Abstract

We report on experimental demodulation of nonstationary shot noise, which is associated with strongly modulated light. For sinusoidal modulation and demodulation, measurements confirm theoretical predictions of 1.8-dB excess noise in the modulation quadrature and 3-dB noise reduction in the opposite quadrature, relative to the standard quantum limit. Demodulation with a third harmonic produces noise correlated with that which is due to the fundamental. Reducing excess noise by 0.8 dB in the modulation quadrature, by combining the fundamental and third harmonics in a 2:1 ratio, is shown to be feasible.

© 1993 Optical Society of America

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References

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  1. B. J. Meers, K. A. Strain, Phys. Rev. A 44, 4693 (1991).
    [CrossRef] [PubMed]
  2. A. J. Stevenson, M. B. Gray, H.-A. Bachor, D. E. McClelland, “Quantum-noise-limited interferometric phase measurements,” Appl. Opt. (to be published).
    [PubMed]
  3. T. M. Biebauer, R. Schilling, K. Danzmann, A. Rudiger, W. Winkler, Phys. Rev. A 43, 5022 (1991).
    [CrossRef]
  4. N. Mio, K. Tsubono, Phys. Lett. A 164, 255 (1992).
    [CrossRef]
  5. H.-A. Bachor, P. J. Manson, J. Mod. Opt. 27, 1727 (1990).
    [CrossRef]

1992 (1)

N. Mio, K. Tsubono, Phys. Lett. A 164, 255 (1992).
[CrossRef]

1991 (2)

B. J. Meers, K. A. Strain, Phys. Rev. A 44, 4693 (1991).
[CrossRef] [PubMed]

T. M. Biebauer, R. Schilling, K. Danzmann, A. Rudiger, W. Winkler, Phys. Rev. A 43, 5022 (1991).
[CrossRef]

1990 (1)

H.-A. Bachor, P. J. Manson, J. Mod. Opt. 27, 1727 (1990).
[CrossRef]

Bachor, H.-A.

H.-A. Bachor, P. J. Manson, J. Mod. Opt. 27, 1727 (1990).
[CrossRef]

A. J. Stevenson, M. B. Gray, H.-A. Bachor, D. E. McClelland, “Quantum-noise-limited interferometric phase measurements,” Appl. Opt. (to be published).
[PubMed]

Biebauer, T. M.

T. M. Biebauer, R. Schilling, K. Danzmann, A. Rudiger, W. Winkler, Phys. Rev. A 43, 5022 (1991).
[CrossRef]

Danzmann, K.

T. M. Biebauer, R. Schilling, K. Danzmann, A. Rudiger, W. Winkler, Phys. Rev. A 43, 5022 (1991).
[CrossRef]

Gray, M. B.

A. J. Stevenson, M. B. Gray, H.-A. Bachor, D. E. McClelland, “Quantum-noise-limited interferometric phase measurements,” Appl. Opt. (to be published).
[PubMed]

Manson, P. J.

H.-A. Bachor, P. J. Manson, J. Mod. Opt. 27, 1727 (1990).
[CrossRef]

McClelland, D. E.

A. J. Stevenson, M. B. Gray, H.-A. Bachor, D. E. McClelland, “Quantum-noise-limited interferometric phase measurements,” Appl. Opt. (to be published).
[PubMed]

Meers, B. J.

B. J. Meers, K. A. Strain, Phys. Rev. A 44, 4693 (1991).
[CrossRef] [PubMed]

Mio, N.

N. Mio, K. Tsubono, Phys. Lett. A 164, 255 (1992).
[CrossRef]

Rudiger, A.

T. M. Biebauer, R. Schilling, K. Danzmann, A. Rudiger, W. Winkler, Phys. Rev. A 43, 5022 (1991).
[CrossRef]

Schilling, R.

T. M. Biebauer, R. Schilling, K. Danzmann, A. Rudiger, W. Winkler, Phys. Rev. A 43, 5022 (1991).
[CrossRef]

Stevenson, A. J.

