Abstract

We demonstrate line-shape measurement of an extremely weak amplitude-fluctuating light source by using photon-counting-based second-order correlation spectroscopy combined with the heterodyne technique. The amplitude fluctuation of a finite bandwidth introduces a low-lying spectral structure in the line shape, and thus its effect can be isolated from that of the phase fluctuation. Our technique provides extreme sensitivity suited for single-atom-level applications.

© 2006 Optical Society of America

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  1. A. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958).
    [CrossRef]
  2. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).
  3. D. Meschede, H. Walther, and G. Müller, Phys. Rev. Lett. 54, 551 (1985).
    [CrossRef] [PubMed]
  4. K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 73, 3375 (1994).
    [CrossRef] [PubMed]
  5. J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, Nature 425, 268 (2003).
    [CrossRef] [PubMed]
  6. A. Kuhn, M. Hennrich, and G. Rempe, Phys. Rev. Lett. 89, 067901 (2002).
    [CrossRef] [PubMed]
  7. J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, Science 303, 1992 (2004).
    [CrossRef] [PubMed]
  8. T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
    [CrossRef]
  9. J. T. Höffges, H. W. Baldauf, W. Lange, and H. Walther, J. Mod. Opt. 44, 1999 (1997).
    [CrossRef]
  10. E. R. Pike, J. Phys. D 5, L23 (1972).
    [CrossRef]
  11. D. Byrne and J. C. Earnshaw, J. Phys. D 12, 1133 (1979).
    [CrossRef]
  12. P. G. Cummins and E. J. Staple, J. Phys. E 14, 1171 (1981).
    [CrossRef]
  13. W. Vogel, Phys. Rev. Lett. 67, 2450 (1991).
    [CrossRef] [PubMed]
  14. G. T. Foster, L. A. Orozco, H. M. Castro-Beltran, and H. J. Carmichael, Phys. Rev. Lett. 85, 3149 (2000).
    [CrossRef] [PubMed]
  15. E. Jakeman, J. Phys. A 3, 201 (1970).
    [CrossRef]
  16. W. Choi, M. Lee, Y.-R. Lee, C. Park, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Rev. Sci. Instrum. 76, 083109 (2005).
    [CrossRef]
  17. W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 96, 093603 (2006).
    [CrossRef] [PubMed]

2006 (1)

W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 96, 093603 (2006).
[CrossRef] [PubMed]

2005 (1)

W. Choi, M. Lee, Y.-R. Lee, C. Park, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Rev. Sci. Instrum. 76, 083109 (2005).
[CrossRef]

2004 (1)

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, Science 303, 1992 (2004).
[CrossRef] [PubMed]

2003 (1)

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, Nature 425, 268 (2003).
[CrossRef] [PubMed]

2002 (1)

A. Kuhn, M. Hennrich, and G. Rempe, Phys. Rev. Lett. 89, 067901 (2002).
[CrossRef] [PubMed]

2000 (1)

G. T. Foster, L. A. Orozco, H. M. Castro-Beltran, and H. J. Carmichael, Phys. Rev. Lett. 85, 3149 (2000).
[CrossRef] [PubMed]

1997 (1)

J. T. Höffges, H. W. Baldauf, W. Lange, and H. Walther, J. Mod. Opt. 44, 1999 (1997).
[CrossRef]

1994 (1)

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 73, 3375 (1994).
[CrossRef] [PubMed]

1991 (1)

W. Vogel, Phys. Rev. Lett. 67, 2450 (1991).
[CrossRef] [PubMed]

1985 (1)

D. Meschede, H. Walther, and G. Müller, Phys. Rev. Lett. 54, 551 (1985).
[CrossRef] [PubMed]

1981 (1)

P. G. Cummins and E. J. Staple, J. Phys. E 14, 1171 (1981).
[CrossRef]

1980 (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

1979 (1)

D. Byrne and J. C. Earnshaw, J. Phys. D 12, 1133 (1979).
[CrossRef]

1972 (1)

E. R. Pike, J. Phys. D 5, L23 (1972).
[CrossRef]

1970 (1)

E. Jakeman, J. Phys. A 3, 201 (1970).
[CrossRef]

1958 (1)

A. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958).
[CrossRef]

An, K.

W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 96, 093603 (2006).
[CrossRef] [PubMed]

W. Choi, M. Lee, Y.-R. Lee, C. Park, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Rev. Sci. Instrum. 76, 083109 (2005).
[CrossRef]

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 73, 3375 (1994).
[CrossRef] [PubMed]

Baldauf, H. W.

J. T. Höffges, H. W. Baldauf, W. Lange, and H. Walther, J. Mod. Opt. 44, 1999 (1997).
[CrossRef]

Boca, A.

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, Science 303, 1992 (2004).
[CrossRef] [PubMed]

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, Nature 425, 268 (2003).
[CrossRef] [PubMed]

Boozer, A. D.

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, Science 303, 1992 (2004).
[CrossRef] [PubMed]

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, Nature 425, 268 (2003).
[CrossRef] [PubMed]

Buck, J. R.

