Abstract

We introduce a novel and useful concept in stochastic excitation spectroscopy:  a pair of complementary noises. This concept realizes a constant power-spectral density over the frequency region of interest by combining two power spectral densities that are complementary to each other. Consequently the pair is free from the limitations associated with a pseudo-random binary code and white noise; the pair is generated in a flexible manner and needs no ensemble averaging to reduce the power-spectral fluctuations. Our theory was supported by the experimental results with the magnetic resonances of Rb atoms.

© 1998 Optical Society of America

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  1. H. Baba and K. Sakurai, “Measurement system for temporal response of atomic and molecular system using the correlation method with pseudorandomly modulated laser,” Rev. Sci. Instrum. 54, 454–457 (1983).
    [Crossref]
  2. K. P. Dinse, M. P. Winters, and J. L. Hall, “Doppler-free optical multiplex spectroscopy with stochastic excitation,” J. Opt. Soc. Am. B 5, 1825–1831 (1988).
    [Crossref]
  3. 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] [PubMed]
  4. T. Kohmoto, T. Murakami, Y. Fukuda, and M. Kunitomo, “Noise excitation spectroscopy in Rb atoms,” in Progress in Crystal Growth and Characterization Materials (Elsevier, New York, 1996), pp. 367–370.
  5. S. Lathi, S. Kasapi, and Y. Yamamoto, “Phase-sensitive frequency-modulation noise spectroscopy with a diode laser,” Opt. Lett. 21, 1600–1602 (1996).
    [Crossref] [PubMed]
  6. K. Rza̧źewski, B. Stone, and M. Wilkens, “Laser-noise-induced intensity fluctuations in resonance fluorescence,” Phys. Rev. A 40, 2788–2789 (1989).
    [Crossref] [PubMed]
  7. P. L. Knight, W. A. Molander, and C. R. Stroud, “Asymmetric resonance fluorescence spectra in partially coherent fields,” Phys. Rev. A 17, 1547–1549 (1978).
    [Crossref]
  8. H. Ritsch, P. Zoller, and J. Cooper, “Power spectra and variance of laser-noise-induced population fluctuations in two-level atoms,” Phys. Rev. A 41, 2653–2667 (1990).
    [Crossref] [PubMed]
  9. Th. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, “Laser-noise-induced population fluctuations in two- and three-level systems,” Phys. Rev. A 38, 5652–5659 (1988).
    [Crossref] [PubMed]
  10. B. A. Ferguson and D. S. Elliott, “Laser-noise-induced intensity fluctuations in an optical interferometer,” Phys. Rev. A 41, 6183–6192 (1990).
    [Crossref] [PubMed]
  11. J. A. Decker, “Experimental realization of the multiplex advantage with a Hadamard-transform spectrometer,” Appl. Opt. 10, 510–514 (1971).
    [Crossref] [PubMed]
  12. T. Kohmoto, Y. Fukuda, M. Kunitomo, K. Ishikawa, K. Ebina, and M. Kaburagi, “Spectral hole burning in NMR: experimental test of relaxation theories by using well-characterized noise fields,” J. Lumin. 64, 51–54 (1995).
    [Crossref]
  13. K. Sköld, “A mechanical correlation chopper for thermal neutron spectroscopy,” Nucl. Instrum. Methods 63, 114–116 (1968).
    [Crossref]
  14. T. Arikawa, “A study of Hadamard mass spectroscopy,” Jpn. J. Appl. Phys. 18, 211–212 (1979).
    [Crossref]
  15. S. Miyamoto, H. Tsunemi, and K. Tsuno, “Some characteristics of the Hadamard transform x-ray telescope,” Nucl. Instrum. Methods 180, 557–572 (1981).
    [Crossref]
  16. H. G. Dehmelt, “Modulation of a light beam by precessing absorbing atoms,” Phys. Rev. 105, 1924 (1957).
    [Crossref]
  17. A. L. Bloom, “Principles of operation of the rubidium vapor magnetometer,” Appl. Opt. 1, 61–68 (1962).
    [Crossref]
  18. W. E. Bell and A. L. Bloom, “Optical detection of magnetic resonance in alkali metal vapor,” Phys. Rev. 107, 1559–1564 (1957).
    [Crossref]

1996 (1)

1995 (1)

