillation associated with particle-hole excitations, which interacts with cavity light field and lead to the observation of NMS in the fermion quadratures and light modes. The numerical results based on the present day laboratory experiments agree with the obtained analytical results.

Graphical abstract

Keywords

Cold Matter and Quantum Gas 

References

  1. 1.
    P. Meystre, Ann. Phys. (Berlin) 525, 215 (2013) ADSCrossRefGoogle Scholar
  2. 2.
    A. Aspelmeyer, T.J. Kippenberg, F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014) ADSCrossRefGoogle Scholar
  3. 3.
    F. Saif, J. Russ. Lasers Res. 34, 496 (2013) ADSCrossRefGoogle Scholar
  4. 4.
    M. Khan, J. Akram, M. Paternostro, F. Saif, Phys. Rev. A 94, 063830 (2016) ADSCrossRefGoogle Scholar
  5. 5.
    B. Rogers, N. Lo Gullo, G.D. Chiara, G.M. Palma, M. Paternostro, Quantum Meas. Quantum Metro. 2, 11 (2014) ADSGoogle Scholar
  6. 6.
    G. Kurizki, P. Bertet, Y. Kubo, K. Mølmer, D. Palma, D. Petrosyan, P. Rabl, J. Schmiedmayer, PNAS 112, 3866 (2015) CrossRefGoogle Scholar
  7. 7.
    J.I. Cirac, P. Zoller, Nature (London) 404, 579 (2015) ADSCrossRefGoogle Scholar
  8. 8.
    S. ul Haq, F. Saif, Optik 124, 5914 (2013) ADSCrossRefGoogle Scholar
  9. 9.
    S. ul Haq, F. Saif, Optik 125, 6616 (2014) ADSCrossRefGoogle Scholar
  10. 10.
    A.H. Khosa, R. ul Islam, F. Saif, J. Bergou, Q. Info. Proc. 12, 129 (2013) CrossRefGoogle Scholar
  11. 11.
    L. Tiang, P. Zoller, Phys. Rev. Lett. 93, 2666403 (2004) Google Scholar
  12. 12.
    W.K. Hensinger et al., Phys. Rev. A 72, 041405 (2005) ADSCrossRefGoogle Scholar
  13. 13.
    C. Genes, D. Vitali, P. Tombesi, Phys. Rev. A 77, 050307 (2008) ADSCrossRefGoogle Scholar
  14. 14.
    M.J. Akram, M.M. Khan, F. Saif, Phys. Rev. A 92, 023846 (2015) ADSCrossRefGoogle Scholar
  15. 15.
    F. Bariani, H. Seok, S. Singh, L.F. Buchmann, M. Vengalattore, P. Meystre, Phys. Rev. A 92, 043817 (2015) ADSCrossRefGoogle Scholar
  16. 16.
    F. Bariani, S. Singh, L.F. Buchmann, M. Vengalattore, P. Meystre, Phys. Rev. A 90, 033838 (2014) ADSCrossRefGoogle Scholar
  17. 17.
    L. Tian, Ann. Phys. (Berlin) 527, 1 (2015) ADSCrossRefGoogle Scholar
  18. 18.
    D.E. Chang, C.A. Regal, S.B. Papp, D.J. Wilson, J. Ye, O. Painter, H.J. Kimble, P. Zoller, PNAS 107, 1005 (2010) ADSCrossRefGoogle Scholar
  19. 19.
    O. Romero-Isart, M.L. Juan, R. Quidant, J.I. Cirac, New J. Phys. 12, 033015 (2010) ADSCrossRefGoogle Scholar
  20. 20.
    T. Li, S. Kheifets, M.G. Raizen, Nat. Phys. 7, 527 (2011) CrossRefGoogle Scholar
  21. 21.
    A.A. Geraci, S.B. Papp, J. Kitching, Phys. Rev. Lett. 105, 101101 (2010) ADSCrossRefGoogle Scholar
  22. 22.
    J. Gieseler, B. Deutsch, R. Quidant, L. Novotny, Phys. Rev. Lett. 109, 103603 (2012) ADSCrossRefGoogle Scholar
  23. 23.
    G.A.T. Pender, P.F. Barker, F. Marquardt, J. Millen, T.S. Monteiro, Phys. Rev. A 85, 021802 (2012) ADSCrossRefGoogle Scholar
  24. 24.
    J. Millen, P.Z.G. Fonseca, T. Mavrogordatos, T.S. Montiero, P.F. Barker, Phys. Rev. Lett. 114, 123602 (2015) ADSCrossRefGoogle Scholar
  25. 25.
    T.W. Hansch, A.L. Schawlow, Opt. Commun. 13, 68 (1975) ADSCrossRefGoogle Scholar
  26. 26.
    D.J. Wineland, R.E. Drullinger, F.L. Walls, Phys. Rev. Lett. 40, 1639 (1978) ADSCrossRefGoogle Scholar
  27. 27.
