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Quantum tomography in position and momentum space

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Abstract

We introduce a method of quantum tomography for a continuous variable system in position and momentum space. We consider a single two-level probe interacting with a quantum harmonic oscillator by means of a class of Hamiltonians, linear in position and momentum variables, during a tunable time span. We study two cases: the reconstruction of the wavefunctions of pure states and the direct measurement of the density matrix of mixed states. We show that our method can be applied to several physical systems where high quantum control can be experimentally achieved.

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References

  1. 1.

    Quantum State Estimation, Lecture Notes in Physics, edited by M. Paris, J. Rehácek (Springer, Berlin, 2004), Vol. 649

  2. 2.

    J.F. Poyatos, R. Walser, J.I. Cirac, P. Zoller, R. Blatt, Phys. Rev. A 53, R1966 (1996)

  3. 3.

    M.G. Raymer, M. Beck, D.F. Mcalister, Phys. Rev. Lett. 72, 1137 (1994)

  4. 4.

    Ch. Kurtsiefer, T. Pfau, J. Mlyneck, Nature 386, 150 (1997)

  5. 5.

    C. Monroe, D.M. Meekhof, B.E. King, D.J. Wineland, Science 272, 1131 (1996)

  6. 6.

    D. Leibfried, D.M. Meekhof, B.E. King, C. Monroe, W.M. Itano, D.J. Wineland, Phys. Rev. Lett. 77, 4281 (1996)

  7. 7.

    D. Leibfried, R. Blatt, C. Monroe, D.J. Wineland, Rev. Mod. Phys. 75, 281 (2003)

  8. 8.

    R. Blatt, D. Wineland, Nature 453, 1008 (2008)

  9. 9.

    J.D. Jost, J.P. Home, J.M. Amini, D. Hanneke, R. Ozeri, C. Langer, J.J. Bollinger, D. Leibfried, D.J. Wineland, Nature 459, 683 (2009)

  10. 10.

    K.R. Brown, C. Ospelkaus, Y. Colombe, A.C. Wilson, D. Leibfried, D.J. Wineland, Nature 471, 197 (2011)

  11. 11.

    M. Harlander, R. Lechner, M. Brownnutt, R. Blatt, W. Hänsel, Nature 471, 200 (2011)

  12. 12.

    J.M. Raimond, M. Brune, S. Haroche, Rev. Mod. Phys. 73, 565 (2001)

  13. 13.

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

  14. 14.

    M. Brune, J. Bernu, C. Guerlin, S. Deleglise, C. Sayrin, S. Gleyzes, S. Kuhr, I. Dotsenko, J.M. Raimond, S. Haroche, Phys. Rev. Lett. 101, 240402 (2008)

  15. 15.

    A. Wallraff, D.I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S.M. Girvin, R.J. Schoelkopf, Nature 431, 162 (2004)

  16. 16.

    A. Blais, R.-S. Huang, A. Wallraff, S.M. Girvin, R.J. Schoelkopf, Phys. Rev. A 69, 062320 (2004)

  17. 17.

    A.A. Houck, D.I. Schuster, J.M. Gambetta, J.A. Schreier, B.R. Johnson, J.M. Chow, L. Frunzio, J. Majer, M.H. Devoret, S.M. Girvin, R.J. Schoelkopf, Nature 449, 328 (2007)

  18. 18.

    H. Wang, M. Hofheinz, M. Ansmann, R.C. Bialczak, E. Lucero, M. Neeley, A.D. O’Connell, D. Sank, J. Wenner, A.N. Cleland, J.M. Martinis, Phys. Rev. Lett. 101, 240401 (2008)

  19. 19.

    F. Deppe, M. Mariantoni, E.P. Menzel, A. Marx, S. Saito, K. Kakuyanagi, H. Tanaka, T. Meno, K. Semba, H. Takayanagi, E. Solano, R. Gross, Nat. Phys. 4, 686 (2008)

  20. 20.

