Abstract

We demonstrate that the large FM noise of a semiconductor laser can be combined with a squeezed AM noise spectrum to make a sub-shot-noise, FM-noise-based spectroscopic measurement. In particular, we probe the spectrum of magneto-optically trapped and cooled rubidium atoms using the FM noise on squeezed AM background noise. The natural absorption line as well as a stimulated Raman transition are clearly visible in the FM-to-AM converted noise even though the signal is below the classical shot-noise level.

© 1998 Optical Society of America

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  1. C. H. Henry, IEEE J. Quantum Electron. QE-18, 259 (1982).
    [CrossRef]
  2. Y. Yamamoto, S. Saito, and T. Mukai, IEEE J. Quantum Electron. QE-19, 47 (1983).
    [CrossRef]
  3. K. Vahala and A. Yariv, IEEE J. Quantum Electron. QE-19, 1102 (1983).
    [CrossRef]
  4. Y. Yamamoto, Science 255, 1219 (1992).
    [CrossRef] [PubMed]
  5. S. Kasapi, S. Lathi, and Y. Yamamoto, Opt. Lett. 22, 478 (1997).
    [CrossRef] [PubMed]
  6. B. Yurke and E. A. Whittaker, Opt. Lett. 12, 236 (1987).
    [CrossRef] [PubMed]
  7. E. S. Polzik, J. Carri, and H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
    [CrossRef] [PubMed]
  8. T. Yabuzaki, T. Mitsui, and U. Tanaka, Phys. Rev. Lett. 67, 2453 (1991).
    [CrossRef] [PubMed]
  9. D. H. McIntyre, C. E. Fairchild, J. Cooper, and R. Walser, Opt. Lett. 18, 1916 (1993).
    [CrossRef]
  10. G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Oritz, Appl. Phys. B 32, 145 (1983).
    [CrossRef]
  11. S. Kasapi, S. Lathi, and Y. Yamamoto, talk presented at the Seventh Rochester Conference on Coherence and Quantum Optics, Rochester, New York, June 1995.
  12. K. Yamada and H. Sasada, talk presented at the Twelfth International Conference on Laser Spectroscopy, Capri, Italy, June 1995.
  13. D. C. Kilper, M. J. Freeman, D. G. Steel, R. Craig, and D. R. Scifres, Proc. SPIE 2378, 64 (1995).
    [CrossRef]
  14. S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 48, 2230 (1993).
    [CrossRef] [PubMed]
  15. H. Wang, M. J. Freeman, and D. G. Steel, Phys. Rev. Lett. 71, 3951 (1993).
    [CrossRef] [PubMed]
  16. C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
    [CrossRef] [PubMed]
  17. K. E. Gibble, S. Kasapi, and S. Chu, Opt. Lett. 17, 526 (1992).
    [CrossRef] [PubMed]
  18. D. Grison, B. Lounis, C. Salomon, J. Y. Courtois, and G. Grynberg, Europhys. Lett. 15, 149 (1991).
    [CrossRef]
  19. J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, Phys. Rev. Lett. 66, 3245 (1991).
    [CrossRef] [PubMed]
  20. S. Lathi, S. Kasapi, and Y. Yamamoto, Opt. Lett. 21, 1600 (1996).
    [CrossRef] [PubMed]

1997 (1)

1996 (1)

1995 (1)

D. C. Kilper, M. J. Freeman, D. G. Steel, R. Craig, and D. R. Scifres, Proc. SPIE 2378, 64 (1995).
[CrossRef]

1993 (3)

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 48, 2230 (1993).
[CrossRef] [PubMed]

H. Wang, M. J. Freeman, and D. G. Steel, Phys. Rev. Lett. 71, 3951 (1993).
[CrossRef] [PubMed]

D. H. McIntyre, C. E. Fairchild, J. Cooper, and R. Walser, Opt. Lett. 18, 1916 (1993).
[CrossRef]

1992 (3)

K. E. Gibble, S. Kasapi, and S. Chu, Opt. Lett. 17, 526 (1992).
[CrossRef] [PubMed]

E. S. Polzik, J. Carri, and H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

Y. Yamamoto, Science 255, 1219 (1992).
[CrossRef] [PubMed]

1991 (3)

T. Yabuzaki, T. Mitsui, and U. Tanaka, Phys. Rev. Lett. 67, 2453 (1991).
[CrossRef] [PubMed]

D. Grison, B. Lounis, C. Salomon, J. Y. Courtois, and G. Grynberg, Europhys. Lett. 15, 149 (1991).
[CrossRef]

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, Phys. Rev. Lett. 66, 3245 (1991).
[CrossRef] [PubMed]

1990 (1)

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

1987 (1)

1983 (3)

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

K. Vahala and A. Yariv, IEEE J. Quantum Electron. QE-19, 1102 (1983).
[CrossRef]

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Oritz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

1982 (1)

C. H. Henry, IEEE J. Quantum Electron. QE-18, 259 (1982).
[CrossRef]

Bjorklund, G. C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Oritz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

Carri, J.

