Abstract

We developed a system for measurements of power spectra of transmitted light intensity fluctuations, in which the extraneous noise, including shot noise, is reduced. In essence, we just apply light, measure the power of the transmitted light, and derive its power spectrum. We use this to observe the spontaneous noise spectra of photon atom interactions. Applying light with frequency modulation, we can also observe the spontaneous noise reflecting the coherence between the hyperfine levels in the excited state. There are two main novel components in the measurement system, the noise reduction scheme and the stabilization of the laser system. The noise reduction mechanism can be used to reduce the shot noise contribution to arbitrarily low levels through averaging, in principle. This is combined with differential detection to keep unwanted noise at low levels. The laser system is stabilized to obtain spectral width below 1 kHz without high frequency (10MHz) noise. These methods are described systematically and the performance of the measurement system is examined through experimental results.

© 2014 Optical Society of America

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  1. E. B. Aleksandrov and V. S. Zapasskii, “Magnetic resonance in the Faraday-rotation noise spectrum,” Zh. Exp. Teor. Fiz. 81, 132–138 (1981).
  2. T. Mitsui, “Spontaneous noise spectroscopy of an atomic magnetic resonance,” Phys. Rev. Lett. 84, 5292–5295 (2000).
    [CrossRef]
  3. S. A. Crooker, D. G. Rickel, A. V. Balatsky, and D. L. Smith, “Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance,” Nature 431, 49–52 (2004).
    [CrossRef]
  4. T. Mitsui and K. Aoki, “Observation of spontaneous quantum fluctuations in photon absorption by atoms,” Eur. Phys. J. D 67, 213–218 (2013).
    [CrossRef]
  5. See, for instanceP. Meystre and M. Sargent, Elements of Quantum Optics (Springer-Verlag, 1990).
  6. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
    [CrossRef]
  7. K. McKenzie, B. C. Buchler, D. A. Shaddock, P. K. Lam, and D. E. McClelland, “Analysis of a sub-shot-noise power recycled Michelson interferometer,” Classical Quantum Gravity 21, S1037–S1043 (2004).
    [CrossRef]
  8. H. Vahlbruch, M. Mehmet, N. Lastzka, B. Hage, S. Chelkowski, A. Franzen, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10  dB quantum noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
    [CrossRef]
  9. T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Handchen, H. Vahlbruch, M. Mehmet, H. Muller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
    [CrossRef]
  10. T. Mitsui and K. Aoki, “Direct optical observations of surface thermal motions at sub-shot noise levels,” Phys. Rev. E 80, 020602(R) (2009).
    [CrossRef]
  11. K. Aoki and T. Mitsui, “Spectral properties of thermal fluctuations on simple liquid surfaces below shot-noise levels,” Phys. Rev. E 86, 011602 (2012).
    [CrossRef]
  12. T. Yabuzaki, T. Mitsui, and U. Tanaka, “New type of high-resolution spectroscopy with a diode laser,” Phys. Rev. Lett. 67, 2453–2456 (1991).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. B. R. Mollow, “Power spectrum of light scattered by two-level systems,” Phys. Rev. 188, 1969–1975 (1969).
    [CrossRef]
  20. F. Schuda, C. R. Stroud, and M. Hercher, “Observation of the resonant Stark effect at optical frequencies,” J. Phys. B 7, L198–L202 (1974).
    [CrossRef]
  21. D. F. Walls and P. Zoller, “Reduced quantum fluctuations in resonance fluorescence,” Phys. Rev. Lett. 47, 709–711 (1981).
    [CrossRef]
  22. L. Mandel, “Squeezed states and sub-Poissonian photon statistics,” Phys. Rev. Lett. 49, 136–138 (1982).
    [CrossRef]
  23. A. M. Bacon, H. Z. Zhao, L. J. Wang, and J. E. Thomas, “Optical dipole noise of two-level atoms,” Phys. Rev. Lett. 75, 1296–1299 (1995).
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2013 (3)

T. Mitsui and K. Aoki, “Observation of spontaneous quantum fluctuations in photon absorption by atoms,” Eur. Phys. J. D 67, 213–218 (2013).
[CrossRef]

T. Mitsui and K. Aoki, “Michelson interferometry with quantum noise reduction,” Phys. Rev. E 87, 042403 (2013).
[CrossRef]

V. S. Zapasskii, “Spin-noise spectroscopy: from proof of principle to applications,” Adv. Opt. Photon. 5, 131–168 (2013).
[CrossRef]

2012 (1)

