Abstract

We demonstrate an elegant way of handling optical signals which are generated using squeezed states of light without losing their improved signal to noise ratio. We do this by amplifying, without significant noise penalty, both signal and noise away from the quantum noise limit into the classical domain. This makes the information robust to losses. Our system achieves a signal transfer coefficient, Ts, close to unity. As a demonstration we amplify a small signal carried by 35% amplitude squeezed light and show that unlike the fragile squeezed input, the signal amplified output is robust to propagation losses. A signal transfer coefficient of Ts = 0.75 is achieved even in the presence of large introduced (86%) downstream losses.

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References

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  1. Y. Yamamoto, S. Machida, S. Saito, N. Imoto, T. Yanagawa, M. Kitagawa and G. Bjork, "Quantum Mechanical Limit in Optical Precision Measurement and Communication", Prog. Opt. XXVIII, 87 (1990).
    [CrossRef]
  2. C. Fabre, "Squeezed states of light", Phys. Rep. 219 215 (1992).
    [CrossRef]
  3. T.C.Ralph, C.C.Harb, H-A.Bachor "Intensity noise of injection locked lasers: quantum theory using linearized input-output method", Phys. Rev. A. 54, 4359 (1996).
    [CrossRef] [PubMed]
  4. C. C. Harb, T. C. Ralph, E. H. Huntington, D. E. McClelland, H.-A. Bachor and I. Freitag, "Intensity Noise Dependence of Nd:YAG Lasers on their Diode-Laser Pump Source", J. Opt. Soc. Am. B 14,2936 (1997).
    [CrossRef]
  5. J. H. Shapiro, G. Saplakoglu, S.-T. Ho, P. Kumar, B. E. A. Saleh and M. C. Teich, "Theory of light detection in the presence of feedback", J. Opt. Soc. Am. B 4,1604 (1987).
    [CrossRef]
  6. M. S. Taubman, H. M. Wiseman, D. E. McClelland and H.-A. Bachor, "Eects of intensity feedback on quantum noise", J. Opt. Soc. Am. B 12, 1792 (1995).
    [CrossRef]
  7. H. M. Wiseman, M. S. Taubman and H.-A. Bachor, "Feedback-enhanced squeezing in second-harmonic generation", Phys. Rev. A 51, 3227 (1995).
    [CrossRef] [PubMed]
  8. H. P. Yuen, "Generation, Detection and Application of High-IntensityPhoton-Number-Eigenstate Fields", Phys. Rev. Lett. 56, 2176(1986).
    [CrossRef] [PubMed]
  9. H. A. Haus and J. A. Mullen, "Quantum noise in linear amplifier", Phys. Rev. A 128, 2407 (1962).
  10. C. M. Caves, " Quantum limits on noise in linear amplifiers", Phys. Rev. D 26, 1817 (1982).
    [CrossRef]
  11. J. A. Levenson, I. Abram, T. Rivera, and P. Fayolle, "Quantum Optical Cloning Amplifier", Phys. Rev. Lett. 70, 267 (1993).
    [CrossRef] [PubMed]
  12. E. Goobar, A. Karlsson and G. Bjoerk, "Experimental realization of a semiconductor photon number amplifier and a quantum optical tap", Phys. Rev. Lett. 71, 2002 (1993).
    [CrossRef] [PubMed]
  13. J.-F. Roch, J.-Ph. Poizat, and P. Grangier, "Sub-shot-noise manipulation of light using semiconductor emitters and receivers", Phys. Rev. Lett. 71, 2006 (1993).
    [CrossRef] [PubMed]
  14. R. C. Dorf, R. H. Bishop, Modern Control Systems, (Addison-Wesley. Reading, Mass. 1995).
  15. A. V. Masalov, A. A. Putilin and M. V. Vasilyev, "Photocurrent noise suppression and optical amplification in negative-feedback opto-electronic loop", Quantum Communications and Measurement, V. P. Belavkin et al. Ed., (Plenum Press, New York 1995) p. 511.
  16. A. V. Masalov, A. A. Putilin and M. V. Vasilyev, "Sub-Poissonian light and photocurrent shot-noise suppression in a closed optoelectronic loop", J. Mod. Opt., 41, 1941 (1994).
    [CrossRef]
  17. V. N. Konopsky, A. V. Masalov, A. A. Putilin and M. V. Vasilyev, "Optical amplifier and oscillator based on modulator", Coherence and Quantum Optics, VII, Eberly, Mandel and Wolf Ed., (Plenum Press, New York 1996) p. 167.
  18. P. K. Lam, T. C. Ralph, E. H. Huntington, H.-A. Bachor, "Noiseless Signal Amplification using Positive Electro-Optic Feedforward", Phys. Rev. Lett. 79, 1471 (1997).
    [CrossRef]
  19. A. G. White, M. S. Taubman, T. C. Ralph, P. K. Lam, D. E. McClelland and H.-A. Bachor, "Experimental test of modular noise propagation theory for quantum optics", Phys. Rev. A 54, 3400 (1996).
    [CrossRef] [PubMed]
  20. T. C. Ralph and H.-A. Bachor, "Noiseless amplification of the coherent amplitude of bright squeezed light using a standard laser amplifier", Opt. Commun. 122, 94 (1995).
    [CrossRef]

