Abstract

Random number sequences are a critical resource in a wide variety of information systems, including applications in cryptography, simulation, and data sampling. We introduce a quantum random number generator based on the phase measurement of Stokes light generated by amplification of zero-point vacuum fluctuations using stimulated Raman scattering. This is an example of quantum noise amplification using the most noise-free process possible: near unitary quantum evolution. The use of phase offers robustness to classical pump noise and the ability to generate multiple bits per measurement. The Stokes light is generated with high intensity and as a result, fast detectors with high signal-to-noise ratios can be used for measurement, eliminating the need for single-photon sensitive devices. The demonstrated implementation uses optical phonons in bulk diamond.

© 2011 OSA

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  1. G. Marsaglia, “On the randomness of pi and other decimal expansions,” InterStat 5 (2005).
  2. Y. Shen, L. Tian, and H. Zou, “Practical quantum random number generator based on measuring the shot noise of vacuum states,” Phys. Rev. A 81, 063814 (2010).
    [CrossRef]
  3. H. Schmidt, “Quantum mechanical random number generator,” J. Appl. Phys. 41, 462–468 (1970).
    [CrossRef]
  4. B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, “High-speed quantum random number generation by measuring phase noise of a single-mode laser,” Opt. Lett. 35, 312–314 (2010).
    [CrossRef] [PubMed]
  5. H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E 81, 051137 (2010).
    [CrossRef]
  6. W. Wei and H. Guo, “Bias-free true random-number generator,” Opt. Lett. 34, 1876–1878 (2009).
    [CrossRef] [PubMed]
  7. 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. A 83, 023820 (2011).
    [CrossRef]
  8. M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. 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]
  9. J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93, 031109 (2008).
    [CrossRef]
  10. S. Pironio, A. Acín, S. Massar, A. Boyer 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,” Nature 464, 1021–1024 (2010).
    [CrossRef] [PubMed]
  11. U. Maurer, “Secret key agreement by public discussion from common information,” IEEE Trans. Inf. Theory 39, 733 –742 (1993).
    [CrossRef]
  12. A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55 (1979).
    [CrossRef]
  13. M. G. Raymer and I. A. Walmsley, “Quantum coherence properties of stimulated Raman scattering,” Prog. Opt. 28, 181 (1990).
    [CrossRef]
  14. M. G. Raymer, K. Rza̦żewski, and J. Mostowski, “Pulse-energy statistics in stimulated Raman scattering,” Opt. Lett. 7, 71–73 (1982).
    [CrossRef] [PubMed]
  15. I. A. Walmsley and M. G. Raymer, “Observation of macroscopic quantum fluctuations in stimulated Raman scattering,” Phys. Rev. Lett. 50, 962–965 (1983).
    [CrossRef]
  16. S. J. Kuo, D. T. Smithey, and M. G. Raymer, “Spatial interference of macroscopic light fields from independent Raman sources,” Phys. Rev. A 43, 4083–4086 (1991).
    [CrossRef] [PubMed]
  17. D. T. Smithey, M. Belsley, K. Wedding, and M. G. Raymer, “Near quantum-limited phase memory in a Raman amplifier,” Phys. Rev. Lett. 67, 2446–2449 (1991).
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  18. M. Belsley, D. T. Smithey, K. Wedding, and M. G. Raymer, “Observation of extreme sensitivity to induced molecular coherence in stimulated Raman scattering,” Phys. Rev. A 48, 1514 (1993).
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    [CrossRef]
  21. M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
    [CrossRef]
  22. J. von Neumann, “Various techniques used in connection with random digits,” Nat. Bur. Stand., Appl. Math Ser. 12, 36–38 (1951).
  23. A. Juels, M. Jakobsson, E. Shriver, and B. Hillyer, “How to turn loaded dice into fair coins,” IEEE Trans. Inf. Theory 46, 911 –921 (2000).
    [CrossRef]
  24. C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge Univ Pr, 2005).
  25. G. Marsaglia, “Diehard battery of tests of randomness,” http://www.stat.fsu.edu/pub/diehard/ .
  26. H. Haken, Encyclopedia of Physics, vol. 25 (Springer, 1970).
  27. W. Louisell, Quantum Statistical Properties of Radiation (John Wiley and Sons, Inc., New York, 1973).