A. J. Stevenson, M. B. Gray, H.-A. Bachor, D. E. McClelland, “Quantum-noise-limited interferometric phase measurements,” Appl. Opt. (to be published).
[PubMed]

Strain, K. A.

B. J. Meers, K. A. Strain, Phys. Rev. A 44, 4693 (1991).
[CrossRef] [PubMed]

Tsubono, K.

N. Mio, K. Tsubono, Phys. Lett. A 164, 255 (1992).
[CrossRef]

Winkler, W.

T. M. Biebauer, R. Schilling, K. Danzmann, A. Rudiger, W. Winkler, Phys. Rev. A 43, 5022 (1991).
[CrossRef]

J. Mod. Opt. (1)

H.-A. Bachor, P. J. Manson, J. Mod. Opt. 27, 1727 (1990).
[CrossRef]

Phys. Lett. A (1)

N. Mio, K. Tsubono, Phys. Lett. A 164, 255 (1992).
[CrossRef]

Phys. Rev. A (2)

T. M. Biebauer, R. Schilling, K. Danzmann, A. Rudiger, W. Winkler, Phys. Rev. A 43, 5022 (1991).
[CrossRef]

B. J. Meers, K. A. Strain, Phys. Rev. A 44, 4693 (1991).
[CrossRef] [PubMed]

Other (1)

A. J. Stevenson, M. B. Gray, H.-A. Bachor, D. E. McClelland, “Quantum-noise-limited interferometric phase measurements,” Appl. Opt. (to be published).
[PubMed]

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Figures (5)

Fig. 1
Fig. 1

(a) Nonstationary noise in(t) = white noise × sin2(2πfmt). (b) i(t)D(t) [D(t) = sin(2πfmt)]. (c) i(t)D(t) [D(t) = cos(2πfmt)].

Fig. 2
Fig. 2

Experimental arrangement for measuring the phase dependence of nonstationary shot noise. BS’s, beam splitters; EOM, electro-optic modulator; HV, high-voltage; PD’s, photodetectors; LP, low-pass; HP, high-pass.

Fig. 3
Fig. 3

(a) Demodulated noise power at 10 MHz (using fundamental harmonic only). Resolution bandwidth, 100 kHz; video bandwidth, 100 Hz. (b) Same as in (a) but sweeping demodulation frequency offset through 0 Hz.

Fig. 4
Fig. 4

D(t) and demodulated noise in(t)D(t): (a) φ = 0, θ = 0, (b) φ = π/2, θ = 0, (c) φ = 0, θ = π, (d) φ = π/2, θ = π.

Fig. 5
Fig. 5

(a) Theoretical demodulated noise, in decibels relative to Psql, with γ = 0.5, φ(t) scanned rapidly, and θ varied slowly. (b) Experimental noise using the first and third harmonics, with γ = 0.36. (c) Experimental noise using the first harmonic (37.5 MHz) only. (d) Experimental noise using the third harmonic (112.5 MHz) only.

Equations (8)

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

i n ( t ) i n ( t + τ ) = e i ( t ) δ ( τ ) ,
y n ( t ) y n ( t + τ ) = e D 2 ( t ) i ( t ) δ ( τ ) .
P n ( f , t ) = 2 e D 2 ( t ) i ( t ) ¯ ,
i ( t ) = i 0 [ 1 - cos ( 4 π f m t ) ] ,
D ( t ) = 2 1 / 2 sin [ 2 π f m t + φ ( t ) ] ,
P n ( f , t ) = P sql { 1 + 1 / 2 cos [ 2 φ ( t ) ] } ,
D ( t ) = 2 1 / 2 { sin [ 2 π f m t + φ ( t ) ] + γ sin [ 6 π f m t + 3 φ ( t ) + θ ] } ,
P n ( f , t ) = P sql { 1 + 1 / 2 cos [ 2 φ ( t ) ] + γ 2 - γ cos [ 2 φ ( t ) + θ ] } .

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