    S. Chu, L. Hollberg, J.E. Bjorkholm, A. Cable, A. Ashkin, Phys. Rev. Lett. 55, 48 (1985) ADSCrossRefGoogle Scholar
  28. 28.
    P.Z.G. Fonseca, E.B. Aranas, J. Millen, T.S. Monteiro, G. Ranjit, C. Montoya, A.A. Geraci, Phys. Rev. A 91, 013416 (2015) ADSCrossRefGoogle Scholar
  29. 29.
    B. Abbott, et al. (LIGO Scientific collaboration), New J. Phys. 11, 073032 (2009) ADSCrossRefGoogle Scholar
  30. 30.
    C.M. Caves, Phys. Rev. Lett. 45, 75 (1980) ADSCrossRefGoogle Scholar
  31. 31.
    V.B. Braginsky, F. Khalili, Quantum Measurement (Cambridge University Press, Cambridge, UK, 1992) Google Scholar
  32. 32.
    V.B. Braginsky, S.E. Strigin, S.P. Vyatchanin, Phys. Lett. A 287, 331 (2001) ADSCrossRefGoogle Scholar
  33. 33.
    A. Dorsel, J.D. McCullen, P. Meystre, E. Vignes, H. Walther, Phys. Rev. Lett. 51, 1550 (1983) ADSCrossRefGoogle Scholar
  34. 34.
    J.D. McCullen, P. Meystre, E.M. Wright, Opt. Lett. 9, 193 (1984) ADSCrossRefGoogle Scholar
  35. 35.
    P. Meystre, E.M. Wright, J.D. McCullen, E. Vignes, J. Opt. Soc. Am. B 2, 1830 (1985) ADSCrossRefGoogle Scholar
  36. 36.
    J.D. Thompson, B.M. Zwickl, A.M. Jayich, F. Marquardt, S.M. Girvin, J.G.E. Harris, Nature (London) 452, 72 (2008) ADSCrossRefGoogle Scholar
  37. 37.
    P. Treutlein, D. Hunger, S. Camerer, T.W. Hänsch, J. Reichel, Phys. Rev. Lett. 99, 140403 (2007) ADSCrossRefGoogle Scholar
  38. 38.
    H. Seok, L.F. Buchmann, S. Singh, S.K. Steinke, P. Meystre, Phys. Rev. A 85, 033822 (2012) ADSCrossRefGoogle Scholar
  39. 39.
    D.W.C.Brooks, T. Botter, S. Schreppler, T.P. Purdy, N. Brahms, D.M. Stamper-Kurn, Nature 488, 476 (2012) ADSCrossRefGoogle Scholar
  40. 40.
    A.H. Safavi-Naeini, S. Groblacher, J.T. Hill, J. Chan, M. Aspelmeyer, O. Painter, Nature 500, 185 (2013) ADSCrossRefGoogle Scholar
  41. 41.
    T.P. Purdy, P.L. Yu, R.W. Peterson, N.S. Kampel, C.A. Regal, Phys. Rev. X 3, 031012 (2013) Google Scholar
  42. 42.
    M. Bhattacharya, P.L. Giscard, P. Meystre, Phys. Rev. A 77, 030303 (2008) ADSCrossRefGoogle Scholar
  43. 43.
    M.J. Hartmann, M.B. Plenio, Phys. Rev. Lett. 101, 200503 (2008) ADSCrossRefGoogle Scholar
  44. 44.
    R. ul Islam, A.H. Khosa, F. Saif, J. Phys. B: At. Mol. Opt. Phys. 41, 035505 (2008) ADSCrossRefGoogle Scholar
  45. 45.
    Z.Q. Yin, Y.J. Han, Phys. Rev. A 79, 024301 (2009) ADSCrossRefGoogle Scholar
  46. 46.
    C.L. Zou, X.B. Zou, F.W. Sun, Z.F. Han, G.C. Guo, Phys. Rev. A 84, 032317 (2011) ADSCrossRefGoogle Scholar
  47. 47.
    M. Asjad, F. Saif, Phys. Lett. A 376, 2608 (2012) ADSCrossRefGoogle Scholar
  48. 48.
    C. Joshi, J. Larson, M. Jonson, E. Andersson, P. Ohberg, Phys. Rev. A 85, 033805 (2012) ADSCrossRefGoogle Scholar
  49. 49.
    L. Tian, Phys. Rev. Lett. 110, 233602 (2013) ADSCrossRefGoogle Scholar
  50. 50.
    Y.D. Wang, A.A. Clerk, Phys. Rev. Lett. 110, 253601 (2013) ADSCrossRefGoogle Scholar
  51. 51.
    T.K. Ghosh, K. Machida, Phys. Rev. A 72, 053623 (2005) ADSCrossRefGoogle Scholar
  52. 52.
    S. Huang, G.S. Agarwal, Phys. Rev. A 80, 033807 (2009) ADSCrossRefGoogle Scholar
  53. 53.
    A. Bhattacherjee, J. Phys. B 40, 143 (2007) ADSCrossRefGoogle Scholar
  54. 54.
    S. Shahidani, M.H. Naderi, M. Soltanolkotabi, J. Mod. Optics 62, 114 (2015) ADSCrossRefGoogle Scholar
  55. 55.
    J.M. Dobrindt, I. Wilson-Rae, T.J. Kippenberg, Phys. Rev. Lett. 101, 263602 (2008) ADSCrossRefGoogle Scholar
