Abstract

We report on the generation of quadrature squeezed light at 1.535 µm via single-pass optical parametric amplification in a periodically poled MgO:LiNbO3 waveguide, and detection with a temporally shaped local oscillator. Squeezing of -4.1 dB was directly measured using the shaped local oscillator. Classical parametric gain of the shaped pulse was also investigated; a deamplification gain of -12.1 dB was observed with the amplification gain of only +13.8 dB. We experimentally show that the use of shaped pulse as local oscillator in homodyne detection allows us efficient squeezing detection with near-unit mode-matching efficiency.

© 2008 Optical Society of America

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  1. S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).
    [CrossRef]
  2. A. Zavatta, S. Viciani, and M. Bellini, "Quantum-to-classical transition with single-photon-added coherent states of light," Science  306, 660-662 (2004).
    [CrossRef] [PubMed]
  3. Y. Takahashi, J. S¨oderholm, K. Hirano, N. Namekata, S. Machida, S. Mori, S. Kurimura, S. Komatsu, and S. Inoue, "Effects of dispersion on squeezing and photon statistics of down-converted light," Phys. Rev. A 77 ,043801 (2008).
    [CrossRef]
  4. R. Okubo, M. Hirano, Y. Zhang, and T. Hirano, "Pulse-resolved measurement of quadrature phase amplitudes of squeezed pulse trains at a repetition rate of 76 MHz," Opt. Lett. 33, 1458-1460, (2008).
    [CrossRef] [PubMed]
  5. H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Go�?ler, K. Danzmann, and R. Schnabel, "Observation of squeezed light with 10-dB quantum-noise reduction," Phys. Rev. Lett. 100, 033602 (2008).
    [CrossRef] [PubMed]
  6. R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, "Pulsed squeezed light," Phys. Rev. Lett. 59, 2566-2569 (1987).
    [CrossRef] [PubMed]
  7. A. La Porta and R. E. Slusher, "Squeezing limits at high parametric gains," Phys. Rev. A 44, 2013-2022 (1991).
    [CrossRef] [PubMed]
  8. C. Kim, R.-D. Li, and P. Kumar, "Deamplification response of a traveling-wave phase-sensitive optical parametric amplifier," Opt. Lett. 19, 132-134 (1994).
    [CrossRef] [PubMed]
  9. O. Ayt¨ur and P. Kumar, "Squeezed-light generation with a mode-locked Q-switched laser and detection by using a matched local oscillator," Opt. Lett. 17, 529-531, (1992).
    [CrossRef] [PubMed]
  10. B. Yurke, P. Grangier, R. E. Slusher, and M. J. Potasek, "Generating and detecting short-duration pulses of squeezed light," Phys. Rev. A 35, 3586-3589(R) (1987).
    [CrossRef] [PubMed]
  11. M. G. Raymer, P. D. Drummond, and S. J. Carter, "Limits to wideband pulsed squeezing in a traveling-wave parametric amplifier with group-velocity dispersion," Opt. Lett. 16, 1189-1191 (1991).
    [CrossRef] [PubMed]
  12. M. J. Werner, M. G. Raymer, M. Beck, and P. D. Drummond, "Ultrashort pulsed squeezing by optical parametric amplification," Phys. Rev. A 52, 4202-4213 (1995).
    [CrossRef] [PubMed]
  13. C. Kim and P. Kumar, "Quadrature-squeezed light detection using a self-generated matched local oscillator," Phys. Rev. Lett. 73, 1605-1608 (1994).
    [CrossRef] [PubMed]
  14. M. E. Anderson, M. Beck, M. G. Raymer, and J. D. Bierlein, "Quadrature squeezing with ultrashort pulses in nonlinear-optical waveguides," Opt. Lett. 20, 620-622 (1995).
    [CrossRef] [PubMed]
  15. Y. Eto, T. Tajima, Y. Zhang, and T. Hirano, "Observation of squeezed light at 1.535 ?m using a pulsed homodyne detector," Opt. Lett. 32, 1698-1700 (2007).
    [CrossRef] [PubMed]
  16. Y. Eto, T. Tajima, Y. Zhang, and T. Hirano, "Pulsed homodyne detection of squeezed light at telecommunication wavelength," Jpn. J. Appl. Phys.  45, L821-L823 (2006).
    [CrossRef]
  17. G. S. Kanter, P. Kumar, R. V. Roussev, J. Kurz, K. R. Parameswaran, and M. M. Fejer, "Squeezing in a LiNbO3 integrated optical waveguide circuit," Opt. Express 10, 177-182 (2002).
    [PubMed]
  18. P. van Loock and S. L. Braunstein, "Multipartite entanglement for continuous variables: a quantum teleportation network," Phys. Rev. Lett. 84, 3482-3485 (2000).
    [CrossRef] [PubMed]

