Abstract

We theoretically propose a precise way to measure the coupling rate in an optomechanical system based on radiation-pressure-induced normal mode splitting. This all-optical method is effective in both weak and strong coupling regions. Simultaneously the vibrational frequency of the mechanical mode can also be detected easily in the reflected probe spectrum. The results are much useful for the extensive applications in optomechanical systems.

© 2010 Optical Society of America

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  1. T. J. Kippenberg and K. J. Vahala, Science 321, 1172 (2008).
    [CrossRef] [PubMed]
  2. T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, Phys. Rev. Lett. 95, 033901 (2005).
    [CrossRef] [PubMed]
  3. S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
    [CrossRef] [PubMed]
  4. A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
    [CrossRef]
  5. J. M. Ward, Y. Wu, V. G. Minogin, and S. Nic Chormaic, Phys. Rev. A 79, 053839 (2009).
    [CrossRef]
  6. C. H. Metzger and K. Karrai, Nature 432, 1002 (2004).
    [CrossRef] [PubMed]
  7. O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, Nature 444, 71 (2006).
    [CrossRef] [PubMed]
  8. J. D. Teufel, J. W. Harlow, C. A. Regal, and K. W. Lehnert, Phys. Rev. Lett. 101, 197203 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  10. J. M. Dobrindt, I. Wilson-Rae, and T. J. Kippenberg, Phys. Rev. Lett. 101, 263602 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. S. Mancini and P. Tombesi, Phys. Rev. A 49, 4055 (1994).
    [CrossRef] [PubMed]
  13. S. Bose, K. Jacobs, and P. L. Knight, Phys. Rev. A 56, 4175 (1997).
    [CrossRef]
  14. M. Bhattacharya, P. L. Giscard, and P. Meystre, Phys. Rev. A 77, 030303 (2008).
    [CrossRef]
  15. M. J. Hartmann and M. B. Plenio, Phys. Rev. Lett. 101, 200503 (2008).
    [CrossRef] [PubMed]
  16. C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, Phys. Rev. A 77, 033804 (2008).
    [CrossRef]
  17. V. Giovannetti and D. Vitali, Phys. Rev. A 63, 023812 (2001).
    [CrossRef]
  18. M. Pinard, Y. Hadjar, and A. Heidmann, Eur. Phys. J. D 7, 107 (1999).
  19. G. S. Agarwal and R. W. Boyd, Phys. Rev. A 60, R2681 (1999).
    [CrossRef]
  20. B. I. Greene, J. F. Mueller, J. Orenstein, D. H. Rapkine, S. Schmitt-Rink, and M. Thakur, Phys. Rev. Lett. 61, 325 (1988).
    [CrossRef] [PubMed]
  21. J. F. Lam, S. R. Forrest, and G. L. Tangonan, Phys. Rev. Lett. 66, 1614 (1991).
    [CrossRef] [PubMed]
  22. R. W. Boyd, Nonlinear Optics (Academic, 2008).
  23. D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, 1998), p. 124.
  24. R. J. Thompson, G. Rempe, and H. J. Kimble, Phys. Rev. Lett. 68, 1132 (1992).
    [CrossRef] [PubMed]
  25. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
    [CrossRef]

2009 (2)

J. M. Ward, Y. Wu, V. G. Minogin, and S. Nic Chormaic, Phys. Rev. A 79, 053839 (2009).
[CrossRef]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, Nature 460, 724 (2009).
[CrossRef] [PubMed]

2008 (7)

M. Bhattacharya, P. L. Giscard, and P. Meystre, Phys. Rev. A 77, 030303 (2008).
[CrossRef]

M. J. Hartmann and M. B. Plenio, Phys. Rev. Lett. 101, 200503 (2008).
[CrossRef] [PubMed]

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, Phys. Rev. A 77, 033804 (2008).
[CrossRef]

J. D. Teufel, J. W. Harlow, C. A. Regal, and K. W. Lehnert, Phys. Rev. Lett. 101, 197203 (2008).
[CrossRef] [PubMed]

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, Nat. Phys. 4, 415 (2008).
[CrossRef]

J. M. Dobrindt, I. Wilson-Rae, and T. J. Kippenberg, Phys. Rev. Lett. 101, 263602 (2008).
[CrossRef] [PubMed]

T. J. Kippenberg and K. J. Vahala, Science 321, 1172 (2008).
[CrossRef] [PubMed]

2006 (3)

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, Nature 444, 71 (2006).
[CrossRef] [PubMed]

2005 (2)

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

2004 (1)

C. H. Metzger and K. Karrai, Nature 432, 1002 (2004).
[CrossRef] [PubMed]

2001 (1)

V. Giovannetti and D. Vitali, Phys. Rev. A 63, 023812 (2001).
[CrossRef]

1999 (2)