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, Science 303, 1992 (2004).
[CrossRef] [PubMed]

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, Nature 425, 268 (2003).
[CrossRef] [PubMed]

Byrne, D.

D. Byrne and J. C. Earnshaw, J. Phys. D 12, 1133 (1979).
[CrossRef]

Carmichael, H. J.

G. T. Foster, L. A. Orozco, H. M. Castro-Beltran, and H. J. Carmichael, Phys. Rev. Lett. 85, 3149 (2000).
[CrossRef] [PubMed]

Castro-Beltran, H. M.

G. T. Foster, L. A. Orozco, H. M. Castro-Beltran, and H. J. Carmichael, Phys. Rev. Lett. 85, 3149 (2000).
[CrossRef] [PubMed]

Childs, J. J.

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 73, 3375 (1994).
[CrossRef] [PubMed]

Choi, W.

W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 96, 093603 (2006).
[CrossRef] [PubMed]

W. Choi, M. Lee, Y.-R. Lee, C. Park, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Rev. Sci. Instrum. 76, 083109 (2005).
[CrossRef]

Cummins, P. G.

P. G. Cummins and E. J. Staple, J. Phys. E 14, 1171 (1981).
[CrossRef]

Dasari, R. R.

W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 96, 093603 (2006).
[CrossRef] [PubMed]

W. Choi, M. Lee, Y.-R. Lee, C. Park, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Rev. Sci. Instrum. 76, 083109 (2005).
[CrossRef]

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 73, 3375 (1994).
[CrossRef] [PubMed]

Earnshaw, J. C.

D. Byrne and J. C. Earnshaw, J. Phys. D 12, 1133 (1979).
[CrossRef]

Fang-Yen, C.

W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 96, 093603 (2006).
[CrossRef] [PubMed]

W. Choi, M. Lee, Y.-R. Lee, C. Park, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Rev. Sci. Instrum. 76, 083109 (2005).
[CrossRef]

Feld, M. S.

W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 96, 093603 (2006).
[CrossRef] [PubMed]

W. Choi, M. Lee, Y.-R. Lee, C. Park, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Rev. Sci. Instrum. 76, 083109 (2005).
[CrossRef]

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 73, 3375 (1994).
[CrossRef] [PubMed]

Foster, G. T.

G. T. Foster, L. A. Orozco, H. M. Castro-Beltran, and H. J. Carmichael, Phys. Rev. Lett. 85, 3149 (2000).
[CrossRef] [PubMed]

Hennrich, M.

A. Kuhn, M. Hennrich, and G. Rempe, Phys. Rev. Lett. 89, 067901 (2002).
[CrossRef] [PubMed]

Höffges, J. T.

J. T. Höffges, H. W. Baldauf, W. Lange, and H. Walther, J. Mod. Opt. 44, 1999 (1997).
[CrossRef]

Jakeman, E.

E. Jakeman, J. Phys. A 3, 201 (1970).
[CrossRef]

Kikuchi, K.

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

Kimble, H. J.

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, Science 303, 1992 (2004).
[CrossRef] [PubMed]

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, Nature 425, 268 (2003).
[CrossRef] [PubMed]

Kuhn, A.

A. Kuhn, M. Hennrich, and G. Rempe, Phys. Rev. Lett. 89, 067901 (2002).
[CrossRef] [PubMed]

Kuzmich, A.

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, Science 303, 1992 (2004).
[CrossRef] [PubMed]

Lange, W.

J. T. Höffges, H. W. Baldauf, W. Lange, and H. Walther, J. Mod. Opt. 44, 1999 (1997).
[CrossRef]

Lee, J.-H.

W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 96, 093603 (2006).
[CrossRef] [PubMed]

W. Choi, M. Lee, Y.-R. Lee, C. Park, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Rev. Sci. Instrum. 76, 083109 (2005).
[CrossRef]

Lee, M.

W. Choi, M. Lee, Y.-R. Lee, C. Park, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Rev. Sci. Instrum. 76, 083109 (2005).
[CrossRef]

Lee, Y.-R.

W. Choi, M. Lee, Y.-R. Lee, C. Park, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Rev. Sci. Instrum. 76, 083109 (2005).
[CrossRef]

McKeever, J.

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, Science 303, 1992 (2004).
[CrossRef] [PubMed]

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, Nature 425, 268 (2003).
[CrossRef] [PubMed]

Meschede, D.

D. Meschede, H. Walther, and G. Müller, Phys. Rev. Lett. 54, 551 (1985).
[CrossRef] [PubMed]

Miller, R.

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, Science 303, 1992 (2004).
[CrossRef] [PubMed]

Müller, G.

D. Meschede, H. Walther, and G. Müller, Phys. Rev. Lett. 54, 551 (1985).
[CrossRef] [PubMed]

Nakayama, A.

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

Okoshi, T.

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

Orozco, L. A.