2011 (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. A 83, 023820 (2011).
[CrossRef]

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. 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]

2010 (5)

S. Pironio, A. Acín, S. Massar, A. Boyer 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,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Y. Shen, L. Tian, and H. Zou, “Practical quantum random number generator based on measuring the shot noise of vacuum states,” Phys. Rev. A 81, 063814 (2010).
[CrossRef]

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

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E 81, 051137 (2010).
[CrossRef]

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diam. Relat. Mater. 19, 1289 – 1295 (2010).
[CrossRef]

2009 (1)

2008 (1)

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

2005 (1)

G. Marsaglia, “On the randomness of pi and other decimal expansions,” InterStat 5 (2005).

2000 (1)

A. Juels, M. Jakobsson, E. Shriver, and B. Hillyer, “How to turn loaded dice into fair coins,” IEEE Trans. Inf. Theory 46, 911 –921 (2000).
[CrossRef]

1993 (2)

M. Belsley, D. T. Smithey, K. Wedding, and M. G. Raymer, “Observation of extreme sensitivity to induced molecular coherence in stimulated Raman scattering,” Phys. Rev. A 48, 1514 (1993).
[CrossRef] [PubMed]

U. Maurer, “Secret key agreement by public discussion from common information,” IEEE Trans. Inf. Theory 39, 733 –742 (1993).
[CrossRef]

1991 (2)

S. J. Kuo, D. T. Smithey, and M. G. Raymer, “Spatial interference of macroscopic light fields from independent Raman sources,” Phys. Rev. A 43, 4083–4086 (1991).
[CrossRef] [PubMed]

D. T. Smithey, M. Belsley, K. Wedding, and M. G. Raymer, “Near quantum-limited phase memory in a Raman amplifier,” Phys. Rev. Lett. 67, 2446–2449 (1991).
[CrossRef] [PubMed]

1990 (1)

M. G. Raymer and I. A. Walmsley, “Quantum coherence properties of stimulated Raman scattering,” Prog. Opt. 28, 181 (1990).
[CrossRef]

1983 (1)

I. A. Walmsley and M. G. Raymer, “Observation of macroscopic quantum fluctuations in stimulated Raman scattering,” Phys. Rev. Lett. 50, 962–965 (1983).
[CrossRef]

1982 (1)

1981 (1)

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
[CrossRef]

1979 (1)

A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55 (1979).
[CrossRef]

1970 (1)

H. Schmidt, “Quantum mechanical random number generator,” J. Appl. Phys. 41, 462–468 (1970).
[CrossRef]

1951 (1)

J. von Neumann, “Various techniques used in connection with random digits,” Nat. Bur. Stand., Appl. Math Ser. 12, 36–38 (1951).

Acín, A.

S. Pironio, A. Acín, S. Massar, A. Boyer 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,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Bashkansky, M.

J. Reintjes and M. Bashkansky, Handbook of Optics, Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics, 3rd ed. (McGraw-Hill Professional, 2010), chap. 15, p. 15.1.

Belsley, M.

M. Belsley, D. T. Smithey, K. Wedding, and M. G. Raymer, “Observation of extreme sensitivity to induced molecular coherence in stimulated Raman scattering,” Phys. Rev. A 48, 1514 (1993).
[CrossRef] [PubMed]

D. T. Smithey, M. Belsley, K. Wedding, and M. G. Raymer, “Near quantum-limited phase memory in a Raman amplifier,” Phys. Rev. Lett. 67, 2446–2449 (1991).
[CrossRef] [PubMed]

Benson, O.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. 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. Röhlicke, H.-J. 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]

Boyer de la Giroday, A.

S. Pironio, A. Acín, S. Massar, A. Boyer 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,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Chi, Y.-M.

Dynes, J. F.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

Gerry, C.

C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge Univ Pr, 2005).

Guo, H.

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E 81, 051137 (2010).
[CrossRef]

W. Wei and H. Guo, “Bias-free true random-number generator,” Opt. Lett. 34, 1876–1878 (2009).
[CrossRef] [PubMed]

Haken, H.

H. Haken, Encyclopedia of Physics, vol. 25 (Springer, 1970).

Hayes, D.

S. Pironio, A. Acín, S. Massar, A. Boyer 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,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Hillyer, B.

A. Juels, M. Jakobsson, E. Shriver, and B. Hillyer, “How to turn loaded dice into fair coins,” IEEE Trans. Inf. Theory 46, 911 –921 (2000).
[CrossRef]

Jakobsson, M.

A. Juels, M. Jakobsson, E. Shriver, and B. Hillyer, “How to turn loaded dice into fair coins,” IEEE Trans. Inf. Theory 46, 911 –921 (2000).
[CrossRef]

Jaksch, D.

