Abstract

Mode matching plays an important role in measuring the continuous variable entanglement. For the signal and idler twin beams generated by a pulse pumped fiber optical parametric amplifier (FOPA), the spatial mode matching is automatically achieved in single mode fiber, but the temporal mode property is complicated because it is highly sensitive to the dispersion and the gain of the FOPA. We study the temporal mode structure and derive the input-output relation for each temporal mode of signal and idler beams after decomposing the joint spectral function of twin beams with the singular-value decomposition method. We analyze the measurement of the quadrature-amplitude entanglement, and find mode matching between the multi-mode twin beams and the local oscillators of homodyne detection systems is crucial to achieve a high degree of entanglement. The results show that the noise contributed by the temporal modes nonorthogonal to local oscillator may be much larger than the vacuum noise, so the mode mis-match can not be accounted for by merely introducing an effective loss. Our study will be useful for developing a source of high quality continuous variable entanglement by using the FOPA.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  28. S. L. Braunstein and D. D. Crouch, “Fundamental limits to observations of squeezing via balanced homodyne detection,” Phys. Rev. A 43, 330–337 (1991).
    [Crossref] [PubMed]
  29. Yoon-Ho Kim and Warren P. Grice, “Measurement of the spectral properties of the two-photon state generated via Type II spontaneous parametric downconversion,” Opt. Lett. 30, 908 (2005).
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    [Crossref] [PubMed]
  31. A. Eckstein, G. Boucher, A. Lemaître, P. Filloux, I. Favero, G. Leo, J. E. Sipe, M. Liscidini, and S. Ducci, “High-resolution spectral characterization of two photon states via classical measurements,” Laser Photonics Rev. 8, L76–L80 (2014).
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    [Crossref] [PubMed]

2014 (1)

A. Eckstein, G. Boucher, A. Lemaître, P. Filloux, I. Favero, G. Leo, J. E. Sipe, M. Liscidini, and S. Ducci, “High-resolution spectral characterization of two photon states via classical measurements,” Laser Photonics Rev. 8, L76–L80 (2014).
[Crossref]

2013 (2)

M. Liscidini and J. E. Sipe, “Stimulated emission tomography,” Phys. Rev. Lett. 111, 193602 (2013).
[Crossref] [PubMed]

X. Guo, X. Li, N. Liu, and Z. Y. Ou, “Multimode theory of pulsed-twin-beam generation using a high-gain fiber-optical parametric amplifier,” Phys. Rev. A 88, 023841 (2013).
[Crossref]

2012 (4)

C. Polycarpou, K. N. Cassemiro, G. Venturi, A. Zavatta, and M. Bellini, “Adaptive detection of arbitrarily shaped ultrashort quantum light states,” Phys. Rev. Lett. 109, 053602 (2012).
[Crossref] [PubMed]

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[Crossref] [PubMed]

E. Flurin, N. Roch, F. Mallet, M. H. Devoret, and B. Huard, “Generating entangled microwave radiation over two transmission lines,” Phys. Rev. Lett. 109, 183901 (2012).
[Crossref] [PubMed]

X. Guo, X. Li, N. Liu, L. Yang, and Z. Y. Ou, “An all-fiber source of pulsed twin beams for quantum communication,” Appl. Phys. Lett. 101, 261111 (2012).
[Crossref]

2011 (3)

T. Eberle, V. Händchen, J. Duhme, T. Franz, R. F. Werner, and R. Schnabel, “Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light source,” Phys. Rev. A 83, 052329 (2011).
[Crossref]

L. Yang, X. Ma, X. Guo, L. Cui, and X. Li, “Characterization of a fiber-based source of heralded single photons,” Phys. Rev. A 83, 053843 (2011).
[Crossref]

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly efficient single-pass source of pulsed single-mode twin beams of light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref] [PubMed]

2009 (2)

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of einstein-podolsky-rosen entanglement,” Nature 457, 859–862 (2009).
[Crossref] [PubMed]

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: the einstein-podolsky-rosen paradox: from concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

2008 (4)

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

P. J. Mosley, J. S. Lundeen, B. J Smith, P. Wasylczyk, A. B. U’Ren, C. Ciberhorn, and I. A Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133601 (2008).
[Crossref] [PubMed]

X. Li, X. Ma, Z. Y. Ou, L. Yang, L. Cui, and D. Yu, “Spectral study of photon pairs generated in dispersion shifted fiber with a pulsed pump,” Opt. Express 16, 32–44 (2008).
[Crossref] [PubMed]

C. J. McKinstrie, S. J. van Enk, M. G. Raymer, and S. Radic, “Multicolor multipartite entanglementproduced by vector four-wave mixingin a fiber,” Opt. Express 16, 2720–2739 (2008).
[Crossref] [PubMed]

2006 (3)

2005 (1)

2004 (1)

V. Josse, A. Dantan, A. Bramati, M. Pinard, and E. Giacobino, “Continuous variable entanglement using cold atoms,” Phys. Rev. Lett. 92, 123601 (2004).
[Crossref] [PubMed]

2002 (2)

C. Silberhorn, N. Korolkova, and G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88, 167902 (2002).
[Crossref] [PubMed]

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” Photonics Technol. Lett. 14, 983–985 (2002).
[Crossref]

2001 (2)

J. E. Sharping, M. Fiorentino, and P. Kumar, “Observation of twin-beam-type quantum correlation in optical fiber,” Opt. Lett. 26, 367–369 (2001).
[Crossref]

C. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable einstein-podolsky-rosen entanglement via the kerr nonlinearity in an optical fiber,” Phys. Rev. Lett. 86, 4267–4270 (2001).
[Crossref] [PubMed]

2000 (1)

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

1997 (1)

Z. Y. Ou, “Parametric down-conversion with coherent pulse pumping and quantum interference between independent fields,” Quantum Semiclass. Opt. 9, 599 (1997).
[Crossref]

1992 (1)

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the einstein-podolsky-rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[Crossref] [PubMed]

1991 (1)

S. L. Braunstein and D. D. Crouch, “Fundamental limits to observations of squeezing via balanced homodyne detection,” Phys. Rev. A 43, 330–337 (1991).
[Crossref] [PubMed]

1985 (1)

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave brillouin scattering,” Phys. Rev. B,  31, 5244 (1985).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, “Nonlinear fiber optics” (Academic Press, 2007).

