Abstract

We demonstrate a novel all-optical quantum random number generator (RNG) based on above-threshold binary phase state selection in a degenerate optical parametric oscillator (OPO). Photodetection is not a part of the random process, and no post processing is required for the generated bit sequence. We show that the outcome is statistically random with 99% confidence, and verify that the randomness is due to the phase of initiating photons generated through spontaneous parametric down conversion of the pump, with negligible contribution of classical noise sources. With the use of micro- and nanoscale OPO resonators, this technique offers a promise for simple, robust, and high-speed on-chip all-optical quantum RNGs.

© 2012 OSA

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  1. S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature464, 1021–1024 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
  3. C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4, 711–715 (2010).
    [CrossRef]
  4. M. Wahl, M. Leifgen, M. Berlin, T. Rhlicke, H. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett.98, 171105 (2011).
    [CrossRef]
  5. M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A83, 023820 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  18. A. Marandi, N. Leindecker, V. Pervak, R. L. Byer, and K. L. Vodopyanov, “Coherence properties of a broadband femtosecond mid-IR optical parametric oscillator operating at degeneracy,” Opt. Express20, 7255–7262 (2012).
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  20. S. Lecomte, R. Paschotta, S. Pawlik, B. Schmidt, K. Furusawa, A. Malinowski, D. J. Richardson, and U. Keller, “Synchronously pumped optical parametric oscillator with a repetition rate of 81.8 GHz,” IEEE Photon. Technol. Lett.17, 483–485 (2005).
    [CrossRef]
  21. J. U. Furst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett.106, 113901 (2011).
    [CrossRef] [PubMed]
  22. J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4, 37–40 (2010).
    [CrossRef]
  23. L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4, 41–45 (2010).
    [CrossRef]
  24. X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics4, 557–560 (2010).
    [CrossRef]

2012 (1)

2011 (6)

N. Leindecker, A. Marandi, R. L. Byer, and K. L. Vodopyanov, “Broadband degenerate OPO for mid-infrared frequency comb generation,” Opt. Express19, 6296–6302 (2011).
[CrossRef] [PubMed]

M. Jofre, M. Curty, F. Steinlechner, G. Anzolin, J. P. Torres, M. W. Mitchell, and V. Pruneri, “True random numbers from amplified quantum vacuum,” Opt. Express19, 20665–20672 (2011)
[CrossRef] [PubMed]

P. J. Bustard, D. Moffatt, R. Lausten, G. Wu, I. A. Walmsley, and B. J. Sussman, “Quantum random bit generation using stimulated Raman scattering,” Opt. Express19, 25173–25180 (2011).
[CrossRef]

M. Wahl, M. Leifgen, M. Berlin, T. Rhlicke, H. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett.98, 171105 (2011).
[CrossRef]

M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A83, 023820 (2011).
[CrossRef]

J. U. Furst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett.106, 113901 (2011).
[CrossRef] [PubMed]

2010 (7)

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4, 37–40 (2010).
[CrossRef]

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4, 41–45 (2010).
[CrossRef]

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics4, 557–560 (2010).
[CrossRef]

B. Qi, Y. Chi, H. Lo, and Li Qian, “High-speed quantum random number generation by measuring phase noise of a single-mode laser,” Opt. Lett.35, 312–314 (2010).
[CrossRef] [PubMed]

S. T. Wong, K. L. Vodopyanov, and R. L. Byer, “Self-phase-locked divide-by-2 optical parametric oscillator as a broadband frequency comb source,” J. Opt. Soc. Am. B27, 876–882 (2010).
[CrossRef]

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature464, 1021–1024 (2010).
[CrossRef] [PubMed]

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4, 711–715 (2010).
[CrossRef]

2007 (1)

M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, “Secure self-calibrating quantum random-bit generator,” Phys. Rev. A75, 032334 (2007).
[CrossRef]

2005 (1)

S. Lecomte, R. Paschotta, S. Pawlik, B. Schmidt, K. Furusawa, A. Malinowski, D. J. Richardson, and U. Keller, “Synchronously pumped optical parametric oscillator with a repetition rate of 81.8 GHz,” IEEE Photon. Technol. Lett.17, 483–485 (2005).
[CrossRef]

1995 (1)

1990 (1)

1988 (1)

Y. H. Shih and C. O. Alley, “New Type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett.61, 2921–2924 (1988).
[CrossRef] [PubMed]

1986 (1)

L. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett.57, 2520–2523 (1986).
[CrossRef] [PubMed]

1967 (1)

S. E. Harris, M. K. Oshman, and R. L. Byer, “Observation of tunable optical parametric fluorescence,” Phys. Rev. Lett.18, 732–734 (1967).
[CrossRef]

1961 (1)

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes I,” Phys. Rev.124, 1646–1654 (1961).
[CrossRef]

Acin, A.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature464, 1021–1024 (2010).
[CrossRef] [PubMed]

Aiello, A.