2008 (3)

Y. Takahashi, J. S¨oderholm, K. Hirano, N. Namekata, S. Machida, S. Mori, S. Kurimura, S. Komatsu, and S. Inoue, "Effects of dispersion on squeezing and photon statistics of down-converted light," Phys. Rev. A 77 ,043801 (2008).
[CrossRef]

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Go�?ler, K. Danzmann, and R. Schnabel, "Observation of squeezed light with 10-dB quantum-noise reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

R. Okubo, M. Hirano, Y. Zhang, and T. Hirano, "Pulse-resolved measurement of quadrature phase amplitudes of squeezed pulse trains at a repetition rate of 76 MHz," Opt. Lett. 33, 1458-1460, (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

Y. Eto, T. Tajima, Y. Zhang, and T. Hirano, "Pulsed homodyne detection of squeezed light at telecommunication wavelength," Jpn. J. Appl. Phys.  45, L821-L823 (2006).
[CrossRef]

2005 (1)

S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).
[CrossRef]

2004 (1)

A. Zavatta, S. Viciani, and M. Bellini, "Quantum-to-classical transition with single-photon-added coherent states of light," Science  306, 660-662 (2004).
[CrossRef] [PubMed]

2002 (1)

2000 (1)

P. van Loock and S. L. Braunstein, "Multipartite entanglement for continuous variables: a quantum teleportation network," Phys. Rev. Lett. 84, 3482-3485 (2000).
[CrossRef] [PubMed]

1995 (2)

M. J. Werner, M. G. Raymer, M. Beck, and P. D. Drummond, "Ultrashort pulsed squeezing by optical parametric amplification," Phys. Rev. A 52, 4202-4213 (1995).
[CrossRef] [PubMed]

M. E. Anderson, M. Beck, M. G. Raymer, and J. D. Bierlein, "Quadrature squeezing with ultrashort pulses in nonlinear-optical waveguides," Opt. Lett. 20, 620-622 (1995).
[CrossRef] [PubMed]

1994 (2)

C. Kim, R.-D. Li, and P. Kumar, "Deamplification response of a traveling-wave phase-sensitive optical parametric amplifier," Opt. Lett. 19, 132-134 (1994).
[CrossRef] [PubMed]

C. Kim and P. Kumar, "Quadrature-squeezed light detection using a self-generated matched local oscillator," Phys. Rev. Lett. 73, 1605-1608 (1994).
[CrossRef] [PubMed]

1992 (1)

1991 (2)

1987 (1)

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, "Pulsed squeezed light," Phys. Rev. Lett. 59, 2566-2569 (1987).
[CrossRef] [PubMed]

Anderson, M. E.

Ayt¨ur, O.

Beck, M.

M. E. Anderson, M. Beck, M. G. Raymer, and J. D. Bierlein, "Quadrature squeezing with ultrashort pulses in nonlinear-optical waveguides," Opt. Lett. 20, 620-622 (1995).
[CrossRef] [PubMed]

M. J. Werner, M. G. Raymer, M. Beck, and P. D. Drummond, "Ultrashort pulsed squeezing by optical parametric amplification," Phys. Rev. A 52, 4202-4213 (1995).
[CrossRef] [PubMed]

Bellini, M.

A. Zavatta, S. Viciani, and M. Bellini, "Quantum-to-classical transition with single-photon-added coherent states of light," Science  306, 660-662 (2004).
[CrossRef] [PubMed]

Bierlein, J. D.

Braunstein, S. L.

S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).
[CrossRef]

P. van Loock and S. L. Braunstein, "Multipartite entanglement for continuous variables: a quantum teleportation network," Phys. Rev. Lett. 84, 3482-3485 (2000).
[CrossRef] [PubMed]

Carter, S. J.