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diam. Relat. Mater. 19, 1289 – 1295 (2010).
[CrossRef]

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. A 83, 023820 (2011).
[CrossRef]

Juels, A.

A. Juels, M. Jakobsson, E. Shriver, and B. Hillyer, “How to turn loaded dice into fair coins,” IEEE Trans. Inf. Theory 46, 911 –921 (2000).
[CrossRef]

Kaiser, W.

A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55 (1979).
[CrossRef]

Knight, P.

C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge Univ Pr, 2005).

Kuo, S. J.

S. J. Kuo, D. T. Smithey, and M. G. Raymer, “Spatial interference of macroscopic light fields from independent Raman sources,” Phys. Rev. A 43, 4083–4086 (1991).
[CrossRef] [PubMed]

Laubereau, A.

A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55 (1979).
[CrossRef]

Lee, K. C.

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diam. Relat. Mater. 19, 1289 – 1295 (2010).
[CrossRef]

Leifgen, M.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. 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]

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. A 83, 023820 (2011).
[CrossRef]

Liu, Y.

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E 81, 051137 (2010).
[CrossRef]

Lo, H.-K.

Lorenz, V. O.

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diam. Relat. Mater. 19, 1289 – 1295 (2010).
[CrossRef]

Louisell, W.

W. Louisell, Quantum Statistical Properties of Radiation (John Wiley and Sons, Inc., New York, 1973).

Luo, L.

S. Pironio, A. Acín, S. Massar, A. Boyer 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,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Manning, T. A.

S. Pironio, A. Acín, S. Massar, A. Boyer 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,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Marsaglia, G.

G. Marsaglia, “On the randomness of pi and other decimal expansions,” InterStat 5 (2005).

Massar, S.

S. Pironio, A. Acín, S. Massar, A. Boyer 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,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Matsukevich, D. N.

S. Pironio, A. Acín, S. Massar, A. Boyer 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,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Maunz, P.

S. Pironio, A. Acín, S. Massar, A. Boyer 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,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Maurer, U.

U. Maurer, “Secret key agreement by public discussion from common information,” IEEE Trans. Inf. Theory 39, 733 –742 (1993).
[CrossRef]

Monroe, C.

S. Pironio, A. Acín, S. Massar, A. Boyer 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,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Mostowski, J.

M. G. Raymer, K. Rza̦żewski, and J. Mostowski, “Pulse-energy statistics in stimulated Raman scattering,” Opt. Lett. 7, 71–73 (1982).
[CrossRef] [PubMed]

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
[CrossRef]

Nunn, J.

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diam. Relat. Mater. 19, 1289 – 1295 (2010).
[CrossRef]

Olmschenk, S.

S. Pironio, A. Acín, S. Massar, A. Boyer 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,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Penzkofer, A.

A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55 (1979).
[CrossRef]

Pironio, S.

S. Pironio, A. Acín, S. Massar, A. Boyer 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,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Prawer, S.

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diam. Relat. Mater. 19, 1289 – 1295 (2010).
[CrossRef]

Qi, B.

Qian, L.

Rahn, H.-J.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. 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]

Raymer, M. G.

M. Belsley, D. T. Smithey, K. Wedding, and M. G. Raymer, “Observation of extreme sensitivity to induced molecular coherence in stimulated Raman scattering,” Phys. Rev. A 48, 1514 (1993).
[CrossRef] [PubMed]

S. J. Kuo, D. T. Smithey, and M. G. Raymer, “Spatial interference of macroscopic light fields from independent Raman sources,” Phys. Rev. A 43, 4083–4086 (1991).
[CrossRef] [PubMed]

D. T. Smithey, M. Belsley, K. Wedding, and M. G. Raymer, “Near quantum-limited phase memory in a Raman amplifier,” Phys. Rev. Lett. 67, 2446–2449 (1991).
[CrossRef] [PubMed]

M. G. Raymer and I. A. Walmsley, “Quantum coherence properties of stimulated Raman scattering,” Prog. Opt. 28, 181 (1990).
[CrossRef]

I. A. Walmsley and M. G. Raymer, “Observation of macroscopic quantum fluctuations in stimulated Raman scattering,” Phys. Rev. Lett. 50, 962–965 (1983).
[CrossRef]

M. G. Raymer, K. Rza̦żewski, and J. Mostowski, “Pulse-energy statistics in stimulated Raman scattering,” Opt. Lett. 7, 71–73 (1982).
[CrossRef] [PubMed]

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
[CrossRef]

Reim, K.

