Abstract

We use balanced homodyne detection to characterize light from a diode laser as it crosses the threshold. We measure the single-time second-order correlation function g(2), and also extract the photon number distribution. Just above the laser threshold, we find that the measured g(2) exceeds the prediction of the semiclassical single-mode laser model. From the reconstructed photon number distributions, we conclude that this excess is due to emission from nonlasing modes. For higher pumping current, the light noise increases due to a different mechanism, possibly mode competition or mode partition noise.

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  1. A. W. Smith and J. A. Armstrong, Phys. Rev. Lett. 16, 1169 (1966).
    [CrossRef]
  2. F. Arecchi, G. Rodari, and A. Sona, Phys. Lett. A 25, 59 (1967).
    [CrossRef]
  3. D. Meltzer, W. Davis, and L. Mandel, Appl. Phys. Lett. 17, 242 (1970).
    [CrossRef]
  4. E. Jakeman, C. J. Oliver, E. R. Pike, M. Lax, and M. Zwanziger, J. Phys. A 3, L52 (1970).
    [CrossRef]
  5. J. A. Abate, H. J. Kimble, and L. Mandel, Phys. Rev. A 14, 788 (1976).
    [CrossRef]
  6. W. E. Lamb, W. P. Schleich, M. O. Scully, and C. H. Townes, Rev. Mod. Phys. 71, S263 (1999).
    [CrossRef]
  7. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995), § 18.3.
  8. C. E. Wieman and L. Hollberg, Rev. Sci. Instrum. 62, 1 (1991).
    [CrossRef]
  9. D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett. 70, 1244 (1993).
    [CrossRef]
  10. R. J. Glauber, Phys. Rev. 130, 2529 (1963).
    [CrossRef]
  11. D. F. McAlister and M. G. Raymer, Phys. Rev. A 55, R1609 (1997).
    [CrossRef]
  12. M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, Phys. Rev. A 52, R924 (1995).
    [CrossRef]
  13. A. I. Lvovsky and M. G. Raymer, Rev. Mod. Phys. 81, 299 (2009).
    [CrossRef]
  14. P. J. Windpassinger, M. Kubasik, M. Koschorreck, A. Boisen, N. Kjærgaard, E. S. Polzik, and J. H. Müller, Meas. Sci. Technol. 20, 055301 (2009).
    [CrossRef]
  15. Y. Yamamoto, S. Saito, and T. Mukai, IEEE J. Quantum Electron. 19, 47 (1983).
    [CrossRef]
  16. W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals (Springer, 1999).
  17. G. Lachs, Phys. Rev. 138, B1012 (1965).
    [CrossRef]
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  21. N. B. Grosse, T. Symul, M. Stobinnska, T. C. Ralph, and P. K. Lam, Phys. Rev. Lett. 98, 153603 (2007).
    [CrossRef]

2009

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

P. J. Windpassinger, M. Kubasik, M. Koschorreck, A. Boisen, N. Kjærgaard, E. S. Polzik, and J. H. Müller, Meas. Sci. Technol. 20, 055301 (2009).
[CrossRef]

2007

N. B. Grosse, T. Symul, M. Stobinnska, T. C. Ralph, and P. K. Lam, Phys. Rev. Lett. 98, 153603 (2007).
[CrossRef]

1999

W. E. Lamb, W. P. Schleich, M. O. Scully, and C. H. Townes, Rev. Mod. Phys. 71, S263 (1999).
[CrossRef]

1998

1997

D. F. McAlister and M. G. Raymer, Phys. Rev. A 55, R1609 (1997).
[CrossRef]

1996

1995

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, Phys. Rev. A 52, R924 (1995).
[CrossRef]

1993

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

1992

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 46, 2757 (1992).
[CrossRef]

