Abstract

We experimentally demonstrate that a type-II pulsed optical parametric amplifier operated in a phase-insensitive configuration works as a near-perfect classical optical amplifier whose noise figure approaches 3 dB at high gains. We further demonstrate that, when operated in a phase-sensitive configuration, this amplifier works as a quantum-optical amplifier whose noise figure goes below 3 dB and approaches 0 dB at high gains. The noise figure of 1.45 ± 0.2 dB, measured for a gain of 9 dB, is clearly in the quantum regime.

© 1993 Optical Society of America

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  1. T. Saitoh, T. Mukai, IEEE J. Quantum Electron. QE-23, 1010 (1987).
    [CrossRef]
  2. M. J. Petit, R. A. Backer, A. Hadjifotiou, Electron. Lett. 25, 273 (1989).
    [CrossRef]
  3. W. H. Louisell, Coupled Mode and Parametric Electronics (Wiley, New York, 1960); Radiation and Noise in Quantum Electronics (McGraw-Hill, New York, 1964).
  4. C. M. Caves, Phys. Rev. D 26, 1817 (1982).
    [CrossRef]
  5. H. P. Yuen, Phys. Rev. Lett. 56, 2176 (1986).
    [CrossRef] [PubMed]
  6. Y. Yamamoto, S. Machida, S. Saito, N. Imoto, T. Yanagawa, M. Kitagawa, G. Bjork, Prog. Opt. 28, 87 (1990).
    [CrossRef]
  7. M. J. Collett, D. F. Walls, Phys. Rev. Lett. 61, 2442 (1988).
    [CrossRef] [PubMed]
  8. N. C. Wong, Opt. Lett. 16, 1698 (1991).
    [CrossRef] [PubMed]
  9. O. Aytur, P. Kumar, Phys. Rev. Lett. 65, 1551 (1990).
    [CrossRef]
  10. R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, M. J. Potasek, Phys. Rev. Lett. 59, 2566 (1987).
    [CrossRef] [PubMed]
  11. P. D. Townsend, R. Loudon, Phys. Rev. A 45, 458 (1992).
    [CrossRef] [PubMed]
  12. A. Laporta, R. E. Slusher, B. Yurke, Phys. Rev. Lett. 62, 28 (1989).
    [CrossRef]
  13. J. A. Levenson, I. Abram, Th. Rivera, Ph. Fayolle, J. C. Garreau, Ph. Grangier, Phys. Rev. Lett. 70, 267 (1993).
    [CrossRef] [PubMed]
  14. A. LaPorta, R. E. Slusher, Phys. Rev. A 44, 2013 (1991).
    [CrossRef]

1993 (1)

J. A. Levenson, I. Abram, Th. Rivera, Ph. Fayolle, J. C. Garreau, Ph. Grangier, Phys. Rev. Lett. 70, 267 (1993).
[CrossRef] [PubMed]

1992 (1)

P. D. Townsend, R. Loudon, Phys. Rev. A 45, 458 (1992).
[CrossRef] [PubMed]

1991 (2)

A. LaPorta, R. E. Slusher, Phys. Rev. A 44, 2013 (1991).
[CrossRef]

N. C. Wong, Opt. Lett. 16, 1698 (1991).
[CrossRef] [PubMed]

1990 (2)

Y. Yamamoto, S. Machida, S. Saito, N. Imoto, T. Yanagawa, M. Kitagawa, G. Bjork, Prog. Opt. 28, 87 (1990).
[CrossRef]

O. Aytur, P. Kumar, Phys. Rev. Lett. 65, 1551 (1990).
[CrossRef]

1989 (2)

M. J. Petit, R. A. Backer, A. Hadjifotiou, Electron. Lett. 25, 273 (1989).
[CrossRef]

A. Laporta, R. E. Slusher, B. Yurke, Phys. Rev. Lett. 62, 28 (1989).
[CrossRef]

1988 (1)

M. J. Collett, D. F. Walls, Phys. Rev. Lett. 61, 2442 (1988).
[CrossRef] [PubMed]

1987 (2)

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, M. J. Potasek, Phys. Rev. Lett. 59, 2566 (1987).
[CrossRef] [PubMed]

T. Saitoh, T. Mukai, IEEE J. Quantum Electron. QE-23, 1010 (1987).
[CrossRef]

1986 (1)

H. P. Yuen, Phys. Rev. Lett. 56, 2176 (1986).
[CrossRef] [PubMed]

1982 (1)

C. M. Caves, Phys. Rev. D 26, 1817 (1982).
[CrossRef]

Abram, I.