Other (20)

Y. Yamamoto, S. Machida, S. Saito, N. Imoto, T. Yanagawa, M. Kitagawa and G. Bjork, "Quantum Mechanical Limit in Optical Precision Measurement and Communication", Prog. Opt. XXVIII, 87 (1990).
[CrossRef]

C. Fabre, "Squeezed states of light", Phys. Rep. 219 215 (1992).
[CrossRef]

T.C.Ralph, C.C.Harb, H-A.Bachor "Intensity noise of injection locked lasers: quantum theory using linearized input-output method", Phys. Rev. A. 54, 4359 (1996).
[CrossRef] [PubMed]

C. C. Harb, T. C. Ralph, E. H. Huntington, D. E. McClelland, H.-A. Bachor and I. Freitag, "Intensity Noise Dependence of Nd:YAG Lasers on their Diode-Laser Pump Source", J. Opt. Soc. Am. B 14,2936 (1997).
[CrossRef]

J. H. Shapiro, G. Saplakoglu, S.-T. Ho, P. Kumar, B. E. A. Saleh and M. C. Teich, "Theory of light detection in the presence of feedback", J. Opt. Soc. Am. B 4,1604 (1987).
[CrossRef]

M. S. Taubman, H. M. Wiseman, D. E. McClelland and H.-A. Bachor, "Eects of intensity feedback on quantum noise", J. Opt. Soc. Am. B 12, 1792 (1995).
[CrossRef]

H. M. Wiseman, M. S. Taubman and H.-A. Bachor, "Feedback-enhanced squeezing in second-harmonic generation", Phys. Rev. A 51, 3227 (1995).
[CrossRef] [PubMed]

H. P. Yuen, "Generation, Detection and Application of High-IntensityPhoton-Number-Eigenstate Fields", Phys. Rev. Lett. 56, 2176(1986).
[CrossRef] [PubMed]

H. A. Haus and J. A. Mullen, "Quantum noise in linear amplifier", Phys. Rev. A 128, 2407 (1962).

C. M. Caves, " Quantum limits on noise in linear amplifiers", Phys. Rev. D 26, 1817 (1982).
[CrossRef]

J. A. Levenson, I. Abram, T. Rivera, and P. Fayolle, "Quantum Optical Cloning Amplifier", Phys. Rev. Lett. 70, 267 (1993).
[CrossRef] [PubMed]

E. Goobar, A. Karlsson and G. Bjoerk, "Experimental realization of a semiconductor photon number amplifier and a quantum optical tap", Phys. Rev. Lett. 71, 2002 (1993).
[CrossRef] [PubMed]

J.-F. Roch, J.-Ph. Poizat, and P. Grangier, "Sub-shot-noise manipulation of light using semiconductor emitters and receivers", Phys. Rev. Lett. 71, 2006 (1993).
[CrossRef] [PubMed]

R. C. Dorf, R. H. Bishop, Modern Control Systems, (Addison-Wesley. Reading, Mass. 1995).

A. V. Masalov, A. A. Putilin and M. V. Vasilyev, "Photocurrent noise suppression and optical amplification in negative-feedback opto-electronic loop", Quantum Communications and Measurement, V. P. Belavkin et al. Ed., (Plenum Press, New York 1995) p. 511.

