Skip to main content

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

Abstract

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.

This is a preview of subscription content, access via your institution.

References

  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)

Download references

Author information

Affiliations

Authors

Corresponding authors

Correspondence to Nicola Bartolo, Fabrizio Minganti or Cristiano Ciuti.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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). https://doi.org/10.1140/epjst/e2016-60385-8

Download citation