Chelkowski, S.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Go�?ler, K. Danzmann, and R. Schnabel, "Observation of squeezed light with 10-dB quantum-noise reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

Danzmann, K.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Go�?ler, K. Danzmann, and R. Schnabel, "Observation of squeezed light with 10-dB quantum-noise reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

Drummond, P. D.

M. J. Werner, M. G. Raymer, M. Beck, and P. D. Drummond, "Ultrashort pulsed squeezing by optical parametric amplification," Phys. Rev. A 52, 4202-4213 (1995).
[CrossRef] [PubMed]

M. G. Raymer, P. D. Drummond, and S. J. Carter, "Limits to wideband pulsed squeezing in a traveling-wave parametric amplifier with group-velocity dispersion," Opt. Lett. 16, 1189-1191 (1991).
[CrossRef] [PubMed]

Eto, Y.

Y. Eto, T. Tajima, Y. Zhang, and T. Hirano, "Observation of squeezed light at 1.535 ?m using a pulsed homodyne detector," Opt. Lett. 32, 1698-1700 (2007).
[CrossRef] [PubMed]

Y. Eto, T. Tajima, Y. Zhang, and T. Hirano, "Pulsed homodyne detection of squeezed light at telecommunication wavelength," Jpn. J. Appl. Phys.  45, L821-L823 (2006).
[CrossRef]

Fejer, M. M.

Franzen, A.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Go�?ler, K. Danzmann, and R. Schnabel, "Observation of squeezed light with 10-dB quantum-noise reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

Go??ler, S.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Go�?ler, K. Danzmann, and R. Schnabel, "Observation of squeezed light with 10-dB quantum-noise reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

Grangier, P.

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, "Pulsed squeezed light," Phys. Rev. Lett. 59, 2566-2569 (1987).
[CrossRef] [PubMed]

Hage, B.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Go�?ler, K. Danzmann, and R. Schnabel, "Observation of squeezed light with 10-dB quantum-noise reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

Hirano, K.

Y. Takahashi, J. S¨oderholm, K. Hirano, N. Namekata, S. Machida, S. Mori, S. Kurimura, S. Komatsu, and S. Inoue, "Effects of dispersion on squeezing and photon statistics of down-converted light," Phys. Rev. A 77 ,043801 (2008).
[CrossRef]

Hirano, M.

Hirano, T.

Inoue, S.

Y. Takahashi, J. S¨oderholm, K. Hirano, N. Namekata, S. Machida, S. Mori, S. Kurimura, S. Komatsu, and S. Inoue, "Effects of dispersion on squeezing and photon statistics of down-converted light," Phys. Rev. A 77 ,043801 (2008).
[CrossRef]

Kanter, G. S.

Kim, C.

C. Kim and P. Kumar, "Quadrature-squeezed light detection using a self-generated matched local oscillator," Phys. Rev. Lett. 73, 1605-1608 (1994).
[CrossRef] [PubMed]

C. Kim, R.-D. Li, and P. Kumar, "Deamplification response of a traveling-wave phase-sensitive optical parametric amplifier," Opt. Lett. 19, 132-134 (1994).
[CrossRef] [PubMed]

Komatsu, S.

Y. Takahashi, J. S¨oderholm, K. Hirano, N. Namekata, S. Machida, S. Mori, S. Kurimura, S. Komatsu, and S. Inoue, "Effects of dispersion on squeezing and photon statistics of down-converted light," Phys. Rev. A 77 ,043801 (2008).
[CrossRef]

Kumar, P.

Kurimura, S.

Y. Takahashi, J. S¨oderholm, K. Hirano, N. Namekata, S. Machida, S. Mori, S. Kurimura, S. Komatsu, and S. Inoue, "Effects of dispersion on squeezing and photon statistics of down-converted light," Phys. Rev. A 77 ,043801 (2008).
[CrossRef]

Kurz, J.

La Porta, A.

A. La Porta and R. E. Slusher, "Squeezing limits at high parametric gains," Phys. Rev. A 44, 2013-2022 (1991).
[CrossRef] [PubMed]

LaPorta, A.

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, "Pulsed squeezed light," Phys. Rev. Lett. 59, 2566-2569 (1987).
[CrossRef] [PubMed]

Lastzka, N.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Go�?ler, K. Danzmann, and R. Schnabel, "Observation of squeezed light with 10-dB quantum-noise reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

Li, R.-D.

Machida, S.