Andersen, U. L.

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[Crossref] [PubMed]

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: the einstein-podolsky-rosen paradox: from concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Bachor, H. A.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: the einstein-podolsky-rosen paradox: from concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Banaszek, K.

W. Wasilewski, A. I. Lvovsky, K. Banaszek, and C. Radzewicz, “Pulsed squeezed light: Simultaneous squeezing of multiple modes,” Phys. Rev. A 73, 063819 (2006).
[Crossref]

W. Wasilewski, P. Wasylczyk, P. Kolenderski, K. Banaszek, and C. Radzewicz, “Joint spectrum of photon pairs measured by coincidence Fourier spectroscopy,” Opt. Lett. 31, 1130 (2006).
[Crossref] [PubMed]

Bayer, P. W.

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave brillouin scattering,” Phys. Rev. B,  31, 5244 (1985).
[Crossref]

Bellini, M.

C. Polycarpou, K. N. Cassemiro, G. Venturi, A. Zavatta, and M. Bellini, “Adaptive detection of arbitrarily shaped ultrashort quantum light states,” Phys. Rev. Lett. 109, 053602 (2012).
[Crossref] [PubMed]

Boucher, G.

A. Eckstein, G. Boucher, A. Lemaître, P. Filloux, I. Favero, G. Leo, J. E. Sipe, M. Liscidini, and S. Ducci, “High-resolution spectral characterization of two photon states via classical measurements,” Laser Photonics Rev. 8, L76–L80 (2014).
[Crossref]

Bowen, W. P.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: the einstein-podolsky-rosen paradox: from concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Boyer, V.

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of einstein-podolsky-rosen entanglement,” Nature 457, 859–862 (2009).
[Crossref] [PubMed]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

Bramati, A.

V. Josse, A. Dantan, A. Bramati, M. Pinard, and E. Giacobino, “Continuous variable entanglement using cold atoms,” Phys. Rev. Lett. 92, 123601 (2004).
[Crossref] [PubMed]

Braunstein, S. L.

S. L. Braunstein and D. D. Crouch, “Fundamental limits to observations of squeezing via balanced homodyne detection,” Phys. Rev. A 43, 330–337 (1991).
[Crossref] [PubMed]

Cassemiro, K. N.

C. Polycarpou, K. N. Cassemiro, G. Venturi, A. Zavatta, and M. Bellini, “Adaptive detection of arbitrarily shaped ultrashort quantum light states,” Phys. Rev. Lett. 109, 053602 (2012).
[Crossref] [PubMed]

Cavalcanti, E. G.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: the einstein-podolsky-rosen paradox: from concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Christ, A.

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly efficient single-pass source of pulsed single-mode twin beams of light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref] [PubMed]

Ciberhorn, C.

P. J. Mosley, J. S. Lundeen, B. J Smith, P. Wasylczyk, A. B. U’Ren, C. Ciberhorn, and I. A Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133601 (2008).
[Crossref] [PubMed]

Cirac, J. I.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

Crouch, D. D.

S. L. Braunstein and D. D. Crouch, “Fundamental limits to observations of squeezing via balanced homodyne detection,” Phys. Rev. A 43, 330–337 (1991).
[Crossref] [PubMed]

Cui, L.

L. Yang, X. Ma, X. Guo, L. Cui, and X. Li, “Characterization of a fiber-based source of heralded single photons,” Phys. Rev. A 83, 053843 (2011).
[Crossref]

X. Li, X. Ma, Z. Y. Ou, L. Yang, L. Cui, and D. Yu, “Spectral study of photon pairs generated in dispersion shifted fiber with a pulsed pump,” Opt. Express 16, 32–44 (2008).
[Crossref] [PubMed]

Dantan, A.

V. Josse, A. Dantan, A. Bramati, M. Pinard, and E. Giacobino, “Continuous variable entanglement using cold atoms,” Phys. Rev. Lett. 92, 123601 (2004).
[Crossref] [PubMed]

Devoret, M. H.

E. Flurin, N. Roch, F. Mallet, M. H. Devoret, and B. Huard, “Generating entangled microwave radiation over two transmission lines,” Phys. Rev. Lett. 109, 183901 (2012).
[Crossref] [PubMed]

Drummond, P. D.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: the einstein-podolsky-rosen paradox: from concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Duan, L.-M.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

Ducci, S.

A. Eckstein, G. Boucher, A. Lemaître, P. Filloux, I. Favero, G. Leo, J. E. Sipe, M. Liscidini, and S. Ducci, “High-resolution spectral characterization of two photon states via classical measurements,” Laser Photonics Rev. 8, L76–L80 (2014).
[Crossref]

Duhme, J.

T. Eberle, V. Händchen, J. Duhme, T. Franz, R. F. Werner, and R. Schnabel, “Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light source,” Phys. Rev. A 83, 052329 (2011).
[Crossref]

Eberle, T.

T. Eberle, V. Händchen, J. Duhme, T. Franz, R. F. Werner, and R. Schnabel, “Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light source,” Phys. Rev. A 83, 052329 (2011).
[Crossref]

Eckstein, A.

A. Eckstein, G. Boucher, A. Lemaître, P. Filloux, I. Favero, G. Leo, J. E. Sipe, M. Liscidini, and S. Ducci, “High-resolution spectral characterization of two photon states via classical measurements,” Laser Photonics Rev. 8, L76–L80 (2014).
[Crossref]

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly efficient single-pass source of pulsed single-mode twin beams of light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref] [PubMed]

Favero, I.