J. U. Furst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett.106, 113901 (2011).
[CrossRef] [PubMed]

Alley, C. O.

Y. H. Shih and C. O. Alley, “New Type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett.61, 2921–2924 (1988).
[CrossRef] [PubMed]

Andersen, U. L.

J. U. Furst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett.106, 113901 (2011).
[CrossRef] [PubMed]

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4, 711–715 (2010).
[CrossRef]

Anzolin, G.

Banks, D.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Van- gel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST special publication 800-22, Rev. 1-a, NIST, Gaithersburg, Maryland, USA, (2010).

Barker, E.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Van- gel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST special publication 800-22, Rev. 1-a, NIST, Gaithersburg, Maryland, USA, (2010).

Beausoleil, R. G.

M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, “Secure self-calibrating quantum random-bit generator,” Phys. Rev. A75, 032334 (2007).
[CrossRef]

Benson, O.

M. Wahl, M. Leifgen, M. Berlin, T. Rhlicke, H. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett.98, 171105 (2011).
[CrossRef]

Berlin, M.

M. Wahl, M. Leifgen, M. Berlin, T. Rhlicke, H. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett.98, 171105 (2011).
[CrossRef]

Bosenberg, W. R.

Bustard, P. J.

Byer, R. L.

Chi, Y.

Chu, S.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4, 41–45 (2010).
[CrossRef]

Curty, M.

Day, T.

de la Giroday, A. B.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature464, 1021–1024 (2010).
[CrossRef] [PubMed]

Dong, R.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4, 711–715 (2010).
[CrossRef]

Dray, J.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Van- gel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST special publication 800-22, Rev. 1-a, NIST, Gaithersburg, Maryland, USA, (2010).

Duchesne, D.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4, 41–45 (2010).
[CrossRef]

Eckardt, R. C.

Elser, D.

J. U. Furst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett.106, 113901 (2011).
[CrossRef] [PubMed]

Fejer, M. M.

Ferrera, M.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4, 41–45 (2010).
[CrossRef]

Fiorentino, M.

M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, “Secure self-calibrating quantum random-bit generator,” Phys. Rev. A75, 032334 (2007).
[CrossRef]

Foster, M. A.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4, 37–40 (2010).
[CrossRef]

Furst, J. U.

J. U. Furst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett.106, 113901 (2011).
[CrossRef] [PubMed]

Furusawa, K.

S. Lecomte, R. Paschotta, S. Pawlik, B. Schmidt, K. Furusawa, A. Malinowski, D. J. Richardson, and U. Keller, “Synchronously pumped optical parametric oscillator with a repetition rate of 81.8 GHz,” IEEE Photon. Technol. Lett.17, 483–485 (2005).
[CrossRef]

Gabriel, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4, 711–715 (2010).
[CrossRef]

Gaeta, A. L.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4, 37–40 (2010).
[CrossRef]

Gondarenko, A.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4, 37–40 (2010).
[CrossRef]

Green, W. M. J.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics4, 557–560 (2010).
[CrossRef]

Hall, J. L.

L. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett.57, 2520–2523 (1986).
[CrossRef] [PubMed]

Harris, S. E.

S. E. Harris, M. K. Oshman, and R. L. Byer, “Observation of tunable optical parametric fluorescence,” Phys. Rev. Lett.18, 732–734 (1967).
[CrossRef]

Hayes, D.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature464, 1021–1024 (2010).
[CrossRef] [PubMed]

Heckert, A.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Van- gel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST special publication 800-22, Rev. 1-a, NIST, Gaithersburg, Maryland, USA, (2010).

Jian, Y.

M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A83, 023820 (2011).
[CrossRef]

Jofre, M.

Keller, U.

S. Lecomte, R. Paschotta, S. Pawlik, B. Schmidt, K. Furusawa, A. Malinowski, D. J. Richardson, and U. Keller, “Synchronously pumped optical parametric oscillator with a repetition rate of 81.8 GHz,” IEEE Photon. Technol. Lett.17, 483–485 (2005).
[CrossRef]

Kimble, H. J.

L. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett.57, 2520–2523 (1986).
[CrossRef] [PubMed]

Lausten, R.

Lecomte, S.