M. Pinard, Y. Hadjar, and A. Heidmann, Eur. Phys. J. D 7, 107 (1999).

G. S. Agarwal and R. W. Boyd, Phys. Rev. A 60, R2681 (1999).
[CrossRef]

1997 (1)

S. Bose, K. Jacobs, and P. L. Knight, Phys. Rev. A 56, 4175 (1997).
[CrossRef]

1994 (1)

S. Mancini and P. Tombesi, Phys. Rev. A 49, 4055 (1994).
[CrossRef] [PubMed]

1992 (1)

R. J. Thompson, G. Rempe, and H. J. Kimble, Phys. Rev. Lett. 68, 1132 (1992).
[CrossRef] [PubMed]

1991 (1)

J. F. Lam, S. R. Forrest, and G. L. Tangonan, Phys. Rev. Lett. 66, 1614 (1991).
[CrossRef] [PubMed]

1988 (1)

B. I. Greene, J. F. Mueller, J. Orenstein, D. H. Rapkine, S. Schmitt-Rink, and M. Thakur, Phys. Rev. Lett. 61, 325 (1988).
[CrossRef] [PubMed]

Agarwal, G. S.

G. S. Agarwal and R. W. Boyd, Phys. Rev. A 60, R2681 (1999).
[CrossRef]

Anetsberger, G.

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, Nat. Phys. 4, 415 (2008).
[CrossRef]

Arcizet, O.

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, Nat. Phys. 4, 415 (2008).
[CrossRef]

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, Nature 444, 71 (2006).
[CrossRef] [PubMed]

Aspelmeyer, M.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, Nature 460, 724 (2009).
[CrossRef] [PubMed]

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, Phys. Rev. A 77, 033804 (2008).
[CrossRef]

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Bäuerle, D.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Bhattacharya, M.

M. Bhattacharya, P. L. Giscard, and P. Meystre, Phys. Rev. A 77, 030303 (2008).
[CrossRef]

Blaser, F.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Böhm, H. R.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Bose, S.

S. Bose, K. Jacobs, and P. L. Knight, Phys. Rev. A 56, 4175 (1997).
[CrossRef]

Boyd, R. W.

G. S. Agarwal and R. W. Boyd, Phys. Rev. A 60, R2681 (1999).
[CrossRef]

R. W. Boyd, Nonlinear Optics (Academic, 2008).

Briant, T.

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, Nature 444, 71 (2006).
[CrossRef] [PubMed]

Carmon, T.

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

Cohadon, P. F.

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, Nature 444, 71 (2006).
[CrossRef] [PubMed]

Del'Haye, P.

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

Dobrindt, J. M.

J. M. Dobrindt, I. Wilson-Rae, and T. J. Kippenberg, Phys. Rev. Lett. 101, 263602 (2008).
[CrossRef] [PubMed]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Forrest, S. R.

J. F. Lam, S. R. Forrest, and G. L. Tangonan, Phys. Rev. Lett. 66, 1614 (1991).
[CrossRef] [PubMed]

Genes, C.

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, Phys. Rev. A 77, 033804 (2008).
[CrossRef]

Gigan, S.

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, Phys. Rev. A 77, 033804 (2008).
[CrossRef]

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Giovannetti, V.

V. Giovannetti and D. Vitali, Phys. Rev. A 63, 023812 (2001).
[CrossRef]

Giscard, P. L.

M. Bhattacharya, P. L. Giscard, and P. Meystre, Phys. Rev. A 77, 030303 (2008).
[CrossRef]

Greene, B. I.

B. I. Greene, J. F. Mueller, J. Orenstein, D. H. Rapkine, S. Schmitt-Rink, and M. Thakur, Phys. Rev. Lett. 61, 325 (1988).
[CrossRef] [PubMed]

Gröblacher, S.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, Nature 460, 724 (2009).
[CrossRef] [PubMed]

Hadjar, Y.

M. Pinard, Y. Hadjar, and A. Heidmann, Eur. Phys. J. D 7, 107 (1999).

Hammerer, K.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, Nature 460, 724 (2009).
[CrossRef] [PubMed]

Harlow, J. W.

J. D. Teufel, J. W. Harlow, C. A. Regal, and K. W. Lehnert, Phys. Rev. Lett. 101, 197203 (2008).
[CrossRef] [PubMed]

Hartmann, M. J.

M. J. Hartmann and M. B. Plenio, Phys. Rev. Lett. 101, 200503 (2008).
[CrossRef] [PubMed]

Heidmann, A.

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, Nature 444, 71 (2006).
[CrossRef] [PubMed]

M. Pinard, Y. Hadjar, and A. Heidmann, Eur. Phys. J. D 7, 107 (1999).

Hertzberg, J. B.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Jacobs, K.