1991

C. E. Wieman and L. Hollberg, Rev. Sci. Instrum. 62, 1 (1991).
[CrossRef]

1983

Y. Yamamoto, S. Saito, and T. Mukai, IEEE J. Quantum Electron. 19, 47 (1983).
[CrossRef]

1976

J. A. Abate, H. J. Kimble, and L. Mandel, Phys. Rev. A 14, 788 (1976).
[CrossRef]

1970

D. Meltzer, W. Davis, and L. Mandel, Appl. Phys. Lett. 17, 242 (1970).
[CrossRef]

E. Jakeman, C. J. Oliver, E. R. Pike, M. Lax, and M. Zwanziger, J. Phys. A 3, L52 (1970).
[CrossRef]

1967

F. Arecchi, G. Rodari, and A. Sona, Phys. Lett. A 25, 59 (1967).
[CrossRef]

1966

A. W. Smith and J. A. Armstrong, Phys. Rev. Lett. 16, 1169 (1966).
[CrossRef]

1965

G. Lachs, Phys. Rev. 138, B1012 (1965).
[CrossRef]

1963

R. J. Glauber, Phys. Rev. 130, 2529 (1963).
[CrossRef]

Abate, J. A.

J. A. Abate, H. J. Kimble, and L. Mandel, Phys. Rev. A 14, 788 (1976).
[CrossRef]

Anderson, M. E.

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, Phys. Rev. A 52, R924 (1995).
[CrossRef]

Arecchi, F.

F. Arecchi, G. Rodari, and A. Sona, Phys. Lett. A 25, 59 (1967).
[CrossRef]

Armstrong, J. A.

A. W. Smith and J. A. Armstrong, Phys. Rev. Lett. 16, 1169 (1966).
[CrossRef]

Beck, M.

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

Boggavarapu, D.

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, Phys. Rev. A 52, R924 (1995).
[CrossRef]

Boisen, A.

P. J. Windpassinger, M. Kubasik, M. Koschorreck, A. Boisen, N. Kjærgaard, E. S. Polzik, and J. H. Müller, Meas. Sci. Technol. 20, 055301 (2009).
[CrossRef]

Chang, T.

Chow, W. W.

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals (Springer, 1999).

Craig, R.

Davis, W.

D. Meltzer, W. Davis, and L. Mandel, Appl. Phys. Lett. 17, 242 (1970).
[CrossRef]

Faridani, A.

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

Glauber, R. J.

R. J. Glauber, Phys. Rev. 130, 2529 (1963).
[CrossRef]

Grangier, P.

Grosse, N. B.

N. B. Grosse, T. Symul, M. Stobinnska, T. C. Ralph, and P. K. Lam, Phys. Rev. Lett. 98, 153603 (2007).
[CrossRef]

Hollberg, L.

C. E. Wieman and L. Hollberg, Rev. Sci. Instrum. 62, 1 (1991).
[CrossRef]

Inoue, S.

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 46, 2757 (1992).
[CrossRef]

Jakeman, E.

E. Jakeman, C. J. Oliver, E. R. Pike, M. Lax, and M. Zwanziger, J. Phys. A 3, L52 (1970).
[CrossRef]

Kilper, D. C.

Kimble, H. J.

J. A. Abate, H. J. Kimble, and L. Mandel, Phys. Rev. A 14, 788 (1976).
[CrossRef]

Kjærgaard, N.

P. J. Windpassinger, M. Kubasik, M. Koschorreck, A. Boisen, N. Kjærgaard, E. S. Polzik, and J. H. Müller, Meas. Sci. Technol. 20, 055301 (2009).
[CrossRef]

Koch, S. W.

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals (Springer, 1999).

Koschorreck, M.

P. J. Windpassinger, M. Kubasik, M. Koschorreck, A. Boisen, N. Kjærgaard, E. S. Polzik, and J. H. Müller, Meas. Sci. Technol. 20, 055301 (2009).
[CrossRef]

Kubasik, M.

P. J. Windpassinger, M. Kubasik, M. Koschorreck, A. Boisen, N. Kjærgaard, E. S. Polzik, and J. H. Müller, Meas. Sci. Technol. 20, 055301 (2009).
[CrossRef]

Lachs, G.

G. Lachs, Phys. Rev. 138, B1012 (1965).
[CrossRef]

Lam, P. K.

N. B. Grosse, T. Symul, M. Stobinnska, T. C. Ralph, and P. K. Lam, Phys. Rev. Lett. 98, 153603 (2007).
[CrossRef]

Lamb, W. E.

W. E. Lamb, W. P. Schleich, M. O. Scully, and C. H. Townes, Rev. Mod. Phys. 71, S263 (1999).
[CrossRef]

Lax, M.