T. Kohmoto, Y. Fukuda, M. Kunitomo, K. Ishikawa, K. Ebina, and M. Kaburagi, “Spectral hole burning in NMR: experimental test of relaxation theories by using well-characterized noise fields,” J. Lumin. 64, 51–54 (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] [PubMed]

1990 (2)

H. Ritsch, P. Zoller, and J. Cooper, “Power spectra and variance of laser-noise-induced population fluctuations in two-level atoms,” Phys. Rev. A 41, 2653–2667 (1990).
[Crossref] [PubMed]

B. A. Ferguson and D. S. Elliott, “Laser-noise-induced intensity fluctuations in an optical interferometer,” Phys. Rev. A 41, 6183–6192 (1990).
[Crossref] [PubMed]

1989 (1)

K. Rza̧źewski, B. Stone, and M. Wilkens, “Laser-noise-induced intensity fluctuations in resonance fluorescence,” Phys. Rev. A 40, 2788–2789 (1989).
[Crossref] [PubMed]

1988 (2)

K. P. Dinse, M. P. Winters, and J. L. Hall, “Doppler-free optical multiplex spectroscopy with stochastic excitation,” J. Opt. Soc. Am. B 5, 1825–1831 (1988).
[Crossref]

Th. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, “Laser-noise-induced population fluctuations in two- and three-level systems,” Phys. Rev. A 38, 5652–5659 (1988).
[Crossref] [PubMed]

1983 (1)

H. Baba and K. Sakurai, “Measurement system for temporal response of atomic and molecular system using the correlation method with pseudorandomly modulated laser,” Rev. Sci. Instrum. 54, 454–457 (1983).
[Crossref]

1981 (1)

S. Miyamoto, H. Tsunemi, and K. Tsuno, “Some characteristics of the Hadamard transform x-ray telescope,” Nucl. Instrum. Methods 180, 557–572 (1981).
[Crossref]

1979 (1)

T. Arikawa, “A study of Hadamard mass spectroscopy,” Jpn. J. Appl. Phys. 18, 211–212 (1979).
[Crossref]

1978 (1)

P. L. Knight, W. A. Molander, and C. R. Stroud, “Asymmetric resonance fluorescence spectra in partially coherent fields,” Phys. Rev. A 17, 1547–1549 (1978).
[Crossref]

1971 (1)

1968 (1)

K. Sköld, “A mechanical correlation chopper for thermal neutron spectroscopy,” Nucl. Instrum. Methods 63, 114–116 (1968).
[Crossref]

1962 (1)

1957 (2)

W. E. Bell and A. L. Bloom, “Optical detection of magnetic resonance in alkali metal vapor,” Phys. Rev. 107, 1559–1564 (1957).
[Crossref]

H. G. Dehmelt, “Modulation of a light beam by precessing absorbing atoms,” Phys. Rev. 105, 1924 (1957).
[Crossref]

Arikawa, T.

T. Arikawa, “A study of Hadamard mass spectroscopy,” Jpn. J. Appl. Phys. 18, 211–212 (1979).
[Crossref]

Baba, H.

H. Baba and K. Sakurai, “Measurement system for temporal response of atomic and molecular system using the correlation method with pseudorandomly modulated laser,” Rev. Sci. Instrum. 54, 454–457 (1983).
[Crossref]

Bell, W. E.

W. E. Bell and A. L. Bloom, “Optical detection of magnetic resonance in alkali metal vapor,” Phys. Rev. 107, 1559–1564 (1957).
[Crossref]

Bloom, A. L.

A. L. Bloom, “Principles of operation of the rubidium vapor magnetometer,” Appl. Opt. 1, 61–68 (1962).
[Crossref]

W. E. Bell and A. L. Bloom, “Optical detection of magnetic resonance in alkali metal vapor,” Phys. Rev. 107, 1559–1564 (1957).
[Crossref]

Cooper, J.

H. Ritsch, P. Zoller, and J. Cooper, “Power spectra and variance of laser-noise-induced population fluctuations in two-level atoms,” Phys. Rev. A 41, 2653–2667 (1990).
[Crossref] [PubMed]

Th. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, “Laser-noise-induced population fluctuations in two- and three-level systems,” Phys. Rev. A 38, 5652–5659 (1988).
[Crossref] [PubMed]

Decker, J. A.

Dehmelt, H. G.

H. G. Dehmelt, “Modulation of a light beam by precessing absorbing atoms,” Phys. Rev. 105, 1924 (1957).
[Crossref]

Dinse, K. P.