S. Bose, K. Jacobs, and P. L. Knight, Phys. Rev. A 56, 4175 (1997).
[CrossRef]

Karrai, K.

C. H. Metzger and K. Karrai, Nature 432, 1002 (2004).
[CrossRef] [PubMed]

Kimble, H. J.

R. J. Thompson, G. Rempe, and H. J. Kimble, Phys. Rev. Lett. 68, 1132 (1992).
[CrossRef] [PubMed]

Kippenberg, T. J.

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, Nat. Phys. 4, 415 (2008).
[CrossRef]

J. M. Dobrindt, I. Wilson-Rae, and T. J. Kippenberg, Phys. Rev. Lett. 101, 263602 (2008).
[CrossRef] [PubMed]

T. J. Kippenberg and K. J. Vahala, Science 321, 1172 (2008).
[CrossRef] [PubMed]

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

Knight, P. L.

S. Bose, K. Jacobs, and P. L. Knight, Phys. Rev. A 56, 4175 (1997).
[CrossRef]

Lam, J. F.

J. F. Lam, S. R. Forrest, and G. L. Tangonan, Phys. Rev. Lett. 66, 1614 (1991).
[CrossRef] [PubMed]

Langer, G.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Lehnert, K. W.

J. D. Teufel, J. W. Harlow, C. A. Regal, and K. W. Lehnert, Phys. Rev. Lett. 101, 197203 (2008).
[CrossRef] [PubMed]

Mancini, S.

S. Mancini and P. Tombesi, Phys. Rev. A 49, 4055 (1994).
[CrossRef] [PubMed]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Metzger, C. H.

C. H. Metzger and K. Karrai, Nature 432, 1002 (2004).
[CrossRef] [PubMed]

Meystre, P.

M. Bhattacharya, P. L. Giscard, and P. Meystre, Phys. Rev. A 77, 030303 (2008).
[CrossRef]

Milburn, G. J.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, 1998), p. 124.

Minogin, V. G.

J. M. Ward, Y. Wu, V. G. Minogin, and S. Nic Chormaic, Phys. Rev. A 79, 053839 (2009).
[CrossRef]

Mueller, J. F.

B. I. Greene, J. F. Mueller, J. Orenstein, D. H. Rapkine, S. Schmitt-Rink, and M. Thakur, Phys. Rev. Lett. 61, 325 (1988).
[CrossRef] [PubMed]

Nic Chormaic, S.

J. M. Ward, Y. Wu, V. G. Minogin, and S. Nic Chormaic, Phys. Rev. A 79, 053839 (2009).
[CrossRef]

Nooshi, N.

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

Orenstein, J.

B. I. Greene, J. F. Mueller, J. Orenstein, D. H. Rapkine, S. Schmitt-Rink, and M. Thakur, Phys. Rev. Lett. 61, 325 (1988).
[CrossRef] [PubMed]

Paternostro, M.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Pinard, M.

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, Nature 444, 71 (2006).
[CrossRef] [PubMed]

M. Pinard, Y. Hadjar, and A. Heidmann, Eur. Phys. J. D 7, 107 (1999).

Plenio, M. B.

M. J. Hartmann and M. B. Plenio, Phys. Rev. Lett. 101, 200503 (2008).
[CrossRef] [PubMed]

Rapkine, D. H.

B. I. Greene, J. F. Mueller, J. Orenstein, D. H. Rapkine, S. Schmitt-Rink, and M. Thakur, Phys. Rev. Lett. 61, 325 (1988).
[CrossRef] [PubMed]

Regal, C. A.

J. D. Teufel, J. W. Harlow, C. A. Regal, and K. W. Lehnert, Phys. Rev. Lett. 101, 197203 (2008).
[CrossRef] [PubMed]

Rempe, G.

R. J. Thompson, G. Rempe, and H. J. Kimble, Phys. Rev. Lett. 68, 1132 (1992).
[CrossRef] [PubMed]

Rivière, R.

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, Nat. Phys. 4, 415 (2008).
[CrossRef]

Rokhsari, H.

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

Scherer, A.

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

Schliesser, A.

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, Nat. Phys. 4, 415 (2008).
[CrossRef]

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

Schmitt-Rink, S.

B. I. Greene, J. F. Mueller, J. Orenstein, D. H. Rapkine, S. Schmitt-Rink, and M. Thakur, Phys. Rev. Lett. 61, 325 (1988).
[CrossRef] [PubMed]

Schwab, K. C.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Tangonan, G. L.

J. F. Lam, S. R. Forrest, and G. L. Tangonan, Phys. Rev. Lett. 66, 1614 (1991).
[CrossRef] [PubMed]

Teufel, J. D.