K. Aoki and T. Mitsui, “Spectral properties of thermal fluctuations on simple liquid surfaces below shot-noise levels,” Phys. Rev. E 86, 011602 (2012).
[CrossRef]

2010 (1)

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Handchen, H. Vahlbruch, M. Mehmet, H. Muller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef]

2009 (1)

T. Mitsui and K. Aoki, “Direct optical observations of surface thermal motions at sub-shot noise levels,” Phys. Rev. E 80, 020602(R) (2009).
[CrossRef]

2008 (1)

H. Vahlbruch, M. Mehmet, N. Lastzka, B. Hage, S. Chelkowski, A. Franzen, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10  dB quantum noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

2004 (2)

S. A. Crooker, D. G. Rickel, A. V. Balatsky, and D. L. Smith, “Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance,” Nature 431, 49–52 (2004).
[CrossRef]

K. McKenzie, B. C. Buchler, D. A. Shaddock, P. K. Lam, and D. E. McClelland, “Analysis of a sub-shot-noise power recycled Michelson interferometer,” Classical Quantum Gravity 21, S1037–S1043 (2004).
[CrossRef]

2000 (1)

T. Mitsui, “Spontaneous noise spectroscopy of an atomic magnetic resonance,” Phys. Rev. Lett. 84, 5292–5295 (2000).
[CrossRef]

1995 (1)

A. M. Bacon, H. Z. Zhao, L. J. Wang, and J. E. Thomas, “Optical dipole noise of two-level atoms,” Phys. Rev. Lett. 75, 1296–1299 (1995).
[CrossRef]

1991 (1)

T. Yabuzaki, T. Mitsui, and U. Tanaka, “New type of high-resolution spectroscopy with a diode laser,” Phys. Rev. Lett. 67, 2453–2456 (1991).
[CrossRef]

1987 (2)

1983 (1)

Y. Yamamoto, S. Saito, and T. Mukai, “AM and FM quantum noise in semiconductor lasers—Part II: comparison of theoretical and experimental results for AlGaAs lasers,” IEEE J. Quantum Electron. QE-19, 47–58 (1983).
[CrossRef]

1982 (1)

L. Mandel, “Squeezed states and sub-Poissonian photon statistics,” Phys. Rev. Lett. 49, 136–138 (1982).
[CrossRef]

1981 (3)

D. F. Walls and P. Zoller, “Reduced quantum fluctuations in resonance fluorescence,” Phys. Rev. Lett. 47, 709–711 (1981).
[CrossRef]

E. B. Aleksandrov and V. S. Zapasskii, “Magnetic resonance in the Faraday-rotation noise spectrum,” Zh. Exp. Teor. Fiz. 81, 132–138 (1981).

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
[CrossRef]

1974 (1)

F. Schuda, C. R. Stroud, and M. Hercher, “Observation of the resonant Stark effect at optical frequencies,” J. Phys. B 7, L198–L202 (1974).
[CrossRef]

1969 (1)

B. R. Mollow, “Power spectrum of light scattered by two-level systems,” Phys. Rev. 188, 1969–1975 (1969).
[CrossRef]

1955 (1)

A. T. Forrester, R. A. Gudmundsen, and P. O. Johnson, “Photoelectric mixing of incoherent light,” Phys. Rev. 99, 1691–1700 (1955).
[CrossRef]

Aleksandrov, E. B.

E. B. Aleksandrov and V. S. Zapasskii, “Magnetic resonance in the Faraday-rotation noise spectrum,” Zh. Exp. Teor. Fiz. 81, 132–138 (1981).

Aoki, K.

T. Mitsui and K. Aoki, “Observation of spontaneous quantum fluctuations in photon absorption by atoms,” Eur. Phys. J. D 67, 213–218 (2013).
[CrossRef]

T. Mitsui and K. Aoki, “Michelson interferometry with quantum noise reduction,” Phys. Rev. E 87, 042403 (2013).
[CrossRef]

K. Aoki and T. Mitsui, “Spectral properties of thermal fluctuations on simple liquid surfaces below shot-noise levels,” Phys. Rev. E 86, 011602 (2012).
[CrossRef]

T. Mitsui and K. Aoki, “Direct optical observations of surface thermal motions at sub-shot noise levels,” Phys. Rev. E 80, 020602(R) (2009).
[CrossRef]

Bacon, A. M.

A. M. Bacon, H. Z. Zhao, L. J. Wang, and J. E. Thomas, “Optical dipole noise of two-level atoms,” Phys. Rev. Lett. 75, 1296–1299 (1995).
[CrossRef]

Balatsky, A. V.