S. Lecomte, R. Paschotta, S. Pawlik, B. Schmidt, K. Furusawa, A. Malinowski, D. J. Richardson, and U. Keller, “Synchronously pumped optical parametric oscillator with a repetition rate of 81.8 GHz,” IEEE Photon. Technol. Lett.17, 483–485 (2005).
[CrossRef]

Leifgen, M.

M. Wahl, M. Leifgen, M. Berlin, T. Rhlicke, H. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett.98, 171105 (2011).
[CrossRef]

Leigh, S.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Van- gel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST special publication 800-22, Rev. 1-a, NIST, Gaithersburg, Maryland, USA, (2010).

Leindecker, N.

Leuchs, G.

J. U. Furst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett.106, 113901 (2011).
[CrossRef] [PubMed]

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4, 711–715 (2010).
[CrossRef]

Levenson, M.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Van- gel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST special publication 800-22, Rev. 1-a, NIST, Gaithersburg, Maryland, USA, (2010).

Levy, J. S.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4, 37–40 (2010).
[CrossRef]

Liang, Y.

M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A83, 023820 (2011).
[CrossRef]

Lipson, M.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4, 37–40 (2010).
[CrossRef]

Little, B. E.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4, 41–45 (2010).
[CrossRef]

Liu, X.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics4, 557–560 (2010).
[CrossRef]

Lo, H.

Louisell, W. H.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes I,” Phys. Rev.124, 1646–1654 (1961).
[CrossRef]

Luo, L.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature464, 1021–1024 (2010).
[CrossRef] [PubMed]

Malinowski, A.

S. Lecomte, R. Paschotta, S. Pawlik, B. Schmidt, K. Furusawa, A. Malinowski, D. J. Richardson, and U. Keller, “Synchronously pumped optical parametric oscillator with a repetition rate of 81.8 GHz,” IEEE Photon. Technol. Lett.17, 483–485 (2005).
[CrossRef]

Manning, T. A.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature464, 1021–1024 (2010).
[CrossRef] [PubMed]

Marandi, A.

Marquardt, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4, 711–715 (2010).
[CrossRef]

Marquardt, Ch.

J. U. Furst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett.106, 113901 (2011).
[CrossRef] [PubMed]

Massar, S.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature464, 1021–1024 (2010).
[CrossRef] [PubMed]

Matsukevich, D. N.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature464, 1021–1024 (2010).
[CrossRef] [PubMed]

Mauerer, W.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4, 711–715 (2010).
[CrossRef]

Maunz, P.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature464, 1021–1024 (2010).
[CrossRef] [PubMed]

Mitchell, M. W.

Moffatt, D.

Monroe, C.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature464, 1021–1024 (2010).
[CrossRef] [PubMed]

Morandotti, R.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4, 41–45 (2010).
[CrossRef]

Moss, D. J.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4, 41–45 (2010).
[CrossRef]

Munro, W. J.

M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, “Secure self-calibrating quantum random-bit generator,” Phys. Rev. A75, 032334 (2007).
[CrossRef]

Myers, L. E.

Nabors, C. D.

Nechvatal, J.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Van- gel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST special publication 800-22, Rev. 1-a, NIST, Gaithersburg, Maryland, USA, (2010).

Olmschenk, S.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature464, 1021–1024 (2010).
[CrossRef] [PubMed]

Osgood, R. M.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics4, 557–560 (2010).
[CrossRef]

Oshman, M. K.

S. E. Harris, M. K. Oshman, and R. L. Byer, “Observation of tunable optical parametric fluorescence,” Phys. Rev. Lett.18, 732–734 (1967).
[CrossRef]

Paschotta, R.

S. Lecomte, R. Paschotta, S. Pawlik, B. Schmidt, K. Furusawa, A. Malinowski, D. J. Richardson, and U. Keller, “Synchronously pumped optical parametric oscillator with a repetition rate of 81.8 GHz,” IEEE Photon. Technol. Lett.17, 483–485 (2005).
[CrossRef]

Pawlik, S.

S. Lecomte, R. Paschotta, S. Pawlik, B. Schmidt, K. Furusawa, A. Malinowski, D. J. Richardson, and U. Keller, “Synchronously pumped optical parametric oscillator with a repetition rate of 81.8 GHz,” IEEE Photon. Technol. Lett.17, 483–485 (2005).
[CrossRef]

Pervak, V.

Pierce, J. W.

Pironio, S.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature464, 1021–1024 (2010).
[CrossRef] [PubMed]

Pruneri, V.

Qi, B.

Qian, Li

Rahn, H.