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diam. Relat. Mater. 19, 1289 – 1295 (2010).
[CrossRef]

Reintjes, J.

J. Reintjes and M. Bashkansky, Handbook of Optics, Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics, 3rd ed. (McGraw-Hill Professional, 2010), chap. 15, p. 15.1.

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. A 83, 023820 (2011).
[CrossRef]

Röhlicke, T.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. 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]

Rza?zewski, K.

Schmidt, H.

H. Schmidt, “Quantum mechanical random number generator,” J. Appl. Phys. 41, 462–468 (1970).
[CrossRef]

Sharpe, A. W.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

Shen, Y.

Y. Shen, L. Tian, and H. Zou, “Practical quantum random number generator based on measuring the shot noise of vacuum states,” Phys. Rev. A 81, 063814 (2010).
[CrossRef]

Shields, A. J.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

Shriver, E.

A. Juels, M. Jakobsson, E. Shriver, and B. Hillyer, “How to turn loaded dice into fair coins,” IEEE Trans. Inf. Theory 46, 911 –921 (2000).
[CrossRef]

Smithey, D. T.

M. Belsley, D. T. Smithey, K. Wedding, and M. G. Raymer, “Observation of extreme sensitivity to induced molecular coherence in stimulated Raman scattering,” Phys. Rev. A 48, 1514 (1993).
[CrossRef] [PubMed]

D. T. Smithey, M. Belsley, K. Wedding, and M. G. Raymer, “Near quantum-limited phase memory in a Raman amplifier,” Phys. Rev. Lett. 67, 2446–2449 (1991).
[CrossRef] [PubMed]

S. J. Kuo, D. T. Smithey, and M. G. Raymer, “Spatial interference of macroscopic light fields from independent Raman sources,” Phys. Rev. A 43, 4083–4086 (1991).
[CrossRef] [PubMed]

Spizzirri, P.

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diam. Relat. Mater. 19, 1289 – 1295 (2010).
[CrossRef]

Sussman, B. J.

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diam. Relat. Mater. 19, 1289 – 1295 (2010).
[CrossRef]

Tang, W.

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E 81, 051137 (2010).
[CrossRef]

Tian, L.

Y. Shen, L. Tian, and H. Zou, “Practical quantum random number generator based on measuring the shot noise of vacuum states,” Phys. Rev. A 81, 063814 (2010).
[CrossRef]

von Neumann, J.

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Wahl, M.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. 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.

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diam. Relat. Mater. 19, 1289 – 1295 (2010).
[CrossRef]

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[CrossRef]

I. A. Walmsley and M. G. Raymer, “Observation of macroscopic quantum fluctuations in stimulated Raman scattering,” Phys. Rev. Lett. 50, 962–965 (1983).
[CrossRef]

Wedding, K.

M. Belsley, D. T. Smithey, K. Wedding, and M. G. Raymer, “Observation of extreme sensitivity to induced molecular coherence in stimulated Raman scattering,” Phys. Rev. A 48, 1514 (1993).
[CrossRef] [PubMed]

D. T. Smithey, M. Belsley, K. Wedding, and M. G. Raymer, “Near quantum-limited phase memory in a Raman amplifier,” Phys. Rev. Lett. 67, 2446–2449 (1991).
[CrossRef] [PubMed]

Wei, W.

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E 81, 051137 (2010).
[CrossRef]

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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. A 83, 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. A 83, 023820 (2011).
[CrossRef]

Yuan, Z. L.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

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. A 83, 023820 (2011).
[CrossRef]

Zou, H.

Y. Shen, L. Tian, and H. Zou, “Practical quantum random number generator based on measuring the shot noise of vacuum states,” Phys. Rev. A 81, 063814 (2010).
[CrossRef]

Appl. Phys. Lett. (2)

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. 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]

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

Diam. Relat. Mater. (1)

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diam. Relat. Mater. 19, 1289 – 1295 (2010).
[CrossRef]

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[CrossRef]

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[CrossRef]

InterStat (1)

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H. Schmidt, “Quantum mechanical random number generator,” J. Appl. Phys. 41, 462–468 (1970).
[CrossRef]

Nat. Bur. Stand., Appl. Math Ser. (1)

J. von Neumann, “Various techniques used in connection with random digits,” Nat. Bur. Stand., Appl. Math Ser. 12, 36–38 (1951).