S. A. Crooker, D. G. Rickel, A. V. Balatsky, and D. L. Smith, “Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance,” Nature 431, 49–52 (2004).
[CrossRef]

Bauchrowitz, J.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Handchen, H. Vahlbruch, M. Mehmet, H. Muller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef]

Buchler, B. C.

K. McKenzie, B. C. Buchler, D. A. Shaddock, P. K. Lam, and D. E. McClelland, “Analysis of a sub-shot-noise power recycled Michelson interferometer,” Classical Quantum Gravity 21, S1037–S1043 (2004).
[CrossRef]

Caves, C. M.

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
[CrossRef]

Chelkowski, S.

H. Vahlbruch, M. Mehmet, N. Lastzka, B. Hage, S. Chelkowski, A. Franzen, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10  dB quantum noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Crooker, S. A.

S. A. Crooker, D. G. Rickel, A. V. Balatsky, and D. L. Smith, “Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance,” Nature 431, 49–52 (2004).
[CrossRef]

Dahmani, B.

Danzmann, K.

H. Vahlbruch, M. Mehmet, N. Lastzka, B. Hage, S. Chelkowski, A. Franzen, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10  dB quantum noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Drullinger, R.

Eberle, T.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Handchen, H. Vahlbruch, M. Mehmet, H. Muller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef]

Forrester, A. T.

A. T. Forrester, R. A. Gudmundsen, and P. O. Johnson, “Photoelectric mixing of incoherent light,” Phys. Rev. 99, 1691–1700 (1955).
[CrossRef]

Franzen, A.

H. Vahlbruch, M. Mehmet, N. Lastzka, B. Hage, S. Chelkowski, A. Franzen, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10  dB quantum noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Goßler, S.

H. Vahlbruch, M. Mehmet, N. Lastzka, B. Hage, S. Chelkowski, A. Franzen, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10  dB quantum noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Gudmundsen, R. A.

A. T. Forrester, R. A. Gudmundsen, and P. O. Johnson, “Photoelectric mixing of incoherent light,” Phys. Rev. 99, 1691–1700 (1955).
[CrossRef]

Hage, B.

H. Vahlbruch, M. Mehmet, N. Lastzka, B. Hage, S. Chelkowski, A. Franzen, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10  dB quantum noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Handchen, V.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Handchen, H. Vahlbruch, M. Mehmet, H. Muller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef]

Hercher, M.

F. Schuda, C. R. Stroud, and M. Hercher, “Observation of the resonant Stark effect at optical frequencies,” J. Phys. B 7, L198–L202 (1974).
[CrossRef]

Hollberg, L.

Johnson, P. O.

A. T. Forrester, R. A. Gudmundsen, and P. O. Johnson, “Photoelectric mixing of incoherent light,” Phys. Rev. 99, 1691–1700 (1955).
[CrossRef]

Kumar, P.

Lam, P. K.

K. McKenzie, B. C. Buchler, D. A. Shaddock, P. K. Lam, and D. E. McClelland, “Analysis of a sub-shot-noise power recycled Michelson interferometer,” Classical Quantum Gravity 21, S1037–S1043 (2004).
[CrossRef]

Lastzka, N.

H. Vahlbruch, M. Mehmet, N. Lastzka, B. Hage, S. Chelkowski, A. Franzen, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10  dB quantum noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Maeda, M. W.

Mandel, L.

L. Mandel, “Squeezed states and sub-Poissonian photon statistics,” Phys. Rev. Lett. 49, 136–138 (1982).
[CrossRef]

McClelland, D. E.

K. McKenzie, B. C. Buchler, D. A. Shaddock, P. K. Lam, and D. E. McClelland, “Analysis of a sub-shot-noise power recycled Michelson interferometer,” Classical Quantum Gravity 21, S1037–S1043 (2004).
[CrossRef]

McKenzie, K.

K. McKenzie, B. C. Buchler, D. A. Shaddock, P. K. Lam, and D. E. McClelland, “Analysis of a sub-shot-noise power recycled Michelson interferometer,” Classical Quantum Gravity 21, S1037–S1043 (2004).
[CrossRef]

Mehmet, M.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Handchen, H. Vahlbruch, M. Mehmet, H. Muller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef]

H. Vahlbruch, M. Mehmet, N. Lastzka, B. Hage, S. Chelkowski, A. Franzen, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10  dB quantum noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Meystre, P.