J. D. Teufel, J. W. Harlow, C. A. Regal, and K. W. Lehnert, Phys. Rev. Lett. 101, 197203 (2008).
[CrossRef] [PubMed]

Thakur, M.

B. I. Greene, J. F. Mueller, J. Orenstein, D. H. Rapkine, S. Schmitt-Rink, and M. Thakur, Phys. Rev. Lett. 61, 325 (1988).
[CrossRef] [PubMed]

Thompson, R. J.

R. J. Thompson, G. Rempe, and H. J. Kimble, Phys. Rev. Lett. 68, 1132 (1992).
[CrossRef] [PubMed]

Tombesi, P.

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, Phys. Rev. A 77, 033804 (2008).
[CrossRef]

S. Mancini and P. Tombesi, Phys. Rev. A 49, 4055 (1994).
[CrossRef] [PubMed]

Vahala, K. J.

T. J. Kippenberg and K. J. Vahala, Science 321, 1172 (2008).
[CrossRef] [PubMed]

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

Vanner, M. R.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, Nature 460, 724 (2009).
[CrossRef] [PubMed]

Vitali, D.

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, Phys. Rev. A 77, 033804 (2008).
[CrossRef]

V. Giovannetti and D. Vitali, Phys. Rev. A 63, 023812 (2001).
[CrossRef]

Walls, D. F.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, 1998), p. 124.

Ward, J. M.

J. M. Ward, Y. Wu, V. G. Minogin, and S. Nic Chormaic, Phys. Rev. A 79, 053839 (2009).
[CrossRef]

Wilson-Rae, I.

J. M. Dobrindt, I. Wilson-Rae, and T. J. Kippenberg, Phys. Rev. Lett. 101, 263602 (2008).
[CrossRef] [PubMed]

Wu, Y.

J. M. Ward, Y. Wu, V. G. Minogin, and S. Nic Chormaic, Phys. Rev. A 79, 053839 (2009).
[CrossRef]

Zeilinger, A.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Eur. Phys. J. D (1)

M. Pinard, Y. Hadjar, and A. Heidmann, Eur. Phys. J. D 7, 107 (1999).

Nat. Phys. (1)

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, Nat. Phys. 4, 415 (2008).
[CrossRef]

Nature (4)

C. H. Metzger and K. Karrai, Nature 432, 1002 (2004).
[CrossRef] [PubMed]

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, Nature 444, 71 (2006).
[CrossRef] [PubMed]

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, Nature 460, 724 (2009).
[CrossRef] [PubMed]

Phys. Rev. A (7)

S. Mancini and P. Tombesi, Phys. Rev. A 49, 4055 (1994).
[CrossRef] [PubMed]

S. Bose, K. Jacobs, and P. L. Knight, Phys. Rev. A 56, 4175 (1997).
[CrossRef]

M. Bhattacharya, P. L. Giscard, and P. Meystre, Phys. Rev. A 77, 030303 (2008).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of a Fabry–Perot cavity with a movable mirror in the presence of a strong driving field and a weak probe field.

Fig. 2
Fig. 2

(a) The plot of Re ( a out + ) as a function of probe-cavity detuning Δ p r = ω p r ω c with G 0 = 0 (solid curve), G 0 = 0.9   MHz (dashed curve), G 0 = 1.2   MHz (dotted curve), and G 0 = 1.5   MHz (dash-dotted curve). (b) Peak-splitting as a function of coupling rate. (c) Energy level diagram of the optomechanical system, where | N and | n denote the number states of mechanical mode and cavity photon, respectively. Other parameter values are E p u = 5   MHz , κ = 2 π × 215   kHz , Δ p u = ω m = 10   MHz , and γ m = 2 π × 140   Hz .

Fig. 3
Fig. 3

The plot of Re ( a out + ) as a function of probe–pump detuning δ with different ω m , Δ p u , and G 0 . Other parameter values are E p u = 1   MHz , κ = 2 π × 215   kHz , and γ m = 2 π × 140   Hz .

Equations (5)

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H = Δ p u a a + 1 2 ω m ( p 2 + q 2 ) G 0 a a q + i E p u ( a a ) + i E p r ( a e i δ t a e i δ t ) .
d a d t = ( i Δ p u + κ ) a + i G 0 a q + E p u + E p r e i δ t ,
d 2 q d t 2 + γ m d q d t + ω m 2 q = ω m G 0 a a ,
a + = E p r [ i δ + ( i Δ p u + κ ) + C ( κ 2 i δ ) 2 + ( Δ p u + i C ) 2 D ] ,
a out ( t ) = a out 0 + a out + e i δ t + a out e i δ t = 2 κ ( a 0 + a + e i δ t + a e i δ t ) .

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