Ebina, K.

T. Kohmoto, Y. Fukuda, M. Kunitomo, K. Ishikawa, K. Ebina, and M. Kaburagi, “Spectral hole burning in NMR: experimental test of relaxation theories by using well-characterized noise fields,” J. Lumin. 64, 51–54 (1995).
[Crossref]

Elliott, D. S.

B. A. Ferguson and D. S. Elliott, “Laser-noise-induced intensity fluctuations in an optical interferometer,” Phys. Rev. A 41, 6183–6192 (1990).
[Crossref] [PubMed]

Ferguson, B. A.

B. A. Ferguson and D. S. Elliott, “Laser-noise-induced intensity fluctuations in an optical interferometer,” Phys. Rev. A 41, 6183–6192 (1990).
[Crossref] [PubMed]

Fukuda, Y.

T. Kohmoto, Y. Fukuda, M. Kunitomo, K. Ishikawa, K. Ebina, and M. Kaburagi, “Spectral hole burning in NMR: experimental test of relaxation theories by using well-characterized noise fields,” J. Lumin. 64, 51–54 (1995).
[Crossref]

T. Kohmoto, T. Murakami, Y. Fukuda, and M. Kunitomo, “Noise excitation spectroscopy in Rb atoms,” in Progress in Crystal Growth and Characterization Materials (Elsevier, New York, 1996), pp. 367–370.

Hall, J. L.

Haslwanter, Th.

Th. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, “Laser-noise-induced population fluctuations in two- and three-level systems,” Phys. Rev. A 38, 5652–5659 (1988).
[Crossref] [PubMed]

Ishikawa, K.

T. Kohmoto, Y. Fukuda, M. Kunitomo, K. Ishikawa, K. Ebina, and M. Kaburagi, “Spectral hole burning in NMR: experimental test of relaxation theories by using well-characterized noise fields,” J. Lumin. 64, 51–54 (1995).
[Crossref]

Kaburagi, M.

T. Kohmoto, Y. Fukuda, M. Kunitomo, K. Ishikawa, K. Ebina, and M. Kaburagi, “Spectral hole burning in NMR: experimental test of relaxation theories by using well-characterized noise fields,” J. Lumin. 64, 51–54 (1995).
[Crossref]

Kasapi, S.

Knight, P. L.

P. L. Knight, W. A. Molander, and C. R. Stroud, “Asymmetric resonance fluorescence spectra in partially coherent fields,” Phys. Rev. A 17, 1547–1549 (1978).
[Crossref]

Kohmoto, T.

T. Kohmoto, Y. Fukuda, M. Kunitomo, K. Ishikawa, K. Ebina, and M. Kaburagi, “Spectral hole burning in NMR: experimental test of relaxation theories by using well-characterized noise fields,” J. Lumin. 64, 51–54 (1995).
[Crossref]

T. Kohmoto, T. Murakami, Y. Fukuda, and M. Kunitomo, “Noise excitation spectroscopy in Rb atoms,” in Progress in Crystal Growth and Characterization Materials (Elsevier, New York, 1996), pp. 367–370.

Kunitomo, M.

T. Kohmoto, Y. Fukuda, M. Kunitomo, K. Ishikawa, K. Ebina, and M. Kaburagi, “Spectral hole burning in NMR: experimental test of relaxation theories by using well-characterized noise fields,” J. Lumin. 64, 51–54 (1995).
[Crossref]

T. Kohmoto, T. Murakami, Y. Fukuda, and M. Kunitomo, “Noise excitation spectroscopy in Rb atoms,” in Progress in Crystal Growth and Characterization Materials (Elsevier, New York, 1996), pp. 367–370.

Lathi, S.

Mitsui, 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] [PubMed]

Miyamoto, S.

S. Miyamoto, H. Tsunemi, and K. Tsuno, “Some characteristics of the Hadamard transform x-ray telescope,” Nucl. Instrum. Methods 180, 557–572 (1981).
[Crossref]

Molander, W. A.

P. L. Knight, W. A. Molander, and C. R. Stroud, “Asymmetric resonance fluorescence spectra in partially coherent fields,” Phys. Rev. A 17, 1547–1549 (1978).
[Crossref]

Murakami, T.

T. Kohmoto, T. Murakami, Y. Fukuda, and M. Kunitomo, “Noise excitation spectroscopy in Rb atoms,” in Progress in Crystal Growth and Characterization Materials (Elsevier, New York, 1996), pp. 367–370.