See, for instanceP. Meystre and M. Sargent, Elements of Quantum Optics (Springer-Verlag, 1990).

Mitsui, T.

T. Mitsui and K. Aoki, “Observation of spontaneous quantum fluctuations in photon absorption by atoms,” Eur. Phys. J. D 67, 213–218 (2013).
[CrossRef]

T. Mitsui and K. Aoki, “Michelson interferometry with quantum noise reduction,” Phys. Rev. E 87, 042403 (2013).
[CrossRef]

K. Aoki and T. Mitsui, “Spectral properties of thermal fluctuations on simple liquid surfaces below shot-noise levels,” Phys. Rev. E 86, 011602 (2012).
[CrossRef]

T. Mitsui and K. Aoki, “Direct optical observations of surface thermal motions at sub-shot noise levels,” Phys. Rev. E 80, 020602(R) (2009).
[CrossRef]

T. Mitsui, “Spontaneous noise spectroscopy of an atomic magnetic resonance,” Phys. Rev. Lett. 84, 5292–5295 (2000).
[CrossRef]

T. Yabuzaki, T. Mitsui, and U. Tanaka, “New type of high-resolution spectroscopy with a diode laser,” Phys. Rev. Lett. 67, 2453–2456 (1991).
[CrossRef]

Mollow, B. R.

B. R. Mollow, “Power spectrum of light scattered by two-level systems,” Phys. Rev. 188, 1969–1975 (1969).
[CrossRef]

Mukai, T.

Y. Yamamoto, S. Saito, and T. Mukai, “AM and FM quantum noise in semiconductor lasers—Part II: comparison of theoretical and experimental results for AlGaAs lasers,” IEEE J. Quantum Electron. QE-19, 47–58 (1983).
[CrossRef]

Muller-Ebhardt, H.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Handchen, H. Vahlbruch, M. Mehmet, H. Muller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef]

Rickel, D. G.

S. A. Crooker, D. G. Rickel, A. V. Balatsky, and D. L. Smith, “Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance,” Nature 431, 49–52 (2004).
[CrossRef]

Saito, S.

Y. Yamamoto, S. Saito, and T. Mukai, “AM and FM quantum noise in semiconductor lasers—Part II: comparison of theoretical and experimental results for AlGaAs lasers,” IEEE J. Quantum Electron. QE-19, 47–58 (1983).
[CrossRef]

Sargent, M.

See, for instanceP. Meystre and M. Sargent, Elements of Quantum Optics (Springer-Verlag, 1990).

Schnabel, R.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Handchen, H. Vahlbruch, M. Mehmet, H. Muller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef]

H. Vahlbruch, M. Mehmet, N. Lastzka, B. Hage, S. Chelkowski, A. Franzen, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10  dB quantum noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Schuda, F.

F. Schuda, C. R. Stroud, and M. Hercher, “Observation of the resonant Stark effect at optical frequencies,” J. Phys. B 7, L198–L202 (1974).
[CrossRef]

Shaddock, D. A.

K. McKenzie, B. C. Buchler, D. A. Shaddock, P. K. Lam, and D. E. McClelland, “Analysis of a sub-shot-noise power recycled Michelson interferometer,” Classical Quantum Gravity 21, S1037–S1043 (2004).
[CrossRef]

Shapiro, J. H.

Smith, D. L.

S. A. Crooker, D. G. Rickel, A. V. Balatsky, and D. L. Smith, “Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance,” Nature 431, 49–52 (2004).
[CrossRef]

Steinlechner, S.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Handchen, H. Vahlbruch, M. Mehmet, H. Muller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef]

Stroud, C. R.

F. Schuda, C. R. Stroud, and M. Hercher, “Observation of the resonant Stark effect at optical frequencies,” J. Phys. B 7, L198–L202 (1974).
[CrossRef]

Tanaka, U.

T. Yabuzaki, T. Mitsui, and U. Tanaka, “New type of high-resolution spectroscopy with a diode laser,” Phys. Rev. Lett. 67, 2453–2456 (1991).
[CrossRef]

Thomas, J. E.

A. M. Bacon, H. Z. Zhao, L. J. Wang, and J. E. Thomas, “Optical dipole noise of two-level atoms,” Phys. Rev. Lett. 75, 1296–1299 (1995).
[CrossRef]

Vahlbruch, H.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Handchen, H. Vahlbruch, M. Mehmet, H. Muller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef]

H. Vahlbruch, M. Mehmet, N. Lastzka, B. Hage, S. Chelkowski, A. Franzen, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10  dB quantum noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Walls, D. F.