    J.M. Fink, R. Bianchetti, M. Baur, M. Göppl, L. Steffen, S. Filipp, P.J. Leek, A. Blais, A. Wallraff, Phys. Rev. Lett. 103, 083601 (2009)

  21. 21.

    M. Hofheinz, H. Wang, M. Ansmann, R.C. Bialczak, E. Lucero, M. Neeley, A.D. O’Connell, D. Sank, J. Wenner, J.M. Martinis, A.N. Cleland, Nature 459, 546 (2009)

  22. 22.

    T. Niemczyk, F. Deppe, H. Huebl, E.P. Menzel, F. Hocke, M.J. Schwarz, J.J. Garcia-Ripoll, D. Zueco, T. Hmmer, E. Solano, A. Marx, R. Gross, Nat. Phys. 6, 772 (2010)

  23. 23.

    O. Astafiev, A.M. Zagoskin, A.A. Abdumalikov Jr., Yu. A. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, J.S. Tsai, Science 327, 840 (2010)

  24. 24.

    T. Tufarelli, M.S. Kim, S. Bose, Phys. Rev. A 83, 062120 (2011)

  25. 25.

    J.E. Mooij, T.P. Orlando, L. Levitov, L. Tian, C.H. van der Wal, S. Lloyd, Science 285, 1036 (1999)

  26. 26.

    J.M. Martinis, S. Nam, J. Aumentado, C. Urbina, Phys. Rev. Lett. 89, 117901 (2002)

  27. 27.

    D. Vion, A. Aassime, A. Cottet, P. Joyez, H. Pothier, C. Urbina, D. Esteve, M.H. Devoret, Science 296, 886 (2006)

  28. 28.

    R.C. Bialczak, M. Ansmann, M. Hofheinz, E. Lucero, M. Neeley, A.D. O’Connell, D. Sank, H. Wang, J. Wenner, M. Steffen, A.N. Cleland, J.M. Martinis, Nat. Phys. 6, 409 (2010)

  29. 29.

    S. Wallentowitz, W. Vogel, Phys. Rev. Lett. 75, 2932 (1995)

  30. 30.

    A.I. Lvovsky, M.G. Raymer, Rev. Mod. Phys. 81, 299 (2009)

  31. 31.

    X.-B. Wang, T. Hiroshima, A. Tomita, M. Hayashi, Phys. Rep. 448, 1 (2007)

  32. 32.

    L.G. Lutterbach, L. Davidovich, Phys. Rev. Lett. 78, 2547 (1997)

  33. 33.

    R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, C.F. Roos, Nature 463, 68 (2010)

  34. 34.

    K. Vogel, H. Risken, Phys. Rev. A 40, 2847 (1989)

  35. 35.

    D.T. Smithey, M. Beck, M.G. Raymer, A. Faridani, Phys. Rev. Lett. 70, 1244 (1993)

  36. 36.

    F. Zähringer, G. Kirchmair, R. Gerritsma, E. Solano, R. Blatt, C.F. Roos, Phys. Rev. Lett. 104, 100503 (2010)

  37. 37.

    J. Casanova, J.J. García-Ripoll, R. Gerritsma, C.F. Roos, E. Solano, Phys. Rev. A 82, 020101(R) (2010)

  38. 38.

    R. Gerritsma, B. Lanyon, G. Kirchmair, F. Zähringer, C. Hempel, J. Casanova, J.J. García-Ripoll, E. Solano, R. Blatt, C.F. Roos, Phys. Rev. Lett. 106, 060503 (2011)

  39. 39.

    E. Solano, G.S. Agarwal, H. Walther, Phys. Rev. Lett. 90, 027903 (2003)

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Correspondence to E. Solano.

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Casanova, J., López, C.E., García-Ripoll, J.J. et al. Quantum tomography in position and momentum space. Eur. Phys. J. D 66, 222 (2012). https://doi.org/10.1140/epjd/e2012-30016-6

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Keywords

  • Quantum Optics