E. Jakeman, C. J. Oliver, E. R. Pike, M. Lax, and M. Zwanziger, J. Phys. A 3, L52 (1970).
[CrossRef]

Lvovsky, A. I.

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

Machida, S.

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 46, 2757 (1992).
[CrossRef]

Mandel, L.

J. A. Abate, H. J. Kimble, and L. Mandel, Phys. Rev. A 14, 788 (1976).
[CrossRef]

D. Meltzer, W. Davis, and L. Mandel, Appl. Phys. Lett. 17, 242 (1970).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995), § 18.3.

McAlister, D. F.

D. F. McAlister and M. G. Raymer, Phys. Rev. A 55, R1609 (1997).
[CrossRef]

Meltzer, D.

D. Meltzer, W. Davis, and L. Mandel, Appl. Phys. Lett. 17, 242 (1970).
[CrossRef]

Mukai, T.

Y. Yamamoto, S. Saito, and T. Mukai, IEEE J. Quantum Electron. 19, 47 (1983).
[CrossRef]

Müller, J. H.

P. J. Windpassinger, M. Kubasik, M. Koschorreck, A. Boisen, N. Kjærgaard, E. S. Polzik, and J. H. Müller, Meas. Sci. Technol. 20, 055301 (2009).
[CrossRef]

Munroe, M.

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, Phys. Rev. A 52, R924 (1995).
[CrossRef]

Ohzu, H.

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 46, 2757 (1992).
[CrossRef]

Oliver, C. J.

E. Jakeman, C. J. Oliver, E. R. Pike, M. Lax, and M. Zwanziger, J. Phys. A 3, L52 (1970).
[CrossRef]

Pike, E. R.

E. Jakeman, C. J. Oliver, E. R. Pike, M. Lax, and M. Zwanziger, J. Phys. A 3, L52 (1970).
[CrossRef]

Poizat, J.-P.

Polzik, E. S.

P. J. Windpassinger, M. Kubasik, M. Koschorreck, A. Boisen, N. Kjærgaard, E. S. Polzik, and J. H. Müller, Meas. Sci. Technol. 20, 055301 (2009).
[CrossRef]

Ralph, T. C.

N. B. Grosse, T. Symul, M. Stobinnska, T. C. Ralph, and P. K. Lam, Phys. Rev. Lett. 98, 153603 (2007).
[CrossRef]

Raymer, M. G.

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

D. F. McAlister and M. G. Raymer, Phys. Rev. A 55, R1609 (1997).
[CrossRef]

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, Phys. Rev. A 52, R924 (1995).
[CrossRef]

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

Ripoll, O.

Rodari, G.

F. Arecchi, G. Rodari, and A. Sona, Phys. Lett. A 25, 59 (1967).
[CrossRef]

Saito, S.

Y. Yamamoto, S. Saito, and T. Mukai, IEEE J. Quantum Electron. 19, 47 (1983).
[CrossRef]

Schleich, W. P.

W. E. Lamb, W. P. Schleich, M. O. Scully, and C. H. Townes, Rev. Mod. Phys. 71, S263 (1999).
[CrossRef]

Scifres, D. R.

Scully, M. O.

W. E. Lamb, W. P. Schleich, M. O. Scully, and C. H. Townes, Rev. Mod. Phys. 71, S263 (1999).
[CrossRef]

Smith, A. W.

A. W. Smith and J. A. Armstrong, Phys. Rev. Lett. 16, 1169 (1966).
[CrossRef]

Smithey, D. T.

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

Sona, A.

F. Arecchi, G. Rodari, and A. Sona, Phys. Lett. A 25, 59 (1967).
[CrossRef]

Steel, D. G.

Stobinnska, M.

N. B. Grosse, T. Symul, M. Stobinnska, T. C. Ralph, and P. K. Lam, Phys. Rev. Lett. 98, 153603 (2007).
[CrossRef]

Symul, T.

N. B. Grosse, T. Symul, M. Stobinnska, T. C. Ralph, and P. K. Lam, Phys. Rev. Lett. 98, 153603 (2007).
[CrossRef]

Townes, C. H.

W. E. Lamb, W. P. Schleich, M. O. Scully, and C. H. Townes, Rev. Mod. Phys. 71, S263 (1999).
[CrossRef]

Wieman, C. E.