D. F. Walls and P. Zoller, “Reduced quantum fluctuations in resonance fluorescence,” Phys. Rev. Lett. 47, 709–711 (1981).
[CrossRef]

Wang, L. J.

A. M. Bacon, H. Z. Zhao, L. J. Wang, and J. E. Thomas, “Optical dipole noise of two-level atoms,” Phys. Rev. Lett. 75, 1296–1299 (1995).
[CrossRef]

Yabuzaki, T.

T. Yabuzaki, T. Mitsui, and U. Tanaka, “New type of high-resolution spectroscopy with a diode laser,” Phys. Rev. Lett. 67, 2453–2456 (1991).
[CrossRef]

Yamamoto, Y.

Y. Yamamoto, S. Saito, and T. Mukai, “AM and FM quantum noise in semiconductor lasers—Part II: comparison of theoretical and experimental results for AlGaAs lasers,” IEEE J. Quantum Electron. QE-19, 47–58 (1983).
[CrossRef]

Zapasskii, V. S.

V. S. Zapasskii, “Spin-noise spectroscopy: from proof of principle to applications,” Adv. Opt. Photon. 5, 131–168 (2013).
[CrossRef]

E. B. Aleksandrov and V. S. Zapasskii, “Magnetic resonance in the Faraday-rotation noise spectrum,” Zh. Exp. Teor. Fiz. 81, 132–138 (1981).

Zhao, H. Z.

A. M. Bacon, H. Z. Zhao, L. J. Wang, and J. E. Thomas, “Optical dipole noise of two-level atoms,” Phys. Rev. Lett. 75, 1296–1299 (1995).
[CrossRef]

Zoller, P.

D. F. Walls and P. Zoller, “Reduced quantum fluctuations in resonance fluorescence,” Phys. Rev. Lett. 47, 709–711 (1981).
[CrossRef]

Adv. Opt. Photon. (1)

Classical Quantum Gravity (1)

K. McKenzie, B. C. Buchler, D. A. Shaddock, P. K. Lam, and D. E. McClelland, “Analysis of a sub-shot-noise power recycled Michelson interferometer,” Classical Quantum Gravity 21, S1037–S1043 (2004).
[CrossRef]

Eur. Phys. J. D (1)

T. Mitsui and K. Aoki, “Observation of spontaneous quantum fluctuations in photon absorption by atoms,” Eur. Phys. J. D 67, 213–218 (2013).
[CrossRef]

IEEE J. Quantum Electron. (1)

Y. Yamamoto, S. Saito, and T. Mukai, “AM and FM quantum noise in semiconductor lasers—Part II: comparison of theoretical and experimental results for AlGaAs lasers,” IEEE J. Quantum Electron. QE-19, 47–58 (1983).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. B (1)

F. Schuda, C. R. Stroud, and M. Hercher, “Observation of the resonant Stark effect at optical frequencies,” J. Phys. B 7, L198–L202 (1974).
[CrossRef]

Nature (1)

S. A. Crooker, D. G. Rickel, A. V. Balatsky, and D. L. Smith, “Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance,” Nature 431, 49–52 (2004).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (2)

B. R. Mollow, “Power spectrum of light scattered by two-level systems,” Phys. Rev. 188, 1969–1975 (1969).
[CrossRef]

A. T. Forrester, R. A. Gudmundsen, and P. O. Johnson, “Photoelectric mixing of incoherent light,” Phys. Rev. 99, 1691–1700 (1955).
[CrossRef]

Phys. Rev. D (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
[CrossRef]

Phys. Rev. E (3)

T. Mitsui and K. Aoki, “Michelson interferometry with quantum noise reduction,” Phys. Rev. E 87, 042403 (2013).
[CrossRef]

T. Mitsui and K. Aoki, “Direct optical observations of surface thermal motions at sub-shot noise levels,” Phys. Rev. E 80, 020602(R) (2009).
[CrossRef]

K. Aoki and T. Mitsui, “Spectral properties of thermal fluctuations on simple liquid surfaces below shot-noise levels,” Phys. Rev. E 86, 011602 (2012).
[CrossRef]

Phys. Rev. Lett. (7)

T. Yabuzaki, T. Mitsui, and U. Tanaka, “New type of high-resolution spectroscopy with a diode laser,” Phys. Rev. Lett. 67, 2453–2456 (1991).
[CrossRef]