Y. Takahashi, J. S¨oderholm, K. Hirano, N. Namekata, S. Machida, S. Mori, S. Kurimura, S. Komatsu, and S. Inoue, "Effects of dispersion on squeezing and photon statistics of down-converted light," Phys. Rev. A 77 ,043801 (2008).
[CrossRef]

Mehmet, M.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Go�?ler, K. Danzmann, and R. Schnabel, "Observation of squeezed light with 10-dB quantum-noise reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

Mori, S.

Y. Takahashi, J. S¨oderholm, K. Hirano, N. Namekata, S. Machida, S. Mori, S. Kurimura, S. Komatsu, and S. Inoue, "Effects of dispersion on squeezing and photon statistics of down-converted light," Phys. Rev. A 77 ,043801 (2008).
[CrossRef]

Namekata, N.

Y. Takahashi, J. S¨oderholm, K. Hirano, N. Namekata, S. Machida, S. Mori, S. Kurimura, S. Komatsu, and S. Inoue, "Effects of dispersion on squeezing and photon statistics of down-converted light," Phys. Rev. A 77 ,043801 (2008).
[CrossRef]

Okubo, R.

Parameswaran, K. R.

Potasek, M. J.

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, "Pulsed squeezed light," Phys. Rev. Lett. 59, 2566-2569 (1987).
[CrossRef] [PubMed]

Raymer, M. G.

Roussev, R. V.

S¨oderholm, J.

Y. Takahashi, J. S¨oderholm, K. Hirano, N. Namekata, S. Machida, S. Mori, S. Kurimura, S. Komatsu, and S. Inoue, "Effects of dispersion on squeezing and photon statistics of down-converted light," Phys. Rev. A 77 ,043801 (2008).
[CrossRef]

Schnabel, R.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Go�?ler, K. Danzmann, and R. Schnabel, "Observation of squeezed light with 10-dB quantum-noise reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

Slusher, R. E.

A. La Porta and R. E. Slusher, "Squeezing limits at high parametric gains," Phys. Rev. A 44, 2013-2022 (1991).
[CrossRef] [PubMed]

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, "Pulsed squeezed light," Phys. Rev. Lett. 59, 2566-2569 (1987).
[CrossRef] [PubMed]

Tajima, T.

Y. Eto, T. Tajima, Y. Zhang, and T. Hirano, "Observation of squeezed light at 1.535 ?m using a pulsed homodyne detector," Opt. Lett. 32, 1698-1700 (2007).
[CrossRef] [PubMed]

Y. Eto, T. Tajima, Y. Zhang, and T. Hirano, "Pulsed homodyne detection of squeezed light at telecommunication wavelength," Jpn. J. Appl. Phys.  45, L821-L823 (2006).
[CrossRef]

Takahashi, Y.

Y. Takahashi, J. S¨oderholm, K. Hirano, N. Namekata, S. Machida, S. Mori, S. Kurimura, S. Komatsu, and S. Inoue, "Effects of dispersion on squeezing and photon statistics of down-converted light," Phys. Rev. A 77 ,043801 (2008).
[CrossRef]

Vahlbruch, H.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Go�?ler, K. Danzmann, and R. Schnabel, "Observation of squeezed light with 10-dB quantum-noise reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

van Loock, P.

S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).
[CrossRef]

P. van Loock and S. L. Braunstein, "Multipartite entanglement for continuous variables: a quantum teleportation network," Phys. Rev. Lett. 84, 3482-3485 (2000).
[CrossRef] [PubMed]

Viciani, S.

A. Zavatta, S. Viciani, and M. Bellini, "Quantum-to-classical transition with single-photon-added coherent states of light," Science  306, 660-662 (2004).
[CrossRef] [PubMed]

Werner, M. J.

M. J. Werner, M. G. Raymer, M. Beck, and P. D. Drummond, "Ultrashort pulsed squeezing by optical parametric amplification," Phys. Rev. A 52, 4202-4213 (1995).
[CrossRef] [PubMed]

Yurke, B.

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, "Pulsed squeezed light," Phys. Rev. Lett. 59, 2566-2569 (1987).
[CrossRef] [PubMed]

Zavatta, A.

A. Zavatta, S. Viciani, and M. Bellini, "Quantum-to-classical transition with single-photon-added coherent states of light," Science  306, 660-662 (2004).
[CrossRef] [PubMed]

Zhang, Y.