G. T. Foster, L. A. Orozco, H. M. Castro-Beltran, and H. J. Carmichael, Phys. Rev. Lett. 85, 3149 (2000).
[CrossRef] [PubMed]

Park, C.

W. Choi, M. Lee, Y.-R. Lee, C. Park, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Rev. Sci. Instrum. 76, 083109 (2005).
[CrossRef]

Pike, E. R.

E. R. Pike, J. Phys. D 5, L23 (1972).
[CrossRef]

Rempe, G.

A. Kuhn, M. Hennrich, and G. Rempe, Phys. Rev. Lett. 89, 067901 (2002).
[CrossRef] [PubMed]

Schawlow, A. L.

A. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958).
[CrossRef]

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).

Staple, E. J.

P. G. Cummins and E. J. Staple, J. Phys. E 14, 1171 (1981).
[CrossRef]

Townes, C. H.

A. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958).
[CrossRef]

Vogel, W.

W. Vogel, Phys. Rev. Lett. 67, 2450 (1991).
[CrossRef] [PubMed]

Walther, H.

J. T. Höffges, H. W. Baldauf, W. Lange, and H. Walther, J. Mod. Opt. 44, 1999 (1997).
[CrossRef]

D. Meschede, H. Walther, and G. Müller, Phys. Rev. Lett. 54, 551 (1985).
[CrossRef] [PubMed]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).

Electron. Lett. (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

J. Mod. Opt. (1)

J. T. Höffges, H. W. Baldauf, W. Lange, and H. Walther, J. Mod. Opt. 44, 1999 (1997).
[CrossRef]

J. Phys. A (1)

E. Jakeman, J. Phys. A 3, 201 (1970).
[CrossRef]

J. Phys. D (2)

E. R. Pike, J. Phys. D 5, L23 (1972).
[CrossRef]

D. Byrne and J. C. Earnshaw, J. Phys. D 12, 1133 (1979).
[CrossRef]

J. Phys. E (1)

P. G. Cummins and E. J. Staple, J. Phys. E 14, 1171 (1981).
[CrossRef]

Nature (1)

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, Nature 425, 268 (2003).
[CrossRef] [PubMed]

Phys. Rev. (1)

A. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958).
[CrossRef]

Phys. Rev. Lett. (6)

D. Meschede, H. Walther, and G. Müller, Phys. Rev. Lett. 54, 551 (1985).
[CrossRef] [PubMed]

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 73, 3375 (1994).
[CrossRef] [PubMed]

W. Vogel, Phys. Rev. Lett. 67, 2450 (1991).
[CrossRef] [PubMed]

G. T. Foster, L. A. Orozco, H. M. Castro-Beltran, and H. J. Carmichael, Phys. Rev. Lett. 85, 3149 (2000).
[CrossRef] [PubMed]

A. Kuhn, M. Hennrich, and G. Rempe, Phys. Rev. Lett. 89, 067901 (2002).
[CrossRef] [PubMed]

W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 96, 093603 (2006).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

W. Choi, M. Lee, Y.-R. Lee, C. Park, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Rev. Sci. Instrum. 76, 083109 (2005).
[CrossRef]

Science (1)

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, Science 303, 1992 (2004).
[CrossRef] [PubMed]

Other (1)

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).

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Figures (3)

Fig. 1
Fig. 1

Experimental scheme. The upper path corresponds to a test source, and the lower path corresponds to a LO. PD, photodiode.

Fig. 2
Fig. 2

(a) Observed g B ( 2 ) ( τ ) with phase fluctuations only. Bin time, 250 ns . (b) Enlarged view of the central region of (a). (c) Normalized spectral density on a linear scale. Gray, conventional HS; black, PCSOCS. (d) Linewidth broadening as a function of the noise rms voltage.

Fig. 3
Fig. 3

(a) Observed g B ( 2 ) ( τ ) with amplitude fluctuations included. (b) Enlarged view of the central region of (a). (c) Normalized spectral density obtained from the Fourier transform of g B ( 2 ) ( τ ) as the ratio of standard deviation SD to dc noise voltage is increased. A Lorentzian fit (dashed curve) is also shown for comparison.

Equations (4)

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

I h ( t ) = E ( t ) + E L ( t ) 2 = E ( t ) 2 + E L ( t ) 2 + E LO * E 0 ( t ) exp { i [ ω B t + ϕ ( t ) ] } + c.c. ,
g B ( 2 ) ( τ ) = I h * ( t ) I h ( t + τ ) I h * ( t ) I h ( t + τ ) = 1 + 2 I 0 I LO ( I 0 + I LO ) 2 g ( 1 ) ( τ ) cos ω B τ + I 0 2 ( I 0 + I LO ) 2 [ g ( 2 ) ( τ ) 1 ] ,
E 0 ( t ) = I 0 ( 1 + a 1 e i Ω t + a 1 e i Ω t + a 2 e i 2 Ω t ) ,
E 0 ( t ) 2 = I 0 [ 1 + m ( Ω ) cos Ω t d Ω ]

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