Abstract

A simple but rigorous analysis of the important sources of noise in homodyne detection is presented. Output noise and signal-to-noise ratios are compared for direct detection, conventional (one-port) homodyning, and two-port homodyning, in which one monitors both output ports of a 50–50 beam splitter. It is shown that two-port homodyning is insensitive to local-oscillator quadrature-phase noise and hence provides (1) a means of detecting reduced quadrature-phase fluctuations (squeezing) that is perhaps more practical than one-port homodyning and (2) an output signal-to-noise ratio that can be a modest to significant improvement over that of one-port homodyning and direct detection.

© 1984 Optical Society of America

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References

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  1. H. P. Yuen, J. H. Shapiro, in Coherence and Quantum Optics IV, L. Mandel, E. Wolf, eds. (Plenum, New York1978).
  2. J. H. Shapiro, H. P. Yuen, J. A. Machado Mata, IEEE Trans. Inf. Theory IT-25, 179 (1979).
    [CrossRef]
  3. H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980).
    [CrossRef]
  4. H. P. Yuen, V. W. S. Chan, Opt. Lett. 8, 177 (1983).
    [CrossRef] [PubMed]
  5. G. L. Abbas, V. W. S. Chan, T. K. Yee, Opt. Lett. 8, 419 (1983).
    [CrossRef] [PubMed]
  6. H. P. Yuen, Phys. Rev. A 13, 2226 (1976).
    [CrossRef]
  7. C. M. Caves, Phys. Rev. D 23, 1693 (1981).
    [CrossRef]
  8. B. L. Schumaker, C. M. Caves, in Coherence and Quantum Optics V, L. Mandel, E. Wolf, eds. (Plenum, New York, 1983).

1983 (2)

1981 (1)

C. M. Caves, Phys. Rev. D 23, 1693 (1981).
[CrossRef]

1980 (1)

H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980).
[CrossRef]

1979 (1)

J. H. Shapiro, H. P. Yuen, J. A. Machado Mata, IEEE Trans. Inf. Theory IT-25, 179 (1979).
[CrossRef]

1976 (1)

H. P. Yuen, Phys. Rev. A 13, 2226 (1976).
[CrossRef]

Abbas, G. L.

Caves, C. M.

C. M. Caves, Phys. Rev. D 23, 1693 (1981).
[CrossRef]

B. L. Schumaker, C. M. Caves, in Coherence and Quantum Optics V, L. Mandel, E. Wolf, eds. (Plenum, New York, 1983).

Chan, V. W. S.

Machado Mata, J. A.

J. H. Shapiro, H. P. Yuen, J. A. Machado Mata, IEEE Trans. Inf. Theory IT-25, 179 (1979).
[CrossRef]

Schumaker, B. L.

B. L. Schumaker, C. M. Caves, in Coherence and Quantum Optics V, L. Mandel, E. Wolf, eds. (Plenum, New York, 1983).

Shapiro, J. H.

H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980).
[CrossRef]

J. H. Shapiro, H. P. Yuen, J. A. Machado Mata, IEEE Trans. Inf. Theory IT-25, 179 (1979).
[CrossRef]

H. P. Yuen, J. H. Shapiro, in Coherence and Quantum Optics IV, L. Mandel, E. Wolf, eds. (Plenum, New York1978).

Yee, T. K.

Yuen, H. P.

H. P. Yuen, V. W. S. Chan, Opt. Lett. 8, 177 (1983).
[CrossRef] [PubMed]

H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980).
[CrossRef]

J. H. Shapiro, H. P. Yuen, J. A. Machado Mata, IEEE Trans. Inf. Theory IT-25, 179 (1979).
[CrossRef]

H. P. Yuen, Phys. Rev. A 13, 2226 (1976).
[CrossRef]

H. P. Yuen, J. H. Shapiro, in Coherence and Quantum Optics IV, L. Mandel, E. Wolf, eds. (Plenum, New York1978).

IEEE Trans. Inf. Theory (2)

J. H. Shapiro, H. P. Yuen, J. A. Machado Mata, IEEE Trans. Inf. Theory IT-25, 179 (1979).
[CrossRef]

H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

H. P. Yuen, Phys. Rev. A 13, 2226 (1976).
[CrossRef]

Phys. Rev. D (1)

C. M. Caves, Phys. Rev. D 23, 1693 (1981).
[CrossRef]

Other (2)

B. L. Schumaker, C. M. Caves, in Coherence and Quantum Optics V, L. Mandel, E. Wolf, eds. (Plenum, New York, 1983).

H. P. Yuen, J. H. Shapiro, in Coherence and Quantum Optics IV, L. Mandel, E. Wolf, eds. (Plenum, New York1978).

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Figures (1)

Fig. 1
Fig. 1

Yuen–Chan1 two-port homodyne detection scheme.