J. A. Levenson, I. Abram, Th. Rivera, Ph. Fayolle, J. C. Garreau, Ph. Grangier, Phys. Rev. Lett. 70, 267 (1993).
[CrossRef] [PubMed]

Aytur, O.

O. Aytur, P. Kumar, Phys. Rev. Lett. 65, 1551 (1990).
[CrossRef]

Backer, R. A.

M. J. Petit, R. A. Backer, A. Hadjifotiou, Electron. Lett. 25, 273 (1989).
[CrossRef]

Bjork, G.

Y. Yamamoto, S. Machida, S. Saito, N. Imoto, T. Yanagawa, M. Kitagawa, G. Bjork, Prog. Opt. 28, 87 (1990).
[CrossRef]

Caves, C. M.

C. M. Caves, Phys. Rev. D 26, 1817 (1982).
[CrossRef]

Collett, M. J.

M. J. Collett, D. F. Walls, Phys. Rev. Lett. 61, 2442 (1988).
[CrossRef] [PubMed]

Fayolle, Ph.

J. A. Levenson, I. Abram, Th. Rivera, Ph. Fayolle, J. C. Garreau, Ph. Grangier, Phys. Rev. Lett. 70, 267 (1993).
[CrossRef] [PubMed]

Garreau, J. C.

J. A. Levenson, I. Abram, Th. Rivera, Ph. Fayolle, J. C. Garreau, Ph. Grangier, Phys. Rev. Lett. 70, 267 (1993).
[CrossRef] [PubMed]

Grangier, P.

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, M. J. Potasek, Phys. Rev. Lett. 59, 2566 (1987).
[CrossRef] [PubMed]

Grangier, Ph.

J. A. Levenson, I. Abram, Th. Rivera, Ph. Fayolle, J. C. Garreau, Ph. Grangier, Phys. Rev. Lett. 70, 267 (1993).
[CrossRef] [PubMed]

Hadjifotiou, A.

M. J. Petit, R. A. Backer, A. Hadjifotiou, Electron. Lett. 25, 273 (1989).
[CrossRef]

Imoto, N.

Y. Yamamoto, S. Machida, S. Saito, N. Imoto, T. Yanagawa, M. Kitagawa, G. Bjork, Prog. Opt. 28, 87 (1990).
[CrossRef]

Kitagawa, M.

Y. Yamamoto, S. Machida, S. Saito, N. Imoto, T. Yanagawa, M. Kitagawa, G. Bjork, Prog. Opt. 28, 87 (1990).
[CrossRef]

Kumar, P.

O. Aytur, P. Kumar, Phys. Rev. Lett. 65, 1551 (1990).
[CrossRef]

LaPorta, A.

A. LaPorta, R. E. Slusher, Phys. Rev. A 44, 2013 (1991).
[CrossRef]

A. Laporta, R. E. Slusher, B. Yurke, Phys. Rev. Lett. 62, 28 (1989).
[CrossRef]

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, M. J. Potasek, Phys. Rev. Lett. 59, 2566 (1987).
[CrossRef] [PubMed]

Levenson, J. A.

J. A. Levenson, I. Abram, Th. Rivera, Ph. Fayolle, J. C. Garreau, Ph. Grangier, Phys. Rev. Lett. 70, 267 (1993).
[CrossRef] [PubMed]

Loudon, R.

P. D. Townsend, R. Loudon, Phys. Rev. A 45, 458 (1992).
[CrossRef] [PubMed]

Louisell, W. H.

W. H. Louisell, Coupled Mode and Parametric Electronics (Wiley, New York, 1960); Radiation and Noise in Quantum Electronics (McGraw-Hill, New York, 1964).

Machida, S.

Y. Yamamoto, S. Machida, S. Saito, N. Imoto, T. Yanagawa, M. Kitagawa, G. Bjork, Prog. Opt. 28, 87 (1990).
[CrossRef]

Mukai, T.

T. Saitoh, T. Mukai, IEEE J. Quantum Electron. QE-23, 1010 (1987).
[CrossRef]

Petit, M. J.

M. J. Petit, R. A. Backer, A. Hadjifotiou, Electron. Lett. 25, 273 (1989).
[CrossRef]

Potasek, M. J.

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, M. J. Potasek, Phys. Rev. Lett. 59, 2566 (1987).
[CrossRef] [PubMed]

Rivera, Th.