A. Eckstein, G. Boucher, A. Lemaître, P. Filloux, I. Favero, G. Leo, J. E. Sipe, M. Liscidini, and S. Ducci, “High-resolution spectral characterization of two photon states via classical measurements,” Laser Photonics Rev. 8, L76–L80 (2014).
[Crossref]

Filip, R.

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[Crossref] [PubMed]

Filloux, P.

A. Eckstein, G. Boucher, A. Lemaître, P. Filloux, I. Favero, G. Leo, J. E. Sipe, M. Liscidini, and S. Ducci, “High-resolution spectral characterization of two photon states via classical measurements,” Laser Photonics Rev. 8, L76–L80 (2014).
[Crossref]

Fiorentino, M.

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” Photonics Technol. Lett. 14, 983–985 (2002).
[Crossref]

J. E. Sharping, M. Fiorentino, and P. Kumar, “Observation of twin-beam-type quantum correlation in optical fiber,” Opt. Lett. 26, 367–369 (2001).
[Crossref]

Flurin, E.

E. Flurin, N. Roch, F. Mallet, M. H. Devoret, and B. Huard, “Generating entangled microwave radiation over two transmission lines,” Phys. Rev. Lett. 109, 183901 (2012).
[Crossref] [PubMed]

Franz, T.

T. Eberle, V. Händchen, J. Duhme, T. Franz, R. F. Werner, and R. Schnabel, “Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light source,” Phys. Rev. A 83, 052329 (2011).
[Crossref]

Gentle, J. E.

J. E. Gentle, Numerical Linear Algebra for Applications in Statistics(Springer-Verlag, 1998).
[Crossref]

Giacobino, E.

V. Josse, A. Dantan, A. Bramati, M. Pinard, and E. Giacobino, “Continuous variable entanglement using cold atoms,” Phys. Rev. Lett. 92, 123601 (2004).
[Crossref] [PubMed]

Giedke, G.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

Grice, Warren P.

Guo, X.

X. Guo, X. Li, N. Liu, and Z. Y. Ou, “Multimode theory of pulsed-twin-beam generation using a high-gain fiber-optical parametric amplifier,” Phys. Rev. A 88, 023841 (2013).
[Crossref]

X. Guo, X. Li, N. Liu, L. Yang, and Z. Y. Ou, “An all-fiber source of pulsed twin beams for quantum communication,” Appl. Phys. Lett. 101, 261111 (2012).
[Crossref]

L. Yang, X. Ma, X. Guo, L. Cui, and X. Li, “Characterization of a fiber-based source of heralded single photons,” Phys. Rev. A 83, 053843 (2011).
[Crossref]

X. Guo, X. Li, N. Liu, and Y. Liu, “Generation and characterization of continuous variable quantum correlations using a fiber optical parametric amplifier,” in Conference on Lssers and Electro Optics (OSA, 2015), p. JW2A.6

Händchen, V.

T. Eberle, V. Händchen, J. Duhme, T. Franz, R. F. Werner, and R. Schnabel, “Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light source,” Phys. Rev. A 83, 052329 (2011).
[Crossref]

Huard, B.

E. Flurin, N. Roch, F. Mallet, M. H. Devoret, and B. Huard, “Generating entangled microwave radiation over two transmission lines,” Phys. Rev. Lett. 109, 183901 (2012).
[Crossref] [PubMed]

Josse, V.

V. Josse, A. Dantan, A. Bramati, M. Pinard, and E. Giacobino, “Continuous variable entanglement using cold atoms,” Phys. Rev. Lett. 92, 123601 (2004).
[Crossref] [PubMed]

Kim, Yoon-Ho

Kimble, H. J.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the einstein-podolsky-rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[Crossref] [PubMed]

Kolenderski, P.

König, F.

C. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable einstein-podolsky-rosen entanglement via the kerr nonlinearity in an optical fiber,” Phys. Rev. Lett. 86, 4267–4270 (2001).
[Crossref] [PubMed]

Koprulu, K. G.

Korolkova, N.

C. Silberhorn, N. Korolkova, and G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88, 167902 (2002).
[Crossref] [PubMed]

C. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable einstein-podolsky-rosen entanglement via the kerr nonlinearity in an optical fiber,” Phys. Rev. Lett. 86, 4267–4270 (2001).
[Crossref] [PubMed]

Kumar, P.

Lam, P. K.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: the einstein-podolsky-rosen paradox: from concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

C. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable einstein-podolsky-rosen entanglement via the kerr nonlinearity in an optical fiber,” Phys. Rev. Lett. 86, 4267–4270 (2001).
[Crossref] [PubMed]

Lassen, M.

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[Crossref] [PubMed]

Lemaître, A.

A. Eckstein, G. Boucher, A. Lemaître, P. Filloux, I. Favero, G. Leo, J. E. Sipe, M. Liscidini, and S. Ducci, “High-resolution spectral characterization of two photon states via classical measurements,” Laser Photonics Rev. 8, L76–L80 (2014).
[Crossref]

Leo, G.

A. Eckstein, G. Boucher, A. Lemaître, P. Filloux, I. Favero, G. Leo, J. E. Sipe, M. Liscidini, and S. Ducci, “High-resolution spectral characterization of two photon states via classical measurements,” Laser Photonics Rev. 8, L76–L80 (2014).
[Crossref]

Lett, P. D.

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of einstein-podolsky-rosen entanglement,” Nature 457, 859–862 (2009).
[Crossref] [PubMed]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

Leuchs, G.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: the einstein-podolsky-rosen paradox: from concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

C. Silberhorn, N. Korolkova, and G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88, 167902 (2002).
[Crossref] [PubMed]

C. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable einstein-podolsky-rosen entanglement via the kerr nonlinearity in an optical fiber,” Phys. Rev. Lett. 86, 4267–4270 (2001).
[Crossref] [PubMed]

Levenson, M. D.