Equations (37)

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E ( t , x ) 1 2 { a exp [ i Ω s ( t x ) ] + a exp [ i Ω s ( t x ) ] } = a 1 cos Ω s ( t x ) + a 2 sin Ω s ( t x ) .
[ c d ] = U [ a b ] , U = e i Δ [ 1 T e i μ T T 1 T e i μ ] = ( U ) 1 .
a = A + Δ a A 1 + i A 2 + Δ a 1 + i Δ a 2 .
e i μ b B + Δ b = B + Δ b 1 + i Δ b 2 .
N a ¯ Δ a Δ a = Δ a 1 2 + Δ a 2 2 1 / 2 ;
N a a a = | A | 2 + N a ¯ ;
Δ N a 2 = Δ N a ¯ 2 + 4 ( A 1 Δ a 1 + A 2 Δ a 2 ) 2 + 4 Δ N a ¯ ( A 1 Δ a 1 + A 2 Δ a 2 ) sym ,
Δ a 1 2 = Δ a 2 2 = 1 4 ( 2 n ¯ + 1 ) , Δ a 1 Δ a 2 sym = 0 ,
N a ¯ = n ¯ , Δ N a ¯ 2 = n ¯ ( n ¯ + 1 ) ,
Δ N a 2 = | A | 2 ( 2 n ¯ + 1 ) + n ¯ ( n ¯ + 1 ) = N a + n ¯ ( n ¯ + 2 | A | 2 ) .
Δ a 1 2 2 = 1 4 e ± 2 r , Δ a 1 Δ a 2 sym = 0 ,
N a ¯ = sinh 2 r , Δ N a ¯ 2 = 1 2 sinh 2 2 r = N a ¯ ( 1 + cosh 2 r ) ,
Δ N a 2 = 1 2 sinh 2 2 r + A 1 2 e 2 r + A 2 2 e 2 r = N a + cosh 2 r sinh 2 r 2 sinh r ( A 1 2 e r A 2 2 e r ) .
N c = ( 1 T ) N a + T N b + T ( 1 T ) P ,
N d = T N a + ( 1 T ) N b T ( 1 T ) P ,
P 2 Re ( e i μ b a ) = 2 ( A 1 + Δ a 1 ) ( B + Δ b 1 ) + 2 Δ a 2 Δ b 2
N c T B 2 + 2 T ( 1 T ) A 1 B + 2 T B ( T Δ b 1 + 1 T Δ a 1 ) ,
N d ( 1 T ) B 2 2 T ( 1 T ) A 1 B + 2 1 T B ( 1 T Δ b 1 T Δ a 1 ) ,
N d = ( 1 T B T A 1 ) 2 ( 1 T ) B 2 2 T ( 1 T ) A 1 B ;
N d sig 2 T ( 1 T ) A 1 B .
Δ N d 2 = 4 ( 1 T B T A 1 ) 2 [ ( 1 T ) Δ b 1 2 + T Δ a 1 2 ] + 4 ( 1 T B T A 1 ) [ ( 1 T ) 3 / 2 Δ N b ¯ Δ b 1 sym T 3 / 2 Δ N a ¯ Δ a 1 sym + ( 1 T ) 2 Δ N b ¯ 2 + T 2 Δ N a ¯ 2 + 4 T ( 1 T ) X ,
X Δ a 1 2 Δ b 1 2 + Δ a 2 2 Δ b 2 2 1 / 8 + 2 Δ a 1 Δ a 2 sym Δ b 1 Δ b 2 sym .
Δ N d 2 = 4 ( 1 T B T A 1 ) 2 [ T Δ a 1 2 + ( 1 T ) Δ b 1 2 ] 4 ( 1 T ) B 2 [ T Δ a 1 2 + ( 1 T ) Δ b 1 2 ]
( SNR ) 1 | N d | sig ( Δ N d 2 ) 1 / 2 T A 1 [ T Δ a 1 2 + ( 1 T ) Δ b 1 2 ] 1 / 2 .
P = 2 B A 1 , Δ P 2 = 4 B 2 Δ a 1 2 + 4 A 1 2 Δ b 1 2 + 4 X 4 B 2 Δ a 1 2 ,
( SNR ) 2 P ( Δ P 2 ) 1 / 2 A 1 ( Δ a 1 2 ) 1 / 2 .
N a A 1 2 , Δ N a 2 4 A 1 2 Δ a 1 2 ,
( SNR ) D N a ( Δ N a 2 ) 1 / 2 A 1 2 ( Δ a 1 2 ) 1 / 2 = 1 2 ( SNR ) 2 .
d = e i Λ ( η d e i ν 1 η d 0 )
N d s i g = η N d s i g 2 η T ( 1 T ) A 1 B ;
Δ N d 2 = η 2 Δ N d 2 + η ( 1 η ) N d ( 1 T ) η 2 B 2 [ 4 T Δ a 1 2 + 4 ( 1 T ) Δ b 1 2 + ( 1 η ) / η ] ;
( SNR ) 1 = 2 T A 1 [ 4 T Δ a 1 2 + 4 ( 1 T ) Δ b 1 2 + ( 1 η ) / η ] 1 / 2 .
P = η P = 2 η B A 1 ,
Δ P 2 = η 2 Δ P 2 + η ( 1 η ) [ N c + N d ] η 2 B 2 [ 4 Δ a 1 2 + ( 1 η ) / η ] ;
( SNR ) 2 2 A 1 [ 4 Δ a 1 2 + ( 1 η ) / η ] 1 / 2 .
N a η N a η A 1 2 , Δ N a 2 η 2 A 1 2 [ 4 Δ a 1 2 + ( 1 η ) / η ] ;
( SNR ) D A 1 [ 4 Δ a 1 2 + ( 1 η ) / η ] 1 / 2 = 1 2 ( SNR ) 2 .

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