J. A. Levenson, I. Abram, Th. Rivera, Ph. Fayolle, J. C. Garreau, Ph. Grangier, Phys. Rev. Lett. 70, 267 (1993).
[CrossRef] [PubMed]

Saito, S.

Y. Yamamoto, S. Machida, S. Saito, N. Imoto, T. Yanagawa, M. Kitagawa, G. Bjork, Prog. Opt. 28, 87 (1990).
[CrossRef]

Saitoh, T.

T. Saitoh, T. Mukai, IEEE J. Quantum Electron. QE-23, 1010 (1987).
[CrossRef]

Slusher, R. E.

A. LaPorta, R. E. Slusher, Phys. Rev. A 44, 2013 (1991).
[CrossRef]

A. Laporta, R. E. Slusher, B. Yurke, Phys. Rev. Lett. 62, 28 (1989).
[CrossRef]

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, M. J. Potasek, Phys. Rev. Lett. 59, 2566 (1987).
[CrossRef] [PubMed]

Townsend, P. D.

P. D. Townsend, R. Loudon, Phys. Rev. A 45, 458 (1992).
[CrossRef] [PubMed]

Walls, D. F.

M. J. Collett, D. F. Walls, Phys. Rev. Lett. 61, 2442 (1988).
[CrossRef] [PubMed]

Wong, N. C.

Yamamoto, Y.

Y. Yamamoto, S. Machida, S. Saito, N. Imoto, T. Yanagawa, M. Kitagawa, G. Bjork, Prog. Opt. 28, 87 (1990).
[CrossRef]

Yanagawa, T.

Y. Yamamoto, S. Machida, S. Saito, N. Imoto, T. Yanagawa, M. Kitagawa, G. Bjork, Prog. Opt. 28, 87 (1990).
[CrossRef]

Yuen, H. P.

H. P. Yuen, Phys. Rev. Lett. 56, 2176 (1986).
[CrossRef] [PubMed]

Yurke, B.

A. Laporta, R. E. Slusher, B. Yurke, Phys. Rev. Lett. 62, 28 (1989).
[CrossRef]

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, M. J. Potasek, Phys. Rev. Lett. 59, 2566 (1987).
[CrossRef] [PubMed]

Electron. Lett. (1)

M. J. Petit, R. A. Backer, A. Hadjifotiou, Electron. Lett. 25, 273 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

T. Saitoh, T. Mukai, IEEE J. Quantum Electron. QE-23, 1010 (1987).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

A. LaPorta, R. E. Slusher, Phys. Rev. A 44, 2013 (1991).
[CrossRef]

P. D. Townsend, R. Loudon, Phys. Rev. A 45, 458 (1992).
[CrossRef] [PubMed]

Phys. Rev. D (1)

C. M. Caves, Phys. Rev. D 26, 1817 (1982).
[CrossRef]

Phys. Rev. Lett. (6)

H. P. Yuen, Phys. Rev. Lett. 56, 2176 (1986).
[CrossRef] [PubMed]

A. Laporta, R. E. Slusher, B. Yurke, Phys. Rev. Lett. 62, 28 (1989).
[CrossRef]

J. A. Levenson, I. Abram, Th. Rivera, Ph. Fayolle, J. C. Garreau, Ph. Grangier, Phys. Rev. Lett. 70, 267 (1993).
[CrossRef] [PubMed]

M. J. Collett, D. F. Walls, Phys. Rev. Lett. 61, 2442 (1988).
[CrossRef] [PubMed]

O. Aytur, P. Kumar, Phys. Rev. Lett. 65, 1551 (1990).
[CrossRef]

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, M. J. Potasek, Phys. Rev. Lett. 59, 2566 (1987).
[CrossRef] [PubMed]

Prog. Opt. (1)

Y. Yamamoto, S. Machida, S. Saito, N. Imoto, T. Yanagawa, M. Kitagawa, G. Bjork, Prog. Opt. 28, 87 (1990).
[CrossRef]

Other (1)

W. H. Louisell, Coupled Mode and Parametric Electronics (Wiley, New York, 1960); Radiation and Noise in Quantum Electronics (McGraw-Hill, New York, 1964).

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Figures (5)

Fig. 1
Fig. 1

Phase-space representations of (a) the phase-insensitive and (b) phase-sensitive amplification of a coherent state.