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave brillouin scattering,” Phys. Rev. B,  31, 5244 (1985).
[Crossref]

Li, X.

X. Guo, X. Li, N. Liu, and Z. Y. Ou, “Multimode theory of pulsed-twin-beam generation using a high-gain fiber-optical parametric amplifier,” Phys. Rev. A 88, 023841 (2013).
[Crossref]

X. Guo, X. Li, N. Liu, L. Yang, and Z. Y. Ou, “An all-fiber source of pulsed twin beams for quantum communication,” Appl. Phys. Lett. 101, 261111 (2012).
[Crossref]

L. Yang, X. Ma, X. Guo, L. Cui, and X. Li, “Characterization of a fiber-based source of heralded single photons,” Phys. Rev. A 83, 053843 (2011).
[Crossref]

X. Li, X. Ma, Z. Y. Ou, L. Yang, L. Cui, and D. Yu, “Spectral study of photon pairs generated in dispersion shifted fiber with a pulsed pump,” Opt. Express 16, 32–44 (2008).
[Crossref] [PubMed]

X. Guo, X. Li, N. Liu, and Y. Liu, “Generation and characterization of continuous variable quantum correlations using a fiber optical parametric amplifier,” in Conference on Lssers and Electro Optics (OSA, 2015), p. JW2A.6

Liscidini, M.

A. Eckstein, G. Boucher, A. Lemaître, P. Filloux, I. Favero, G. Leo, J. E. Sipe, M. Liscidini, and S. Ducci, “High-resolution spectral characterization of two photon states via classical measurements,” Laser Photonics Rev. 8, L76–L80 (2014).
[Crossref]

M. Liscidini and J. E. Sipe, “Stimulated emission tomography,” Phys. Rev. Lett. 111, 193602 (2013).
[Crossref] [PubMed]

Liu, N.

X. Guo, X. Li, N. Liu, and Z. Y. Ou, “Multimode theory of pulsed-twin-beam generation using a high-gain fiber-optical parametric amplifier,” Phys. Rev. A 88, 023841 (2013).
[Crossref]

X. Guo, X. Li, N. Liu, L. Yang, and Z. Y. Ou, “An all-fiber source of pulsed twin beams for quantum communication,” Appl. Phys. Lett. 101, 261111 (2012).
[Crossref]

X. Guo, X. Li, N. Liu, and Y. Liu, “Generation and characterization of continuous variable quantum correlations using a fiber optical parametric amplifier,” in Conference on Lssers and Electro Optics (OSA, 2015), p. JW2A.6

Liu, Y.

X. Guo, X. Li, N. Liu, and Y. Liu, “Generation and characterization of continuous variable quantum correlations using a fiber optical parametric amplifier,” in Conference on Lssers and Electro Optics (OSA, 2015), p. JW2A.6

Lundeen, J. S.

P. J. Mosley, J. S. Lundeen, B. J Smith, P. Wasylczyk, A. B. U’Ren, C. Ciberhorn, and I. A Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133601 (2008).
[Crossref] [PubMed]

Lvovsky, A. I.

W. Wasilewski, A. I. Lvovsky, K. Banaszek, and C. Radzewicz, “Pulsed squeezed light: Simultaneous squeezing of multiple modes,” Phys. Rev. A 73, 063819 (2006).
[Crossref]

Ma, X.

L. Yang, X. Ma, X. Guo, L. Cui, and X. Li, “Characterization of a fiber-based source of heralded single photons,” Phys. Rev. A 83, 053843 (2011).
[Crossref]

X. Li, X. Ma, Z. Y. Ou, L. Yang, L. Cui, and D. Yu, “Spectral study of photon pairs generated in dispersion shifted fiber with a pulsed pump,” Opt. Express 16, 32–44 (2008).
[Crossref] [PubMed]

Madsen, L. S.

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[Crossref] [PubMed]

Mallet, F.

E. Flurin, N. Roch, F. Mallet, M. H. Devoret, and B. Huard, “Generating entangled microwave radiation over two transmission lines,” Phys. Rev. Lett. 109, 183901 (2012).
[Crossref] [PubMed]

Marino, A. M.

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of einstein-podolsky-rosen entanglement,” Nature 457, 859–862 (2009).
[Crossref] [PubMed]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

McKinstrie, C. J.

Mosley, P. J.

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly efficient single-pass source of pulsed single-mode twin beams of light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref] [PubMed]

P. J. Mosley, J. S. Lundeen, B. J Smith, P. Wasylczyk, A. B. U’Ren, C. Ciberhorn, and I. A Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133601 (2008).
[Crossref] [PubMed]

Ou, Z. Y.

X. Guo, X. Li, N. Liu, and Z. Y. Ou, “Multimode theory of pulsed-twin-beam generation using a high-gain fiber-optical parametric amplifier,” Phys. Rev. A 88, 023841 (2013).
[Crossref]

X. Guo, X. Li, N. Liu, L. Yang, and Z. Y. Ou, “An all-fiber source of pulsed twin beams for quantum communication,” Appl. Phys. Lett. 101, 261111 (2012).
[Crossref]

X. Li, X. Ma, Z. Y. Ou, L. Yang, L. Cui, and D. Yu, “Spectral study of photon pairs generated in dispersion shifted fiber with a pulsed pump,” Opt. Express 16, 32–44 (2008).
[Crossref] [PubMed]

Z. Y. Ou, “Parametric down-conversion with coherent pulse pumping and quantum interference between independent fields,” Quantum Semiclass. Opt. 9, 599 (1997).
[Crossref]

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the einstein-podolsky-rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[Crossref] [PubMed]

Peng, K. C.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the einstein-podolsky-rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[Crossref] [PubMed]

Pereira, S. F.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the einstein-podolsky-rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[Crossref] [PubMed]

Pinard, M.

V. Josse, A. Dantan, A. Bramati, M. Pinard, and E. Giacobino, “Continuous variable entanglement using cold atoms,” Phys. Rev. Lett. 92, 123601 (2004).
[Crossref] [PubMed]

Polycarpou, C.