C. E. Wieman and L. Hollberg, Rev. Sci. Instrum. 62, 1 (1991).
[CrossRef]

Windpassinger, P. J.

P. J. Windpassinger, M. Kubasik, M. Koschorreck, A. Boisen, N. Kjærgaard, E. S. Polzik, and J. H. Müller, Meas. Sci. Technol. 20, 055301 (2009).
[CrossRef]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995), § 18.3.

Yamamoto, Y.

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 46, 2757 (1992).
[CrossRef]

Y. Yamamoto, S. Saito, and T. Mukai, IEEE J. Quantum Electron. 19, 47 (1983).
[CrossRef]

Zwanziger, M.

E. Jakeman, C. J. Oliver, E. R. Pike, M. Lax, and M. Zwanziger, J. Phys. A 3, L52 (1970).
[CrossRef]

Appl. Phys. Lett.

D. Meltzer, W. Davis, and L. Mandel, Appl. Phys. Lett. 17, 242 (1970).
[CrossRef]

IEEE J. Quantum Electron.

Y. Yamamoto, S. Saito, and T. Mukai, IEEE J. Quantum Electron. 19, 47 (1983).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. A

E. Jakeman, C. J. Oliver, E. R. Pike, M. Lax, and M. Zwanziger, J. Phys. A 3, L52 (1970).
[CrossRef]

Meas. Sci. Technol.

P. J. Windpassinger, M. Kubasik, M. Koschorreck, A. Boisen, N. Kjærgaard, E. S. Polzik, and J. H. Müller, Meas. Sci. Technol. 20, 055301 (2009).
[CrossRef]

Opt. Lett.

Phys. Lett. A

F. Arecchi, G. Rodari, and A. Sona, Phys. Lett. A 25, 59 (1967).
[CrossRef]

Phys. Rev.

G. Lachs, Phys. Rev. 138, B1012 (1965).
[CrossRef]

R. J. Glauber, Phys. Rev. 130, 2529 (1963).
[CrossRef]

Phys. Rev. A

D. F. McAlister and M. G. Raymer, Phys. Rev. A 55, R1609 (1997).
[CrossRef]

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, Phys. Rev. A 52, R924 (1995).
[CrossRef]

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 46, 2757 (1992).
[CrossRef]

J. A. Abate, H. J. Kimble, and L. Mandel, Phys. Rev. A 14, 788 (1976).
[CrossRef]

Phys. Rev. Lett.

A. W. Smith and J. A. Armstrong, Phys. Rev. Lett. 16, 1169 (1966).
[CrossRef]

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

N. B. Grosse, T. Symul, M. Stobinnska, T. C. Ralph, and P. K. Lam, Phys. Rev. Lett. 98, 153603 (2007).
[CrossRef]

Rev. Mod. Phys.

W. E. Lamb, W. P. Schleich, M. O. Scully, and C. H. Townes, Rev. Mod. Phys. 71, S263 (1999).
[CrossRef]

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

Rev. Sci. Instrum.

C. E. Wieman and L. Hollberg, Rev. Sci. Instrum. 62, 1 (1991).
[CrossRef]

Other

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995), § 18.3.

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals (Springer, 1999).

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Figures (3)

Fig. 1.
Fig. 1.

Schematic of the homodyne detection setup.

Fig. 2.
Fig. 2.

Top: circles, measured source intensity from Eq. (2), in units of (number of photons)/(LO pulse), plotted as a function of the drive current. Dashed curve, measured optical power. Bottom: measured second-order correlation function g(2) (g(2)1 is plotted). The dashed curve is the prediction of the semiclassical single-mode laser model. Circles show the points for which we reconstruct the photon number distribution in Fig. 3.

Fig. 3.
Fig. 3.

Extracted photon number distributions for four different values of the drive current (marked with large circles in Fig. 2). We compare the data to three different states of equal intensity. Continuous line, mixture of a coherent and thermal state with the same g(2); dashed curve, prediction of the semiclassical laser model; dotted curve, coherent state.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

Q^=NLO(eiϕa^S+eiϕa^S),
a^Sa^S=12(Q^2NLO1),
a^Sa^Sa^Sa^S=Q^46NLO22a^Sa^S12.
g(2)(t,t)g(2)=a^Sa^Sa^Sa^Sa^Sa^S2

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