E. S. Polzik, J. Carri, and H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

Chen, G.

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, Phys. Rev. Lett. 66, 3245 (1991).
[CrossRef] [PubMed]

Chu, S.

Cooper, J.

Courtois, J. Y.

D. Grison, B. Lounis, C. Salomon, J. Y. Courtois, and G. Grynberg, Europhys. Lett. 15, 149 (1991).
[CrossRef]

Craig, R.

D. C. Kilper, M. J. Freeman, D. G. Steel, R. Craig, and D. R. Scifres, Proc. SPIE 2378, 64 (1995).
[CrossRef]

Fairchild, C. E.

Freeman, M. J.

D. C. Kilper, M. J. Freeman, D. G. Steel, R. Craig, and D. R. Scifres, Proc. SPIE 2378, 64 (1995).
[CrossRef]

H. Wang, M. J. Freeman, and D. G. Steel, Phys. Rev. Lett. 71, 3951 (1993).
[CrossRef] [PubMed]

Gibble, K. E.

Grison, D.

D. Grison, B. Lounis, C. Salomon, J. Y. Courtois, and G. Grynberg, Europhys. Lett. 15, 149 (1991).
[CrossRef]

Grynberg, G.

D. Grison, B. Lounis, C. Salomon, J. Y. Courtois, and G. Grynberg, Europhys. Lett. 15, 149 (1991).
[CrossRef]

Henry, C. H.

C. H. Henry, IEEE J. Quantum Electron. QE-18, 259 (1982).
[CrossRef]

Hu, Z.

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, Phys. Rev. Lett. 66, 3245 (1991).
[CrossRef] [PubMed]

Inoue, S.

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 48, 2230 (1993).
[CrossRef] [PubMed]

Kasapi, S.

Kilper, D. C.

D. C. Kilper, M. J. Freeman, D. G. Steel, R. Craig, and D. R. Scifres, Proc. SPIE 2378, 64 (1995).
[CrossRef]

Kimble, H. J.

E. S. Polzik, J. Carri, and H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, Phys. Rev. Lett. 66, 3245 (1991).
[CrossRef] [PubMed]

Lathi, S.

Lee, R. B.

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, Phys. Rev. Lett. 66, 3245 (1991).
[CrossRef] [PubMed]

Lenth, W.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Oritz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

Levenson, M. D.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Oritz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

Lounis, B.

D. Grison, B. Lounis, C. Salomon, J. Y. Courtois, and G. Grynberg, Europhys. Lett. 15, 149 (1991).
[CrossRef]

Machida, S.

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 48, 2230 (1993).
[CrossRef] [PubMed]

McIntyre, D. H.

Mitsui, T.

T. Yabuzaki, T. Mitsui, and U. Tanaka, Phys. Rev. Lett. 67, 2453 (1991).
[CrossRef] [PubMed]

Monroe, C.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

Mukai, T.

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

Ohzu, H.

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 48, 2230 (1993).
[CrossRef] [PubMed]

Oritz, C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Oritz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

Polzik, E. S.

E. S. Polzik, J. Carri, and H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

Robinson, H.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

Saito, S.

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

Salomon, C.

D. Grison, B. Lounis, C. Salomon, J. Y. Courtois, and G. Grynberg, Europhys. Lett. 15, 149 (1991).
[CrossRef]

Scifres, D. R.

D. C. Kilper, M. J. Freeman, D. G. Steel, R. Craig, and D. R. Scifres, Proc. SPIE 2378, 64 (1995).
[CrossRef]

Steel, D. G.

D. C. Kilper, M. J. Freeman, D. G. Steel, R. Craig, and D. R. Scifres, Proc. SPIE 2378, 64 (1995).
[CrossRef]

H. Wang, M. J. Freeman, and D. G. Steel, Phys. Rev. Lett. 71, 3951 (1993).
[CrossRef] [PubMed]

Swann, W.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

Tabosa, J. W. R.

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, Phys. Rev. Lett. 66, 3245 (1991).
[CrossRef] [PubMed]

Tanaka, U.

T. Yabuzaki, T. Mitsui, and U. Tanaka, Phys. Rev. Lett. 67, 2453 (1991).
[CrossRef] [PubMed]

Vahala, K.