C. Polycarpou, K. N. Cassemiro, G. Venturi, A. Zavatta, and M. Bellini, “Adaptive detection of arbitrarily shaped ultrashort quantum light states,” Phys. Rev. Lett. 109, 053602 (2012).
[Crossref] [PubMed]

Pooser, R. C.

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of einstein-podolsky-rosen entanglement,” Nature 457, 859–862 (2009).
[Crossref] [PubMed]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

Radic, S.

Radzewicz, C.

W. Wasilewski, P. Wasylczyk, P. Kolenderski, K. Banaszek, and C. Radzewicz, “Joint spectrum of photon pairs measured by coincidence Fourier spectroscopy,” Opt. Lett. 31, 1130 (2006).
[Crossref] [PubMed]

W. Wasilewski, A. I. Lvovsky, K. Banaszek, and C. Radzewicz, “Pulsed squeezed light: Simultaneous squeezing of multiple modes,” Phys. Rev. A 73, 063819 (2006).
[Crossref]

Raymer, M. G.

Reid, M. D.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: the einstein-podolsky-rosen paradox: from concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Roch, N.

E. Flurin, N. Roch, F. Mallet, M. H. Devoret, and B. Huard, “Generating entangled microwave radiation over two transmission lines,” Phys. Rev. Lett. 109, 183901 (2012).
[Crossref] [PubMed]

Schnabel, R.

T. Eberle, V. Händchen, J. Duhme, T. Franz, R. F. Werner, and R. Schnabel, “Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light source,” Phys. Rev. A 83, 052329 (2011).
[Crossref]

Sharping, J. E.

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” Photonics Technol. Lett. 14, 983–985 (2002).
[Crossref]

J. E. Sharping, M. Fiorentino, and P. Kumar, “Observation of twin-beam-type quantum correlation in optical fiber,” Opt. Lett. 26, 367–369 (2001).
[Crossref]

Shelby, R. M.

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave brillouin scattering,” Phys. Rev. B,  31, 5244 (1985).
[Crossref]

Silberhorn, C.

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly efficient single-pass source of pulsed single-mode twin beams of light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref] [PubMed]

C. Silberhorn, N. Korolkova, and G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88, 167902 (2002).
[Crossref] [PubMed]

C. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable einstein-podolsky-rosen entanglement via the kerr nonlinearity in an optical fiber,” Phys. Rev. Lett. 86, 4267–4270 (2001).
[Crossref] [PubMed]

Sipe, J. E.

A. Eckstein, G. Boucher, A. Lemaître, P. Filloux, I. Favero, G. Leo, J. E. Sipe, M. Liscidini, and S. Ducci, “High-resolution spectral characterization of two photon states via classical measurements,” Laser Photonics Rev. 8, L76–L80 (2014).
[Crossref]

M. Liscidini and J. E. Sipe, “Stimulated emission tomography,” Phys. Rev. Lett. 111, 193602 (2013).
[Crossref] [PubMed]

Smith, B. J

P. J. Mosley, J. S. Lundeen, B. J Smith, P. Wasylczyk, A. B. U’Ren, C. Ciberhorn, and I. A Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133601 (2008).
[Crossref] [PubMed]

U’Ren, A. B.

P. J. Mosley, J. S. Lundeen, B. J Smith, P. Wasylczyk, A. B. U’Ren, C. Ciberhorn, and I. A Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133601 (2008).
[Crossref] [PubMed]

Usenko, V. C.

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[Crossref] [PubMed]

van Enk, S. J.

Venturi, G.

C. Polycarpou, K. N. Cassemiro, G. Venturi, A. Zavatta, and M. Bellini, “Adaptive detection of arbitrarily shaped ultrashort quantum light states,” Phys. Rev. Lett. 109, 053602 (2012).
[Crossref] [PubMed]

Voss, P. L.

P. L. Voss, K. G. Koprulu, and P. Kumar, “Raman-noise-induced quantum limits for χ(3) nondegenerate phase-sensitive amplification and quadrature squeezing,” J. Opt. Soc. Am. B,  23, 598–610 (2006).
[Crossref]

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” Photonics Technol. Lett. 14, 983–985 (2002).
[Crossref]

Walmsley, I. A

P. J. Mosley, J. S. Lundeen, B. J Smith, P. Wasylczyk, A. B. U’Ren, C. Ciberhorn, and I. A Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133601 (2008).
[Crossref] [PubMed]

Wasilewski, W.

W. Wasilewski, P. Wasylczyk, P. Kolenderski, K. Banaszek, and C. Radzewicz, “Joint spectrum of photon pairs measured by coincidence Fourier spectroscopy,” Opt. Lett. 31, 1130 (2006).
[Crossref] [PubMed]

W. Wasilewski, A. I. Lvovsky, K. Banaszek, and C. Radzewicz, “Pulsed squeezed light: Simultaneous squeezing of multiple modes,” Phys. Rev. A 73, 063819 (2006).
[Crossref]

Wasylczyk, P.

P. J. Mosley, J. S. Lundeen, B. J Smith, P. Wasylczyk, A. B. U’Ren, C. Ciberhorn, and I. A Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133601 (2008).
[Crossref] [PubMed]

W. Wasilewski, P. Wasylczyk, P. Kolenderski, K. Banaszek, and C. Radzewicz, “Joint spectrum of photon pairs measured by coincidence Fourier spectroscopy,” Opt. Lett. 31, 1130 (2006).
[Crossref] [PubMed]

Weiß, O.

C. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable einstein-podolsky-rosen entanglement via the kerr nonlinearity in an optical fiber,” Phys. Rev. Lett. 86, 4267–4270 (2001).
[Crossref] [PubMed]

Werner, R. F.

T. Eberle, V. Händchen, J. Duhme, T. Franz, R. F. Werner, and R. Schnabel, “Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light source,” Phys. Rev. A 83, 052329 (2011).
[Crossref]

Yang, L.