Fig. 2
Fig. 2

Experimental setup. A frequency-doubled mode-locked (ML) Q-switched (QS) YLF:Nd laser pumps (at 527 nm) a traveling-wave parametric amplifier composed of two type-II KTP crystals. The polarization of the input signal (at 1054 nm) is rotated by the half-wavelength plate (λ/2) to achieve phase-insensitive or phase-sensitive amplification. The photodiode current is split 90/10, with each partial current measured by use of a spectrum analyzer and a boxcar combination.

Fig. 3
Fig. 3

Noise power of the parametric output in the phase-insensitive configuration as a function of gain (triangles), fitted to Eq. (28). The squares represent the measured noise power of a coherent beam.

Fig. 4
Fig. 4

NF of the phase-insensitive (triangles) and phase-sensitive (stars) parametric amplifiers, fitted to Eqs. (29) and (33), respectively.

Fig. 5
Fig. 5

Noise power of the parametric output in the phase-sensitive configuration as a function of phase-sensitive gain (stars), fitted to Eq. (31). The squares represent the measured noise power of a coherent beam.

Equations (33)

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

NF = SNR in SNR out .
Δ E 1 Δ E 2 = 1 ,
H = γ υ ( a + b + + a b ) ,
a out = cosh ( γ z ) a + sinh ( γ z ) b + , a out + = cosh ( γ z ) a + + sinh ( γ z ) b .
N = a out + a out = cosh 2 ( γ z ) a + a + sinh 2 ( γ z ) b b + + cosh ( γ z ) sinh ( γ z ) ( a + b + + a b ) .
N PIA = a out + a out = n cosh 2 ( γ z ) + sinh 2 ( γ z ) ,
G PIA = cosh 2 ( γ z ) ,
N = n 2 [ cosh ( 2 γ z ) + sinh ( 2 γ z ) cos ( ϕ ) ] ,
G ϕ = cosh ( 2 γ z ) + sinh ( 2 γ z ) cos ( ϕ ) ,
G 0 = exp ( 2 γ z ) .
G π = exp ( 2 γ z ) = 1 / G 0 ,
Δ N 2 = N 2 N 2 .
Δ N 2 PIA = n cosh 2 ( γ z ) [ cosh 2 ( γ z ) + sinh 2 ( γ z ) ] ,
( SNR ) out = α n cosh 2 ( γ z ) cosh 2 ( γ z ) + sinh 2 ( γ z ) ,
( SNR ) in = α n ,
NF PIA = cosh 2 ( γ z ) + sinh 2 ( γ z ) cosh 2 ( γ z ) = 2 1 G PIA ,
Δ N ϕ = n 2 [ cosh ( 2 γ z ) + sinh ( 2 γ z ) cos ( ϕ ) ] cosh ( 2 γ z ) ,
NF ϕ = 2 cosh ( 2 γ z ) ( cosh ( 2 γ z ) + sinh ( 2 γ z ) cos ( ϕ ) = G 0 + ( 1 / G 0 ) G ϕ .
NF 0 = 1 + 1 G 0 2 .
d ± = ( a ± b ) / 2 ,
H = γ 2 υ ( d + + d + + + d + d + ) γ 2 υ ( d + d + + d d ) ,
N TOTAL = n [ cosh ( 2 γ z ) + sinh ( 2 γ z ) cos ( ϕ ) ] ,
Δ N 2 TOTAL = n [ cosh ( 4 γ z ) + sinh ( 4 γ z ) cos ( ϕ ) ] ,
NF 0 = 1 ,
a out = η a in + 1 η c in ,
N det = η [ cosh 2 ( γ z ) a + a + sinh 2 ( γ z ) b b + + cosh ( γ z ) sinh ( γ z ) ( a + b + + a b ) ] + ( 1 η ) c + c + η ( 1 η ) [ cosh ( γ z ) a + c + sinh ( γ z ) b c + cosh ( γ z ) a c + + sinh ( γ z ) b + c + ] .
N det = η n cosh 2 ( γ z ) = η n G PIA ,
Δ N 2 det = η n cosh 2 ( γ z ) [ 1 + 2 η sinh 2 ( γ z ) ] = 2 η 2 n G PIA + ( 1 2 η ) G PIA 2 .
NF PIA = 2 2 G PIA + 1 η G PIA ,
N ϕ = η n 2 G ϕ ,
Δ N ϕ = η n 2 G ϕ [ η cosh ( 2 γ z ) + 1 η ] ,
NF ϕ = 2 [ η cosh ( 2 γ z ) + 1 η ] η G ϕ .
NF 0 = 1 + 1 G 0 2 + 2 ( 1 η ) n G 0 .

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