  56. 56.
    M.S. Groblacher, K. Hammerer, M.R. Aspelmeyer, Nature (London) 460, 724 (2009) ADSCrossRefGoogle Scholar
  57. 57.
    T.J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, K.J. Vahala, Phys. Rev. Lett. 95, 033901 (2005) ADSCrossRefGoogle Scholar
  58. 58.
    T. Carmon, H. Rokhsari, L. Yang, T.J. Kippenberg, K.J. Vahala, Phys. Rev. Lett. 94, 223902 (2005) ADSCrossRefGoogle Scholar
  59. 59.
    H. Rokhsari, T.J. Kippenberg, T. Carmon, K.J. Vahala, Opt. Express 13, 5293 (2005) ADSCrossRefGoogle Scholar
  60. 60.
    M.G. Raizen, R.J. Thompson, R.J. Brecha, H.J. Kimble, H.J. Carmichael, Phys. Rev. Lett. 63, 240 (1989) ADSCrossRefGoogle Scholar
  61. 61.
    A. Boca, R. Miller, K.M. Birnbaum, A.D. Boozer, J. McKeever, H.J. Kimble, Phys. Rev. Lett. 93, 233603 (2004) ADSCrossRefGoogle Scholar
  62. 62.
    P. Maunz, T. Puppe, I. Schuster, N. Syassen, P.W.H. Pinkse, G. Rempe, Phys. Rev. Lett. 94, 033002 (2005) ADSCrossRefGoogle Scholar
  63. 63.
    W. Wallraff, D.I. Schuster, A. Blais et al., Nature (London) 431, 162 (2004) ADSCrossRefGoogle Scholar
  64. 64.
    J.P. Reithmaier, G. Sek, A. Loffeler et al., Nature (London) 432, 197 (2004) ADSCrossRefGoogle Scholar
  65. 65.
    M. Asjad, F. Saif, Phys. Rev. A 84, 033606 (2011) ADSCrossRefGoogle Scholar
  66. 66.
    A.B. Bhattacherjee, Phys. Rev. A 80, 043607 (2009) ADSCrossRefGoogle Scholar
  67. 67.
    J.D. Teufel, J.W. Harlow, C.A. Regal, K.W. Lehnert, Phys. Rev. Lett. 101, 197203 (2008) ADSCrossRefGoogle Scholar
  68. 68.
    A. Schliesser et al., Nat. Phys. 4, 415 (2008) CrossRefGoogle Scholar
  69. 69.
    K.W. Murch et al., Nat. Phys. 4, 561 (2008) CrossRefGoogle Scholar
  70. 70.
    F. Brennecke et al., Science 322, 235 (2008) ADSCrossRefGoogle Scholar
  71. 71.
    M. Asjad, F. Saif, Optik 125, 5455 (2014) ADSCrossRefGoogle Scholar
  72. 72.
    R. Kanamoto, P. Meystre, Phys. Rev. Lett. 104, 063601 (2010) ADSCrossRefGoogle Scholar
  73. 73.
    R. Kanamoto, P. Meystre, Phys. Scr. 82, 038111 (2010) ADSCrossRefGoogle Scholar
  74. 74.
    M. Asjad, M.A. Shahzad, F. Saif, Eur. Phys. J. D 67, 198 (2013) ADSCrossRefGoogle Scholar
  75. 75.
    C. Maschler, H. Ritsch, Phys. Rev. Lett. 95, 260401 (2005) ADSCrossRefGoogle Scholar
  76. 76.
    H. Christ, C.P. Search, P. Meystre, Phys. Rev. A 67, 063611 (2003) ADSCrossRefGoogle Scholar
  77. 77.
    D. Meiser, C.P. Search, P. Meystre, Phys. Rev. A 71, 013404 (2005) ADSCrossRefGoogle Scholar
  78. 78.
    A.G. Rojo, J.L. Cohen, P.R. Berman, Phys. Rev. A 60, 1482 (1999) ADSCrossRefGoogle Scholar
  79. 79.
    T. Giamarchi, Quantum Physics in one Dimension (Oxford University Press, Oxford, 2004) Google Scholar
  80. 80.
    C.W.Gardiner, P. Zoller, Quantum Noise (Springer-Verlag, Berlin, 1991) Google Scholar
  81. 81.
    D.F. Walls, G.J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1991) Google Scholar
  82. 82.
    A. Hurwitz, in Selected papers on mathematical trends in control theory, edited by R. Bellman, R. Kalaba (Dover, New York, 1964) Google Scholar
  83. 83.
    E.X. Dejesus, C. Kaufman, Phys. Rev. A 35, 5288 (1987) ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhysicsQuaid-i-Azam UniversityIslamabadPakistan
  2. 2.Department of ElectronicsQuaid-i-Azam UniversityIslamabadPakistan

Personalised recommendations