A. V. Masalov, A. A. Putilin and M. V. Vasilyev, "Sub-Poissonian light and photocurrent shot-noise suppression in a closed optoelectronic loop", J. Mod. Opt., 41, 1941 (1994).
[CrossRef]

V. N. Konopsky, A. V. Masalov, A. A. Putilin and M. V. Vasilyev, "Optical amplifier and oscillator based on modulator", Coherence and Quantum Optics, VII, Eberly, Mandel and Wolf Ed., (Plenum Press, New York 1996) p. 167.

P. K. Lam, T. C. Ralph, E. H. Huntington, H.-A. Bachor, "Noiseless Signal Amplification using Positive Electro-Optic Feedforward", Phys. Rev. Lett. 79, 1471 (1997).
[CrossRef]

A. G. White, M. S. Taubman, T. C. Ralph, P. K. Lam, D. E. McClelland and H.-A. Bachor, "Experimental test of modular noise propagation theory for quantum optics", Phys. Rev. A 54, 3400 (1996).
[CrossRef] [PubMed]

T. C. Ralph and H.-A. Bachor, "Noiseless amplification of the coherent amplitude of bright squeezed light using a standard laser amplifier", Opt. Commun. 122, 94 (1995).
[CrossRef]

Supplementary Material (4)

» Media 1: MOV (18 KB)     
» Media 2: MOV (23 KB)     
» Media 3: MOV (21 KB)     
» Media 4: MOV (16 KB)     

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Figures (7)

Figure 1.
Figure 1.

Schematics of an electro-optic feedback noise eater.

Figure 2.
Figure 2.

Bode plot of a typical feedback open loop gain.

Figure 3.
Figure 3.

The effect of a noise eater on input laser noise. Output noise spectra are shown in black. Various input noise levels (V las=300, 100, 30, 10, 3, 1) are shown. Regions where the black traces are below the reds are regions of noise suppression. [Media 1]

Figure 4.
Figure 4.

Schematics of an electro-optic feedforward amplifier.

Figure 5.
Figure 5.

(i) and (ii). Signal transfer coefficient for varying electronic gain, λ, at one detection frequency for different beam splitter reflectivity (10%, 30%, 50%, 70%, 80%, 90%, 95%). (i) Ideal system with no detector or modulator losses. The plots show that there is always a positive feedforward gain which yields Ts = 1 corresponding to noiseless amplification. The negative feedforward values which give Ts = 0 correspond to optimum noise-eating operation. (ii) Realistic system with ηi = 0.90 and ηoεm = 0.60. In this case the maximum Ts values for each reflectivity describe a locus of points asymptoting to the in-loop detector efficiency. [Media 2] [Media 3]

Figure 6.
Figure 6.

Experimental results of the electro-optic feedforward scheme. The in-loop detector efficiency is ηi = 0.92. (i) ε = 0.5. The maximum Ts occurs at λopt in agreement with theory. (ii) ε = 0.1, for low transmittivity, the maximum Ts occurs at high signal gain. Traces shown are limiting cases: (a) is the Ts value corresponding to the in-loop signal. Points above this line are evidence of the cancellation of quantum noise; (b) is the T s,max of the scheme limited mainly by the in-loop detector efficiency. (iii) Locus of T s,max, obtained for various transmittivity ε. Also shown is the best possible performance of a phase insensitive amplifier.

Figure 7.
Figure 7.

Experimental demonstration of lossy transmission and noiseless amplification of amplitude squeezed light [Media 4]

Equations (11)

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

V out ( Ω ) = ε 1 1 h ( Ω ) 2 V las ( Ω ) .
V out ( Ω ) = ε V las ( Ω ) + 1 ε h ( Ω ) 2 V 1 + h ( Ω ) 2 ε ( 1 η ) V 2 1 h ( Ω ) 2
V out ( Ω ) = 1 + ε h ( Ω ) 2 η ( 1 ε ) 1 h ( Ω ) 2 .
V out ( Ω ) = ε m η o ε + λ ( Ω ) ( 1 ε ) η i 2 V in ( Ω )
+ ε m η o ( 1 ε ) λ ( Ω ) ε η i 2 V 1
+ ε m η o λ ( Ω ) ( 1 η i ) 2 V 2
+ ( 1 ε m η o ) V 3 ,
V out ( Ω ) = ( ε + λ ( Ω ) ( 1 ε ) ) 2 V in ( Ω )
+ ( ( 1 ε ) λ ( Ω ) ε ) 2 ,
V out ( Ω ) = 1 1 ε
V out ( Ω ) = 1 ε V in ( Ω ) .

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