H. Vahlbruch, M. Mehmet, N. Lastzka, B. Hage, S. Chelkowski, A. Franzen, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10  dB quantum noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Handchen, H. Vahlbruch, M. Mehmet, H. Muller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef]

T. Mitsui, “Spontaneous noise spectroscopy of an atomic magnetic resonance,” Phys. Rev. Lett. 84, 5292–5295 (2000).
[CrossRef]

D. F. Walls and P. Zoller, “Reduced quantum fluctuations in resonance fluorescence,” Phys. Rev. Lett. 47, 709–711 (1981).
[CrossRef]

L. Mandel, “Squeezed states and sub-Poissonian photon statistics,” Phys. Rev. Lett. 49, 136–138 (1982).
[CrossRef]

A. M. Bacon, H. Z. Zhao, L. J. Wang, and J. E. Thomas, “Optical dipole noise of two-level atoms,” Phys. Rev. Lett. 75, 1296–1299 (1995).
[CrossRef]

Zh. Exp. Teor. Fiz. (1)

E. B. Aleksandrov and V. S. Zapasskii, “Magnetic resonance in the Faraday-rotation noise spectrum,” Zh. Exp. Teor. Fiz. 81, 132–138 (1981).

Other (2)

See, for instanceP. Meystre and M. Sargent, Elements of Quantum Optics (Springer-Verlag, 1990).

D. A. Steck, “Rubidium 85 D Line Data,” “Rubidium 87 D Line Data,” http://steck.us/alkalidata (2010).

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Figures (4)

Fig. 1.
Fig. 1.

Schematics for the measurement systems. (a) A straightforward scheme for measuring intensity fluctuations of light passing through a vapor cell. (b) Measurement system with differential detection. (c) A measurement system with shot noise reduction. (d) A measurement system with both differential detection and shot noise reduction. BS, beam splitter; FFT, fast Fourier transform.

Fig. 2.
Fig. 2.

Schematics of the stabilized laser system used in the experiment. λ/2 and λ/4, half- and quarter-wave plates; lockin, lock-in amplifier; FR, Faraday rotator; PBS, polarizing beam splitter; PZT, piezoelectric transducer.

Fig. 3.
Fig. 3.

Spectra measured using the measurement systems ad, for (a) P=28, (b) 564 μW. The notations are the same for both figures. a: Straightforward measurement with no noise reduction, Eq. (2), Fig. 1(a) (red). b: Measurement with differential detection, Eq. (4), Fig. 1(b) (green). c: Measurement with shot noise reduction, Eq. (5), Fig. 1(c) (blue). d: Measurement with both differential detection and shot noise reduction, Eq. (6), Fig. 1(d) (magenta). The shot noise level (black, dashed). Measurement systems a and b are at the shot noise level at higher frequencies. System a is essentially indistinguishable from b in (a), but system a has visibly more noise at around f=105Hz in (b). Spectra at subshot noise levels are obtained for systems c and d, and c has visibly more extraneous noise (see text).

Fig. 4.
Fig. 4.

Spontaneous noise spectrum of Rb85-D2 transitions when a light source with FM noise is used. P=250 (red), 552 (blue), and 1240 μW (cyan). The vertical black line indicates F=2, 4 hyperfine splitting in the excited state, 184.0 MHz. A clear peak structure at this frequency, irrespective of the light power, is seen for P=552,1240μW cases, when the spontaneous noise is also appreciable at this frequency. The spectrum has larger values for larger P. The beam waist is 0.14 mm. The spontaneous noise spectrum obtained using a light source with approximately the same parameters, without the FM noise are also shown (black). These spectra do not have peak behavior at the frequency corresponding to hyperfine splitting, but otherwise agree quite well with the spectra obtained using a source with FM modulation. The overall magnitude of these reference spectra has been rescaled to make the comparisons clearer.

Equations (6)

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(ΔI)2=2eIΔf.
|D˜a(ω)|2=|S˜(ω)|2+|L˜(ω)|2+|N˜(ω)|2.
12|D˜b(ω)|2=12(|S˜A(ω)|2+|S˜B(ω)|2+|N˜A(ω)|2+|N˜B(ω)|2)
=|S˜(ω)|2+|N˜(ω)|2.
D˜c1(ω)¯D˜c2(ω)|S˜(ω)|2+|L˜(ω)|2,
12D˜d1(ω)¯D˜d2(ω)=12(|S˜A(ω)|2+|S˜B(ω)|2)=|S˜(ω)|2.

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