Ritsch, H.

H. Ritsch, P. Zoller, and J. Cooper, “Power spectra and variance of laser-noise-induced population fluctuations in two-level atoms,” Phys. Rev. A 41, 2653–2667 (1990).
[Crossref] [PubMed]

Th. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, “Laser-noise-induced population fluctuations in two- and three-level systems,” Phys. Rev. A 38, 5652–5659 (1988).
[Crossref] [PubMed]

Rza¸zewski, K.

K. Rza̧źewski, B. Stone, and M. Wilkens, “Laser-noise-induced intensity fluctuations in resonance fluorescence,” Phys. Rev. A 40, 2788–2789 (1989).
[Crossref] [PubMed]

Sakurai, K.

H. Baba and K. Sakurai, “Measurement system for temporal response of atomic and molecular system using the correlation method with pseudorandomly modulated laser,” Rev. Sci. Instrum. 54, 454–457 (1983).
[Crossref]

Sköld, K.

K. Sköld, “A mechanical correlation chopper for thermal neutron spectroscopy,” Nucl. Instrum. Methods 63, 114–116 (1968).
[Crossref]

Stone, B.

K. Rza̧źewski, B. Stone, and M. Wilkens, “Laser-noise-induced intensity fluctuations in resonance fluorescence,” Phys. Rev. A 40, 2788–2789 (1989).
[Crossref] [PubMed]

Stroud, C. R.

P. L. Knight, W. A. Molander, and C. R. Stroud, “Asymmetric resonance fluorescence spectra in partially coherent fields,” Phys. Rev. A 17, 1547–1549 (1978).
[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] [PubMed]

Tsunemi, H.

S. Miyamoto, H. Tsunemi, and K. Tsuno, “Some characteristics of the Hadamard transform x-ray telescope,” Nucl. Instrum. Methods 180, 557–572 (1981).
[Crossref]

Tsuno, K.

S. Miyamoto, H. Tsunemi, and K. Tsuno, “Some characteristics of the Hadamard transform x-ray telescope,” Nucl. Instrum. Methods 180, 557–572 (1981).
[Crossref]

Wilkens, M.

K. Rza̧źewski, B. Stone, and M. Wilkens, “Laser-noise-induced intensity fluctuations in resonance fluorescence,” Phys. Rev. A 40, 2788–2789 (1989).
[Crossref] [PubMed]

Winters, M. P.

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] [PubMed]

Yamamoto, Y.

Zoller, P.

H. Ritsch, P. Zoller, and J. Cooper, “Power spectra and variance of laser-noise-induced population fluctuations in two-level atoms,” Phys. Rev. A 41, 2653–2667 (1990).
[Crossref] [PubMed]

Th. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, “Laser-noise-induced population fluctuations in two- and three-level systems,” Phys. Rev. A 38, 5652–5659 (1988).
[Crossref] [PubMed]

Appl. Opt. (2)

J. Lumin. (1)

T. Kohmoto, Y. Fukuda, M. Kunitomo, K. Ishikawa, K. Ebina, and M. Kaburagi, “Spectral hole burning in NMR: experimental test of relaxation theories by using well-characterized noise fields,” J. Lumin. 64, 51–54 (1995).
[Crossref]

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

Jpn. J. Appl. Phys. (1)

T. Arikawa, “A study of Hadamard mass spectroscopy,” Jpn. J. Appl. Phys. 18, 211–212 (1979).
[Crossref]

Nucl. Instrum. Methods (2)

S. Miyamoto, H. Tsunemi, and K. Tsuno, “Some characteristics of the Hadamard transform x-ray telescope,” Nucl. Instrum. Methods 180, 557–572 (1981).
[Crossref]

K. Sköld, “A mechanical correlation chopper for thermal neutron spectroscopy,” Nucl. Instrum. Methods 63, 114–116 (1968).
[Crossref]

Opt. Lett. (1)

Phys. Rev. (2)

H. G. Dehmelt, “Modulation of a light beam by precessing absorbing atoms,” Phys. Rev. 105, 1924 (1957).
[Crossref]

W. E. Bell and A. L. Bloom, “Optical detection of magnetic resonance in alkali metal vapor,” Phys. Rev. 107, 1559–1564 (1957).
[Crossref]

Phys. Rev. A (5)