M. Wahl, M. Leifgen, M. Berlin, T. Rhlicke, H. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett.98, 171105 (2011).
[CrossRef]

Razzari, L.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4, 41–45 (2010).
[CrossRef]

Ren, M.

M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A83, 023820 (2011).
[CrossRef]

Rhlicke, T.

M. Wahl, M. Leifgen, M. Berlin, T. Rhlicke, H. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett.98, 171105 (2011).
[CrossRef]

Richardson, D. J.

S. Lecomte, R. Paschotta, S. Pawlik, B. Schmidt, K. Furusawa, A. Malinowski, D. J. Richardson, and U. Keller, “Synchronously pumped optical parametric oscillator with a repetition rate of 81.8 GHz,” IEEE Photon. Technol. Lett.17, 483–485 (2005).
[CrossRef]

Rukhin, A.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Van- gel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST special publication 800-22, Rev. 1-a, NIST, Gaithersburg, Maryland, USA, (2010).

Santori, C.

M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, “Secure self-calibrating quantum random-bit generator,” Phys. Rev. A75, 032334 (2007).
[CrossRef]

Schmidt, B.

S. Lecomte, R. Paschotta, S. Pawlik, B. Schmidt, K. Furusawa, A. Malinowski, D. J. Richardson, and U. Keller, “Synchronously pumped optical parametric oscillator with a repetition rate of 81.8 GHz,” IEEE Photon. Technol. Lett.17, 483–485 (2005).
[CrossRef]

Shih, Y. H.

Y. H. Shih and C. O. Alley, “New Type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett.61, 2921–2924 (1988).
[CrossRef] [PubMed]

Siegman, A. E.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes I,” Phys. Rev.124, 1646–1654 (1961).
[CrossRef]

Smid, M.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Van- gel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST special publication 800-22, Rev. 1-a, NIST, Gaithersburg, Maryland, USA, (2010).

Soto, J.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Van- gel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST special publication 800-22, Rev. 1-a, NIST, Gaithersburg, Maryland, USA, (2010).

Spillane, S. M.

M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, “Secure self-calibrating quantum random-bit generator,” Phys. Rev. A75, 032334 (2007).
[CrossRef]

Steinlechner, F.

Strekalov, D. V.

J. U. Furst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett.106, 113901 (2011).
[CrossRef] [PubMed]

Sussman, B. J.

Sych, D.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4, 711–715 (2010).
[CrossRef]

Torres, J. P.

Turner-Foster, A. C.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4, 37–40 (2010).
[CrossRef]

Van- gel, M.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Van- gel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST special publication 800-22, Rev. 1-a, NIST, Gaithersburg, Maryland, USA, (2010).

Vlasov, Y. A.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics4, 557–560 (2010).
[CrossRef]

Vo, S.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Van- gel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST special publication 800-22, Rev. 1-a, NIST, Gaithersburg, Maryland, USA, (2010).

Vodopyanov, K. L.

Wahl, M.

M. Wahl, M. Leifgen, M. Berlin, T. Rhlicke, H. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett.98, 171105 (2011).
[CrossRef]

Walmsley, I. A.

Wittmann, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4, 711–715 (2010).
[CrossRef]

Wong, S. T.

Wu, E.

M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A83, 023820 (2011).
[CrossRef]

Wu, G.

M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A83, 023820 (2011).
[CrossRef]

P. J. Bustard, D. Moffatt, R. Lausten, G. Wu, I. A. Walmsley, and B. J. Sussman, “Quantum random bit generation using stimulated Raman scattering,” Opt. Express19, 25173–25180 (2011).
[CrossRef]

Wu, H.

L. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett.57, 2520–2523 (1986).
[CrossRef] [PubMed]

Wu, L.

L. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett.57, 2520–2523 (1986).
[CrossRef] [PubMed]

Yang, S. T.

Yariv, A.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes I,” Phys. Rev.124, 1646–1654 (1961).
[CrossRef]

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, 2007).

Yeh, P.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, 2007).

Zeng, H.