Nature (1)

S. Pironio, A. Acín, S. Massar, A. Boyer 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,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Opt. Lett. (3)

Phys. Rev. A (5)

S. J. Kuo, D. T. Smithey, and M. G. Raymer, “Spatial interference of macroscopic light fields from independent Raman sources,” Phys. Rev. A 43, 4083–4086 (1991).
[CrossRef] [PubMed]

M. Belsley, D. T. Smithey, K. Wedding, and M. G. Raymer, “Observation of extreme sensitivity to induced molecular coherence in stimulated Raman scattering,” Phys. Rev. A 48, 1514 (1993).
[CrossRef] [PubMed]

Y. Shen, L. Tian, and H. Zou, “Practical quantum random number generator based on measuring the shot noise of vacuum states,” Phys. Rev. A 81, 063814 (2010).
[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. A 83, 023820 (2011).
[CrossRef]

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
[CrossRef]

Phys. Rev. E (1)

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E 81, 051137 (2010).
[CrossRef]

Phys. Rev. Lett. (2)

D. T. Smithey, M. Belsley, K. Wedding, and M. G. Raymer, “Near quantum-limited phase memory in a Raman amplifier,” Phys. Rev. Lett. 67, 2446–2449 (1991).
[CrossRef] [PubMed]

I. A. Walmsley and M. G. Raymer, “Observation of macroscopic quantum fluctuations in stimulated Raman scattering,” Phys. Rev. Lett. 50, 962–965 (1983).
[CrossRef]

Prog. Opt. (1)

M. G. Raymer and I. A. Walmsley, “Quantum coherence properties of stimulated Raman scattering,” Prog. Opt. 28, 181 (1990).
[CrossRef]

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A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55 (1979).
[CrossRef]

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C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge Univ Pr, 2005).

G. Marsaglia, “Diehard battery of tests of randomness,” http://www.stat.fsu.edu/pub/diehard/ .

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W. Louisell, Quantum Statistical Properties of Radiation (John Wiley and Sons, Inc., New York, 1973).

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Figures (2)

Fig. 1
Fig. 1

Schematic diagram of Raman random number generator. A pump pulse is focussed into a 3 mm CVD diamond plate, generating a Stokes field with random phase. The pump field is filtered out using a bandpass filter, leaving only the Stokes field which is then combined with a reference pulse at a beamsplitter. A small lateral tilt is introduced and an interferogram is then measured using a linear CCD array. Inset: A Λ-level diagram shows the Raman transition in diamond used to generate the randomly-phased Raman Stokes light. Pump photons at 532 nm are annihilated; Stokes photons at 573 nm are generated along with vibrational phonons at Ω = 1332 cm−1.

Fig. 2
Fig. 2

Typical interferogram of two Stokes pulses generated by spontaneously initiated stimulated Raman scattering. The fringe phase is random for each measurement.

Tables (1)

Tables Icon

Table 1 Results of the DIEHARD statistical tests imposed on the Raman random number bit strings.

Equations (12)

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

z E ^ S ( ) ( z , τ ) = i κ 2 E p ( τ ) Q ^ ( z , τ )
τ Q ^ ( z , τ ) = Γ Q ^ ( z , τ ) + F ^ ( z , τ ) + i κ 1 E p * ( τ ) E ^ S ( ) ( z , τ ) .
Q ^ ( z , 0 ) Q ^ ( z , 0 ) = 1 ρ δ ( z z ) ,
F ^ ( z , τ ) = F ^ ( z , τ ) = 0 ,
F ^ ( z , τ ) F ^ ( z , τ ) = 2 Γ ρ δ ( z z ) δ ( τ τ ) ,
F ^ ( z , τ ) F ^ ( z , τ ) = 0 ,
Q ^ ( z , τ ) = τ F ^ ( z , τ ) e Γ ( τ τ ) d τ .
E ^ S ( ) ( L , τ ) = i κ 2 E p ( τ ) τ d τ 0 L d z [ e Γ ( τ τ ) K ( L , z ; τ , τ ) F ^ ( z , τ ) ] ,
K ( L , z ; τ , τ ) = I 0 ( 4 κ 1 κ 2 ( L z ) p ( τ , τ ) ) ,
p ( τ 1 , τ 2 ) = τ 2 τ 1 d τ | E p ( τ ) | 2 .
S int | E r ( z , τ ) | E ^ S ( ) ( L , τ ) e i ( Δ k x + ϕ r ) + h . c .
S int = G 1 [ F ( z , τ ) ] + G 2 [ F ( z , τ ) ] = 0 ,

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