K. Rza̧źewski, B. Stone, and M. Wilkens, “Laser-noise-induced intensity fluctuations in resonance fluorescence,” Phys. Rev. A 40, 2788–2789 (1989).
[Crossref] [PubMed]

P. L. Knight, W. A. Molander, and C. R. Stroud, “Asymmetric resonance fluorescence spectra in partially coherent fields,” Phys. Rev. A 17, 1547–1549 (1978).
[Crossref]

H. Ritsch, P. Zoller, and J. Cooper, “Power spectra and variance of laser-noise-induced population fluctuations in two-level atoms,” Phys. Rev. A 41, 2653–2667 (1990).
[Crossref] [PubMed]

Th. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, “Laser-noise-induced population fluctuations in two- and three-level systems,” Phys. Rev. A 38, 5652–5659 (1988).
[Crossref] [PubMed]

B. A. Ferguson and D. S. Elliott, “Laser-noise-induced intensity fluctuations in an optical interferometer,” Phys. Rev. A 41, 6183–6192 (1990).
[Crossref] [PubMed]

Phys. Rev. Lett. (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] [PubMed]

Rev. Sci. Instrum. (1)

H. Baba and K. Sakurai, “Measurement system for temporal response of atomic and molecular system using the correlation method with pseudorandomly modulated laser,” Rev. Sci. Instrum. 54, 454–457 (1983).
[Crossref]

Other (1)

T. Kohmoto, T. Murakami, Y. Fukuda, and M. Kunitomo, “Noise excitation spectroscopy in Rb atoms,” in Progress in Crystal Growth and Characterization Materials (Elsevier, New York, 1996), pp. 367–370.

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Figures (4)

Fig. 1
Fig. 1

Example of the power spectra for a pair of complementary noises, NI(t) and NII(t), and for a white noise, N(t):  (a) QnI for NI(t), (b) QnII for NII(t), (c) QnI+QnII, and (d) Qn for N(t). Details are described in the experimental section.

Fig. 2
Fig. 2

Magnetic resonance probed with optical pumping. The geometry of the magnetic fields and the laser beams is shown, which is detailed in the text.

Fig. 3
Fig. 3

Experimental setup. The optical configuration was almost the same as that in Fig. 2, except that a single laser beam serves both for the pumping and the probing simultaneously. AWG, arbitrary waveform generator; WM, waveform memory.

Fig. 4
Fig. 4

Output power spectra for the magnetic resonance of 85Rb excited with a PCN and a white noise:  (a) PnI excited with NI(t), (b) PnII excited with NII(t), (c) PnI+PnII, (d) Pn excited with the white noise in Fig. 1(d).

Equations (24)

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

Qn=0Tdt N(t)exp(inΔωt)2
k=0m-1Δt N(kΔt)exp(inΔωkΔt)2.
g(t)=exp[-(γ-iω0)t],
I(t)=-tdtN(t)exp[(γ-iω0)(t-t)]+c.c.,
Pn=0Tdtexp(inΔωt)I(t)2
=Qn(nΔω-ω0)2+γ2,
NI(t)=AT Ren=-(m/2)(m/2)-1 exp(iθn-inΔωt)=ATn=-(m/2)(m/2)-1 cos(θn-nΔωt),
NII(t)=AT Imn=-(m/2)(m/2)-1 exp(iθn-inΔωt)=ATn=-(m/2)(m/2)-1 sin(θn-nΔωt),
QnI=0Tdt NI(t)exp(inΔωt)2=A22 [1+cos(θn+θ-n)],
QnII=0Tdt NII(t)exp(inΔωt)2=A22 [1-cos(θn+θ-n)] .
QnI+QnII=A2.
NI(t)=n=-(m/2)(m/2)-1Cn exp(-inΔωt).
2TCnA=exp(iθn)+exp(-iθ-n).
Pnh=0Tdt exp(inΔωt)Ih(t)2,
=Qnh(nΔω-ω0)2+γ2,
ddtMx=γgHzMy-(Γ+P)Mx,
ddtMy=-γgHzMx-(Γ+P)My+γgHx(t)Mz,
ddtMz=-(Γ+P)Mz-γgHx(t)My+P,
MzPΓ+P.
ddtM˜=(iγgHz-Γ-P)M˜+γgMzHx(t).
M˜=exp[-(γ-iω0)t]-tdtN(t)exp[(γ-iω0)t].
γ=Γ+P,
ω0=γgHz,
N(t)=γgMzHx(t),

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