X. Guo, X. Li, N. Liu, L. Yang, and Z. Y. Ou, “An all-fiber source of pulsed twin beams for quantum communication,” Appl. Phys. Lett. 101, 261111 (2012).
[Crossref]

L. Yang, X. Ma, X. Guo, L. Cui, and X. Li, “Characterization of a fiber-based source of heralded single photons,” Phys. Rev. A 83, 053843 (2011).
[Crossref]

X. Li, X. Ma, Z. Y. Ou, L. Yang, L. Cui, and D. Yu, “Spectral study of photon pairs generated in dispersion shifted fiber with a pulsed pump,” Opt. Express 16, 32–44 (2008).
[Crossref] [PubMed]

Yu, D.

Zavatta, A.

C. Polycarpou, K. N. Cassemiro, G. Venturi, A. Zavatta, and M. Bellini, “Adaptive detection of arbitrarily shaped ultrashort quantum light states,” Phys. Rev. Lett. 109, 053602 (2012).
[Crossref] [PubMed]

Zoller, P.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

X. Guo, X. Li, N. Liu, L. Yang, and Z. Y. Ou, “An all-fiber source of pulsed twin beams for quantum communication,” Appl. Phys. Lett. 101, 261111 (2012).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Photonics Rev. (1)

A. Eckstein, G. Boucher, A. Lemaître, P. Filloux, I. Favero, G. Leo, J. E. Sipe, M. Liscidini, and S. Ducci, “High-resolution spectral characterization of two photon states via classical measurements,” Laser Photonics Rev. 8, L76–L80 (2014).
[Crossref]

Nat. Commun. (1)

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[Crossref] [PubMed]

Nature (1)

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of einstein-podolsky-rosen entanglement,” Nature 457, 859–862 (2009).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (3)

Photonics Technol. Lett. (1)

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” Photonics Technol. Lett. 14, 983–985 (2002).
[Crossref]

Phys. Rev. A (5)

L. Yang, X. Ma, X. Guo, L. Cui, and X. Li, “Characterization of a fiber-based source of heralded single photons,” Phys. Rev. A 83, 053843 (2011).
[Crossref]

T. Eberle, V. Händchen, J. Duhme, T. Franz, R. F. Werner, and R. Schnabel, “Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light source,” Phys. Rev. A 83, 052329 (2011).
[Crossref]

S. L. Braunstein and D. D. Crouch, “Fundamental limits to observations of squeezing via balanced homodyne detection,” Phys. Rev. A 43, 330–337 (1991).
[Crossref] [PubMed]

W. Wasilewski, A. I. Lvovsky, K. Banaszek, and C. Radzewicz, “Pulsed squeezed light: Simultaneous squeezing of multiple modes,” Phys. Rev. A 73, 063819 (2006).
[Crossref]

X. Guo, X. Li, N. Liu, and Z. Y. Ou, “Multimode theory of pulsed-twin-beam generation using a high-gain fiber-optical parametric amplifier,” Phys. Rev. A 88, 023841 (2013).
[Crossref]

Phys. Rev. B (1)

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave brillouin scattering,” Phys. Rev. B,  31, 5244 (1985).
[Crossref]

Phys. Rev. Lett. (10)

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

P. J. Mosley, J. S. Lundeen, B. J Smith, P. Wasylczyk, A. B. U’Ren, C. Ciberhorn, and I. A Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133601 (2008).
[Crossref] [PubMed]

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly efficient single-pass source of pulsed single-mode twin beams of light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref] [PubMed]

M. Liscidini and J. E. Sipe, “Stimulated emission tomography,” Phys. Rev. Lett. 111, 193602 (2013).
[Crossref] [PubMed]

C. Polycarpou, K. N. Cassemiro, G. Venturi, A. Zavatta, and M. Bellini, “Adaptive detection of arbitrarily shaped ultrashort quantum light states,” Phys. Rev. Lett. 109, 053602 (2012).
[Crossref] [PubMed]

E. Flurin, N. Roch, F. Mallet, M. H. Devoret, and B. Huard, “Generating entangled microwave radiation over two transmission lines,” Phys. Rev. Lett. 109, 183901 (2012).
[Crossref] [PubMed]

C. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable einstein-podolsky-rosen entanglement via the kerr nonlinearity in an optical fiber,” Phys. Rev. Lett. 86, 4267–4270 (2001).
[Crossref] [PubMed]

C. Silberhorn, N. Korolkova, and G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88, 167902 (2002).
[Crossref] [PubMed]

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the einstein-podolsky-rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[Crossref] [PubMed]

V. Josse, A. Dantan, A. Bramati, M. Pinard, and E. Giacobino, “Continuous variable entanglement using cold atoms,” Phys. Rev. Lett. 92, 123601 (2004).
[Crossref] [PubMed]

Quantum Semiclass. Opt. (1)

Z. Y. Ou, “Parametric down-conversion with coherent pulse pumping and quantum interference between independent fields,” Quantum Semiclass. Opt. 9, 599 (1997).
[Crossref]

Rev. Mod. Phys. (1)

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: the einstein-podolsky-rosen paradox: from concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Science (1)

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

Other (3)

G. P. Agrawal, “Nonlinear fiber optics” (Academic Press, 2007).

X. Guo, X. Li, N. Liu, and Y. Liu, “Generation and characterization of continuous variable quantum correlations using a fiber optical parametric amplifier,” in Conference on Lssers and Electro Optics (OSA, 2015), p. JW2A.6

