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Homodyne versus photon-counting quantum trajectories for dissipative Kerr resonators with two-photon driving


We investigate two different kinds of quantum trajectories for a nonlinear photon resonator subject to two-photon pumping, a configuration recently studied for the generation of photonic Schrödinger cat states. In the absence of feedback control and in the strong-driving limit, the steady-state density matrix is a statistical mixture of two states with equal weight. While along a single photon-counting trajectory the systems intermittently switches between an odd and an even cat state, we show that upon homodyne detection the situation is different. Indeed, homodyne quantum trajectories reveal switches between coherent states of opposite phase.

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  1. 1.

    I. Bloch, Nature Physics 1, 23 (2005)

    ADS  Article  Google Scholar 

  2. 2.

    I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)

    ADS  Article  Google Scholar 

  3. 3.

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

    ADS  Article  Google Scholar 

  4. 4.

    R. Blatt, C.F. Roos, Nat. Phys. 8, 277 (2012)

    Article  Google Scholar 

  5. 5.

    C. Weisbuch, M. Nishioka, A. Ishikawa, Y. Arakawa, Phys. Rev. Lett. 69, 3314 (1992)

    ADS  Article  Google Scholar 

  6. 6.

    B. Deveaud, The Physics of Semiconductor Microcavities (Wiley, 2007)

  7. 7.

    R.J. Schoelkopf, S.M. Girvin, Nature 451, 664 (2008)

    ADS  Article  Google Scholar 

  8. 8.

    J.Q. You, F. Nori, Nature 474, 589 (2011)

    ADS  Article  Google Scholar 

  9. 9.

    I. Carusotto, C. Ciuti, Rev. Mod. Phys. 85, 299 (2013)

    ADS  Article  Google Scholar 

  10. 10.

    Z. Leghtas, S. Touzard, I.M. Pop, A. Kou, B. Vlastakis, A. Petrenko, K.M. Sliwa, A. Narla, S. Shankar, M.J. Hatridge, M. Reagor, L. Frunzio, R.J. Schoelkopf, M. Mirrahimi, M.H. Devoret, Science 347, 853 (2015)

    ADS  Article  Google Scholar 

  11. 11.

    F. Minganti, N. Bartolo, J. Lolli, W. Casteels, C. Ciuti, Sci. Rep. 6, 26987 (2016)

    ADS  Article  Google Scholar 

  12. 12.

    J. Dalibard, Y. Castin, K. Mølmer, Phys. Rev. Lett. 68, 580 (1992)

    ADS  Article  Google Scholar 

  13. 13.

    H.J. Carmichael, Phys. Rev. Lett. 70, 2273 (1993)

    ADS  Article  Google Scholar 

  14. 14.

    K. Mølmer, Y. Castin, J. Dalibard, J. Opt. Soc. Am. B 10, 524 (1993)

    ADS  Article  Google Scholar 

  15. 15.

    M.B. Plenio, P.L. Knight, Rev. Mod. Phys. 70, 101 (1998)

    ADS  Article  Google Scholar 

  16. 16.

    S. Haroche, J. Raimond, Exploring the Quantum: Atoms, Cavities, and Photons (OUP Oxford, 2006)

  17. 17.

    H. Carmichael, Statistical Methods in Quantum Optics 1 (Springer-Verlag, 1999)

  18. 18.

    D.F. Walls, G.J. Milburn, Quantum Optics (Springer, 2008)

  19. 19.

    G. Kryuchkyan, K. Kheruntsyan, Opt. Commun. 127, 230 (1996)

    ADS  Article  Google Scholar 

  20. 20.

    C.H. Meaney, H. Nha, T. Duty, G.J. Milburn, Eur. Phys. J. Quant. Tech. 1, 1 (2014)

    Google Scholar 

  21. 21.

    M. Elliott, E. Ginossar, Phys. Rev. A 94, 043840 (2016)

    ADS  Article  Google Scholar 

  22. 22.

    N. Bartolo, F. Minganti, W. Casteels, C. Ciuti, Phys. Rev. A 94, 033841 (2016)

    ADS  Article  Google Scholar 

  23. 23.

    H.M. Wiseman, G.J. Milburn, Quantum Measurement and Control (Cambridge University Press, 2009)

  24. 24.

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

    ADS  Article  Google Scholar 

  25. 25.

    A. Zavatta, S. Viciani, M. Bellini, Phys. Rev. A 70, 053821 (2004)

    ADS  Article  Google Scholar 

  26. 26.

    P. Campagne-Ibarcq, P. Six, L. Bretheau, A. Sarlette, M. Mirrahimi, P. Rouchon, B. Huard, Phys. Rev. X 6, 011002 (2016)

    Google Scholar 

  27. 27.

    P.D. Drummond, D.F. Walls, J. Phys. A: Math. Gen. 13, 725 (1980)

    ADS  Article  Google Scholar 

  28. 28.

    T.C. Ralph, A. Gilchrist, G.J. Milburn, W.J. Munro, S. Glancy, Phys. Rev. A 68, 042319 (2003)

    ADS  Article  Google Scholar 

  29. 29.

    A. Gilchrist, K. Nemoto, W.J. Munro, T.C. Ralph, S. Glancy, S.L. Braunstein, G.J. Milburn, J. Opt. B: Quantum Semiclass. Opt. 6, (2004) S828

    ADS  Article  Google Scholar 

  30. 30.

    M. Mirrahimi, Z. Leghtas, V.V. Albert, S. Touzard, R.J. Schoelkopf, L. Jiang, M.H. Devoret, New J. Phys. 16, 045014 (2014)

    ADS  Article  Google Scholar 

  31. 31.

    S. Puri, A. Blais, arXiv:1605.09408 (2016)

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Correspondence to Nicola Bartolo, Fabrizio Minganti or Cristiano Ciuti.

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Bartolo, N., Minganti, F., Lolli, J. et al. Homodyne versus photon-counting quantum trajectories for dissipative Kerr resonators with two-photon driving. Eur. Phys. J. Spec. Top. 226, 2705–2713 (2017).

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