K. Vahala and A. Yariv, IEEE J. Quantum Electron. QE-19, 1102 (1983).
[CrossRef]

Walser, R.

Wang, H.

H. Wang, M. J. Freeman, and D. G. Steel, Phys. Rev. Lett. 71, 3951 (1993).
[CrossRef] [PubMed]

Whittaker, E. A.

Wieman, C.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

Yabuzaki, T.

T. Yabuzaki, T. Mitsui, and U. Tanaka, Phys. Rev. Lett. 67, 2453 (1991).
[CrossRef] [PubMed]

Yamamoto, Y.

S. Kasapi, S. Lathi, and Y. Yamamoto, Opt. Lett. 22, 478 (1997).
[CrossRef] [PubMed]

S. Lathi, S. Kasapi, and Y. Yamamoto, Opt. Lett. 21, 1600 (1996).
[CrossRef] [PubMed]

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 48, 2230 (1993).
[CrossRef] [PubMed]

Y. Yamamoto, Science 255, 1219 (1992).
[CrossRef] [PubMed]

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

Yariv, A.

K. Vahala and A. Yariv, IEEE J. Quantum Electron. QE-19, 1102 (1983).
[CrossRef]

Yurke, B.

Appl. Phys. B (1)

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Oritz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

Europhys. Lett. (1)

D. Grison, B. Lounis, C. Salomon, J. Y. Courtois, and G. Grynberg, Europhys. Lett. 15, 149 (1991).
[CrossRef]

IEEE J. Quantum Electron. (3)

C. H. Henry, IEEE J. Quantum Electron. QE-18, 259 (1982).
[CrossRef]

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

K. Vahala and A. Yariv, IEEE J. Quantum Electron. QE-19, 1102 (1983).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (1)

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 48, 2230 (1993).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

H. Wang, M. J. Freeman, and D. G. Steel, Phys. Rev. Lett. 71, 3951 (1993).
[CrossRef] [PubMed]

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, Phys. Rev. Lett. 66, 3245 (1991).
[CrossRef] [PubMed]

E. S. Polzik, J. Carri, and H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

T. Yabuzaki, T. Mitsui, and U. Tanaka, Phys. Rev. Lett. 67, 2453 (1991).
[CrossRef] [PubMed]

Proc. SPIE (1)

D. C. Kilper, M. J. Freeman, D. G. Steel, R. Craig, and D. R. Scifres, Proc. SPIE 2378, 64 (1995).
[CrossRef]

Science (1)

Y. Yamamoto, Science 255, 1219 (1992).
[CrossRef] [PubMed]

Other (2)

S. Kasapi, S. Lathi, and Y. Yamamoto, talk presented at the Seventh Rochester Conference on Coherence and Quantum Optics, Rochester, New York, June 1995.

K. Yamada and H. Sasada, talk presented at the Twelfth International Conference on Laser Spectroscopy, Capri, Italy, June 1995.

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Figures (5)

Fig. 1
Fig. 1

Qualitative description of the analogy between coherent FM spectroscopy and FM noise spectroscopy. The FM noise sidebands at ω0-ωm and ω0+ωm play the role of the coherent FM side bands.

Fig. 2
Fig. 2

Setup for sub-shot-noise FM noise spectroscopy of magneto-optically trapped rubidium atoms. Two percent of the master laser output is used to injection lock the slave laser. The slave laser beam was expanded and used to probe the trapped rubidium atoms. After the interaction with the atoms, the slave laser beam was detected by a double-balanced detector to measure the laser noise (sum of the two detector outputs) and corresponding shot noise (difference of the two detector outputs).

Fig. 3
Fig. 3

Level diagram for 85Rb. Diagram also shows the trap laser frequency with the repumping sideband and the frequency of the squeezed slave laser that probes the atoms.

Fig. 4
Fig. 4

Trace showing sub-shot-noise FM noise spectroscopy data of trapped 85Rb atoms. The upper trace is the shot-noise level, and the lower trace is the AM noise of the slave laser measured without the trap.

Fig. 5
Fig. 5

Coherent FM spectroscopy data of magneto-optically trapped 85Rb. Peak A corresponds to the Stark-shifted natural absorption at ω0s, and peak B corresponds to the stimulated Raman resonance among Zeeman levels in the ground state at ωt (the trapping frequency).

Equations (3)

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iS2=12 I02(Δδ2+Δϕ2)M2Δf,
1n2={2eηI0[1-γ(ωm)]+2eI0η(1-η)}Δf,
iS2in2=I0(Δδ2+Δϕ2)M24e{η[1-γ(ωm)]+η(1-η)}

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