J. E. Gentle, Numerical Linear Algebra for Applications in Statistics(Springer-Verlag, 1998).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Conceptual diagram of generating quadrature amplitude entanglement from a fiber optical parametric amplifier (FOPA). a ^ s ( i ) ( ω S ( i ) ), the operator of input signal (idler) field; b ^ s ( i ) ( ω S ( i ) ), the operator of the output signal (idler) field; HDs/HDi, homodyne detection system for signal/idler field; LOs/LOi: Local oscillators of HDs/HDi; i ^ s ( i ): the operator of photocurrent out of HDs/HDi.
Fig. 2
Fig. 2 Spectral properties of twin beams generated by a pulse pumped FOPA with broad gain bandwidth in telecom band. (a) Normalized absolute value and (b) phase of the JSF, |Fsi)/F(0,0)| and arctan ( Re { F ( Ω s , Ω i ) } Im { F ( Ω s , Ω i ) } ). (c) Relative mode strength rk/r1 for the decomposed k-th order temporal mode of twin beams ϕk(ωs)ψk(ωi). (d) The intensity and (e) phase of the first three decomposed mode in signal field ϕks) (k = 1,2,3). (f) The intensity and (g) phase of the first three decomposed mode in idler field ψki) (k = 1,2,3). In plots (d)-(g), solid, dashed and dot-dashed lines are for the mode with index k = 1, k = 2, and k = 3, respectively. In the calculation, we have 2 γ P p + β 2 4 Δ 2 = 0, β 2 = 0.2 × 2 σ p L Δ and β 3 = 0.2 × 2 σ p L Δ 2 in Eq. (24)
Fig. 3
Fig. 3 Mode matching efficiency |ξks|2 (|ξki|2) and phase θks (θki) for the kth order decomposed signal (idler) mode ϕk(ωs) (ψk(ωi)) when the bandwidths of LOs and LOi are σL = 0.6σp (plots (a)–(d)), σL = 2σp (plots (e)–(h)), and σL = 3σp (plots (i)–(l)), respectively. The parameters of the FOPA are the same as those in Fig. 2
Fig. 4
Fig. 4 Measured inseparability of twin beams, Iexp, as a function of gain coefficient G when the bandwidths of LOs and LOi are σL = 0.6σp, σL = 2σp and σL = 3σp, respectively. As a comparison, Iexp=I1 for the LOs and LOi with the spectra the same as the fundamental modes ϕ1(ωs) and ψ1(ωi) is also plotted. The results obtained for the JSF in Fig. 2 are marked by cross points between the data and dashed line.

Equations (55)