M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A83, 023820 (2011).
[CrossRef]

Appl. Phys. Lett. (1)

M. Wahl, M. Leifgen, M. Berlin, T. Rhlicke, H. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett.98, 171105 (2011).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. Lecomte, R. Paschotta, S. Pawlik, B. Schmidt, K. Furusawa, A. Malinowski, D. J. Richardson, and U. Keller, “Synchronously pumped optical parametric oscillator with a repetition rate of 81.8 GHz,” IEEE Photon. Technol. Lett.17, 483–485 (2005).
[CrossRef]

J. Opt. Soc. Am. B (3)

Nat. Photonics (4)

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4, 711–715 (2010).
[CrossRef]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4, 37–40 (2010).
[CrossRef]

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4, 41–45 (2010).
[CrossRef]

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics4, 557–560 (2010).
[CrossRef]

Nature (1)

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature464, 1021–1024 (2010).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. (1)

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes I,” Phys. Rev.124, 1646–1654 (1961).
[CrossRef]

Phys. Rev. A (2)

M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A83, 023820 (2011).
[CrossRef]

M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, “Secure self-calibrating quantum random-bit generator,” Phys. Rev. A75, 032334 (2007).
[CrossRef]

Phys. Rev. Lett. (4)

J. U. Furst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett.106, 113901 (2011).
[CrossRef] [PubMed]

L. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett.57, 2520–2523 (1986).
[CrossRef] [PubMed]

Y. H. Shih and C. O. Alley, “New Type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett.61, 2921–2924 (1988).
[CrossRef] [PubMed]

S. E. Harris, M. K. Oshman, and R. L. Byer, “Observation of tunable optical parametric fluorescence,” Phys. Rev. Lett.18, 732–734 (1967).
[CrossRef]

Other (2)

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, 2007).

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Van- gel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST special publication 800-22, Rev. 1-a, NIST, Gaithersburg, Maryland, USA, (2010).

Supplementary Material (1)

» Media 1: AVI (4857 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

(a) Phase sensitive gain in a degenerate OPO – the amplitude incremental gain of the signal (g|s|) versus the relative phase between the pump and the signal – (θs = ϕsϕp/2 +π/4, where ϕs and ϕp are the signal and pump phases, respectively), (b) Schematic of the all-optical quantum RNG. PD: Photodetector, BS: non-polarizing beam splitter, (c) Electric fields of the signal pulses compared to the pump in the two possible phase states of a short-pulse degenerate OPO.

Fig. 2.
Fig. 2.

(a) Schematic of the experimental setup consisting of the twin degenerate OPO followed by an un-equal arm Michelson interferometer. The round-trip length difference of the arms in the interferometer is equal to the separation length of pump pulses. The output of the interferometer is filtered to eliminate the pump. An AOM is used to restart the twin OPO at a clock rate of 10 kbps, while the zeroth order output (non-diffracted beam) pumps the OPO. The detector PD1 and a piezoelectric transducer (PZT) on M4 are parts of the “dither-and-lock” servo loop for stabilizing the cavity length to a resonance [16]. The interferometer arm length difference is stabilized using the interference of the undepleted pump and a PZT on M11 (not shown in this schematic) resulting in a fringe visibility of greater than 60% throughout the experiment. OC: Output Coupler, (b) Pump and signal pulse trains for a twin OPO in which the cavity roundtrip time (Tcavity) is twice the repetition period of the pump (Trep); this results in two independent OPOs with signal pulse trains at half the repetition frequency of the pump, marked by OPO1 and OPO2 on the pulse trains.

Fig. 3.
Fig. 3.

(a) Optical spectrum of the pump and signal, (b) complementary fringe patterns at the output of the Michelson interferometer, i.e. maximum on one pattern is minimum on the other and vice versa, (c) (Media 1) sample time domain signal of the interferometer output, i.e. the random sequence, along with the clock signal at 10 kbps.

Fig. 4.
Fig. 4.

Summary of the results of the NIST statistical tests [19] on a sequence of 1 billion bits. The sequence is chopped into 500 shorter sequences and each test is performed on all sequences. Horizontal axes shows the name of the tests, P – Value is the result of χ2 distribution evaluation for all short sequences, and Proportion is the proportion of the short sequences passed each test with a significance level of 0.01. The final decision on if the whole sequence has passed a test is made based on these criteria: P – Value > 0.0001 and Proportion > 0.976 [19], which are satisfied for all the tests.

Fig. 5.
Fig. 5.

(a) Dependence of the randomness on the clock speed; for each clock speed a sequence of 100 kb is recorded, and the rate of bit flip is calculated by counting the number of changes in the bit value and dividing it to the sequence length, for a random sequence the rate of bit flip is close to 0.5 and for a single-value sequence it is zero; The transition from random to non-random output occurred around 25 kbps which is close to the estimated value of 30 kbps taking into account the experiment parameters. This value can be increased by decreasing the overall pump power and approaching the threshold. To record the 1 Gb of data, the pump power was reduced so that the randomness would not break until 200 kbps (the measurement limit). (b, c, d) a sample of the output sequence when clock speed is (b) 20 kbps, (c) 30 kbps, and (d) 40 kbps.

Equations (1)

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τ off = T 2 δ E 2 δ E P off P t h ,

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