Jpn. J. Appl. Phys (1)

Y. Eto, T. Tajima, Y. Zhang, and T. Hirano, "Pulsed homodyne detection of squeezed light at telecommunication wavelength," Jpn. J. Appl. Phys.  45, L821-L823 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. A (3)

Y. Takahashi, J. S¨oderholm, K. Hirano, N. Namekata, S. Machida, S. Mori, S. Kurimura, S. Komatsu, and S. Inoue, "Effects of dispersion on squeezing and photon statistics of down-converted light," Phys. Rev. A 77 ,043801 (2008).
[CrossRef]

A. La Porta and R. E. Slusher, "Squeezing limits at high parametric gains," Phys. Rev. A 44, 2013-2022 (1991).
[CrossRef] [PubMed]

M. J. Werner, M. G. Raymer, M. Beck, and P. D. Drummond, "Ultrashort pulsed squeezing by optical parametric amplification," Phys. Rev. A 52, 4202-4213 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

C. Kim and P. Kumar, "Quadrature-squeezed light detection using a self-generated matched local oscillator," Phys. Rev. Lett. 73, 1605-1608 (1994).
[CrossRef] [PubMed]

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Go�?ler, K. Danzmann, and R. Schnabel, "Observation of squeezed light with 10-dB quantum-noise reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, "Pulsed squeezed light," Phys. Rev. Lett. 59, 2566-2569 (1987).
[CrossRef] [PubMed]

P. van Loock and S. L. Braunstein, "Multipartite entanglement for continuous variables: a quantum teleportation network," Phys. Rev. Lett. 84, 3482-3485 (2000).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).
[CrossRef]

Science (1)

A. Zavatta, S. Viciani, and M. Bellini, "Quantum-to-classical transition with single-photon-added coherent states of light," Science  306, 660-662 (2004).
[CrossRef] [PubMed]

Other (1)

B. Yurke, P. Grangier, R. E. Slusher, and M. J. Potasek, "Generating and detecting short-duration pulses of squeezed light," Phys. Rev. A 35, 3586-3589(R) (1987).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1.
Fig. 1.

Experimental setup. Blue (red) line indicates the light pulse at wavelength 1.535 µm (767 nm). The arrows and double circles on blue line indicate the polarization directions at 1.535 µm. The light pulse at 767 nm always horizontally polarized. The dielectrical polarizing beam splitters (DPBS1 and 2) act as a polarizing beam splitter (PBS) only for 1.535 µm, and is configured to transmit only vertically polarized light at 1.535 µm. The harmonic wave plates (HWP1 and 2) serve as a λ/2 plate for wavelength of 1.535 µm and as a λ plate for 767 nm wavelength. Harmonic separator mirror (HM) has high reflectivity (R ~99) for 767 nm and high transmissivity (T ~99) for 1.535 µm.

Fig. 2.
Fig. 2.

(a) The blue envelope is the temporal shape of the FWP shaped by OPA process in PPLNLO. The black envelope is the shape of FWP before PPLNLO. (b) The pulse duration ratio of FWP (the shaped FWP/the input FWP) and the amplification gain versus the output pump average power.

Fig. 3.
Fig. 3.

The noise performance of the balanced homodyne detector.

Fig. 4.
Fig. 4.

(a) Classical parametric gain measured using shaped and non-shaped probe pulse versus output pump average power from PPLN2. (b) Estimated squeezing parameter, r, and mode-matching efficiency, ηcm , versus square root of the pump average power. Blue and red marks denote that of shaped and non-shaped pulse respectively, and dotted lines are liner fitting lines for the obtained r.

Fig. 5.
Fig. 5.

The measured noise level versus relative phase at pump average power of 0.14 mW. The noise variance is obtained from 2000 pulses at each relative phase.

Fig. 6.
Fig. 6.

(a) Squeezing level and antisqueezing level using shaped and non-shaped LO versus output pump average power from PPLN2 (b) Estimated squeezing parameter, r, and overall detection efficiency, η, versus square root of pump average power from PPLN2. Blue and red marks denote that of shaped and non-shaped pulse, respectively.

Equations (3)

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

G ± = η cm exp ( ± 2 r ) + 1 η cm ,
S ± = η exp ( ± 2 r ) + 1 η .
η = η qm × η waveguide × η ol × η PD .

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