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H ^ ( t ) = C 1 χ ( 3 ) d V [ E p 1 ( t ) E p 2 ( t ) E ^ s ( ) ( t ) E ^ i ( ) ( t ) + h . c . ] ,
E p n ( t ) = E 0 e i γ P p z e ( ω p n ω p 0 ) 2 / 2 σ p 2 e i ( k p z ω p n t ) d ω p n ( n = 1 , 2 ) ,
E ^ s ( ) ( t ) = 1 2 π d ω s a ^ s ( ω s ) e i ( k s z ω s t )
E ^ i ( ) ( t ) = 1 2 π d ω i a ^ i ( ω i ) e i ( k i z ω i t )
H ^ ( t ) = 2 C 1 γ P p L c A e f f 2 3 ω p 0 π 2 σ p 2 d ω p 1 d ω p 2 d ω s d ω i a ^ s ( ω s ) a ^ i ( ω i ) sin c ( Δ k L 2 ) exp { ( ω p 1 ω p 0 ) 2 + ( ω p 2 ω p 0 ) 2 2 σ p 2 } e i ( ω p 1 + ω p 2 ω s ω i ) t + h . c .
b ^ s ( ω s ) = U ^ a ^ s ( ω s ) U ^ = S h 1 s ( ω s , ω s ) a ^ s ( ω s ) d ω s + I h 2 s ( ω s , ω i ) a ^ i ( ω i ) d ω i
b ^ i ( ω i ) = U ^ a ^ i ( ω i ) U ^ = I h 1 i ( ω i , ω i ) a ^ i ( ω i ) d ω i + S h 2 i ( ω i , ω s ) a ^ s ( ω s ) d ω s ,
U ^ = exp { H ^ ( t ) d t i h ¯ } = exp { G [ F ( ω s , ω i ) a ^ s ( ω s ) a ^ i ( ω i ) d ω s d ω i h . c . ] } ,
F ( ω s , ω i ) = C N exp ( i Δ k L 2 ) exp { ( ω s + ω i 2 ω p 0 ) 2 4 σ p 2 } sin c ( Δ kL 2 ) ,
h 1 s ( ω s , ω s ) = δ ( ω s ω s ) + n = 1 G 2 n ( 2 n ) ! d ω 1 d ω 2 d ω 2 n 1 { F ( ω s , ω 1 ) F ( ω 2 , ω 3 ) F ( ω 4 , ω 5 ) F ( ω 2 n 2 , ω 2 n 1 ) × F * ( ω 2 , ω 1 ) F * ( ω 4 , ω 3 ) F * ( ω 6 , ω 5 ) F * ( ω s , ω 2 n 1 ) }
h 2 s ( ω s , ω i ) = G F ( ω s , ω i ) + n = 1 G 2 n + 1 ( 2 n + 1 ) ! d ω 1 d ω 2 d ω 2 n { F * ( ω 2 , ω 1 ) F * ( ω 4 , ω 3 ) F * ( ω 2 n , ω 2 n 1 ) × F ( ω s , ω 1 ) F ( ω 2 , ω 3 ) F ( ω 4 , ω 5 ) F ( ω 2 n , ω i ) }
h 1 i ( ω i , ω i ) = δ ( ω i ω i ) + n = 1 G 2 n ( 2 n ) ! d ω 1 d ω 2 d ω 2 n 1 { F ( ω 1 , ω i ) F ( ω 3 , ω 2 ) F ( ω 5 , ω 4 ) F ( ω 2 n 1 , ω 2 n 2 ) × F * ( ω 1 , ω 2 ) F * ( ω 3 , ω 4 ) F * ( ω 5 , ω 6 ) F * ( ω 2 n 1 , ω i ) }
h 2 i ( ω i , ω s ) = G ψ ( ω s , ω i ) + n = 1 G 2 n + 1 ( 2 n + 1 ) ! d ω 1 d ω 2 d ω 2 n { F * ( ω 1 , ω 2 ) F * ( ω 3 , ω 4 ) F * ( ω 2 n 1 , ω 2 n ) × F ( ω 1 , ω i ) F ( ω 3 , ω 2 ) ψ ( ω 5 , ω 4 ) F ( ω s , ω 2 n ) } .
F ( ω s , ω i ) = k r k ϕ k ( ω s ) ψ k ( ω i ) ( k = 1 , 2 , ) ,
h 1 s ( ω s , ω s ) = δ ( ω s ω s ) + k [ cosh ( r k × G ) 1 ] ϕ k ( ω s ) ϕ k * ( ω s )
h 2 s ( ω s , ω i ) = k sinh ( r k × G ) ϕ k ( ω s ) ψ k ( ω i )
h 1 i ( ω i , ω i ) = δ ( ω i ω i ) + k [ cosh ( r k × G ) 1 ] ψ k ( ω i ) ψ k * ( ω i )
h 2 i ( ω i , ω s ) = k sinh ( r k × G ) ψ k ( ω i ) ϕ k ( ω s ) .
B ^ k s = cosh ( G × r k ) A ^ k s + sinh ( r k × G ) A ^ k i
B ^ k i = cosh ( G × r k ) A ^ k i + sinh ( r k × G ) A ^ k s ,
A ^ k s S ϕ k * ( ω s ) a ^ s ( ω s ) d ω s
A ^ k i I ψ k * ( ω i ) a ^ i ( ω i ) d ω i
B ^ k s S ϕ k * ( ω s ) b ^ s ( ω s ) d ω s
B ^ k i I ψ k * ( ω i ) b ^ i ( ω i ) d ω i .
F ( Ω s , Ω i ) = C N exp ( i Δ k L 2 ) exp { ( Ω s + Ω i ) 2 4 σ p 2 } sin c ( Δ kL 2 ) ,
Δ k 2 γ P p + β 2 4 Δ 2 + β 2 2 Δ ( Ω s Ω i ) + β 3 8 Δ 2 ( Ω s + Ω i ) ,
X ^ k s ( k i ) = 1 2 ( B ^ k s ( k i ) + B ^ k s ( k i ) )
Y ^ k s ( k i ) = 1 2 ( B ^ k s ( k i ) B ^ k s ( k i ) ) .
Δ X ^ s ( i ) 2 = Δ Y ^ s ( i ) 2 = cosh 2 ( r k G ) + sinh 2 ( r k G ) 2 .
Δ ( X ^ k s X ^ k i ) 2 = Δ ( Y ^ k s + Y ^ k i ) 2 = 1 [ cosh ( r k G ) + sinh ( r k G ) ] 2 .
I k = 2 [ cosh ( r k G ) + sinh ( r k G ) ] 2 < 2 ,
E L s ( L i ) ( t ) = | α L s ( L i ) | e i θ L s ( i ) A L s ( L i ) ( ω ) e i ω t d ω + c . c . ,
c ^ s ( ω s ) = η s b ^ s ( ω s ) + i 1 η s v ^ s ( ω s )
c ^ i ( ω i ) = η i b ^ i ( ω i ) + i 1 η i v ^ i ( ω i ) ,
i s ( i ) = q [ E L s ( L i ) E ^ s ( i ) ( ) + h . c . ] d t ,
E ^ s ( i ) ( ) = 1 2 π c ^ s ( i ) ( ω ) e i ω t d ω .
A L s ( ω s ) = k ξ k s ϕ k ( ω s )
A L i ( ω i ) = k ξ k i ψ k ( ω i ) ,
ξ k s = | ξ k s | e i θ k s = S A L s ( ω s ) ϕ k * ( ω s ) d ω s
ξ k i = | ξ k i | e i θ k i = I A L i ( ω i ) ψ k * ( ω i ) d ω i ,
i ^ s = q | α L s | k [ | ξ k s | η s X ^ k s ( θ s ) + 1 η s X ^ v ]
i ^ i = q | α L i | k [ | ξ k i | η i X ^ k i ( θ i ) + 1 η i X ^ v ] ,
X ^ k s ( k i ) ( θ s ( i ) ) = 1 2 ( e i θ s ( i ) B ^ k s ( k i ) + e i θ s ( i ) B ^ k s ( k i ) ) .
A L s ( ω s ) = ϕ k ( ω s )
A L i ( ω i ) = ψ k ( ω i ) ,
I exp = Δ X ^ 2 exp + Δ Y ^ + 2 exp ,
Δ X ^ 2 exp = Δ ( i ^ s i ^ i ) 2 q 2 | α L s | | α L i | θ
Δ Y ^ + 2 exp = Δ ( i ^ s + i ^ i ) 2 q 2 | α L s | | α L i | θ + π 2
Δ X ^ 2 exp = V X s + V X i 2 C X
Δ Y ^ + 2 exp = V Y s + V Y i + 2 C Y ,
V X s = V Y s = k = 1 | ξ k s | 2 [ cosh 2 ( r k × G ) + sinh 2 ( r k × G ) ] / 2
V X i = V Y i = k = 1 | ξ k i | 2 [ cosh 2 ( r k × G ) + sinh 2 ( r k × G ) ] / 2 ,
C X = k = 1 C X k = k = 1 | ξ k s ξ k i | cosh ( r k × G ) sinh ( r k × G ) cos ( θ L s + θ L i + θ k s + θ k i ) ,
C Y = k = 1 C Y k = k = 1 | ξ k s ξ k i | cosh ( r k × G ) sinh ( r k × G ) cos ( θ L s + θ L i + θ k s + θ k i ) .
A L s ( L i ) ( ω s ( i ) ) = 1 π 1 / 2 σ L exp { ( ω s ( i ) ω s 0 ( i 0 ) ) 2 2 σ L 2 } .

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