## All-optical quantum random bit generation from intrinsically binary phase of parametric oscillators |

Optics Express, Vol. 20, Issue 17, pp. 19322-19330 (2012)

http://dx.doi.org/10.1364/OE.20.019322

Acrobat PDF (1200 KB)

### 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

## 1. Introduction

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,” Nature **464**, 1021–1024 (2010). [CrossRef] [PubMed]

8. 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. Express **19**, 25173–25180 (2011). [CrossRef]

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,” Nature **464**, 1021–1024 (2010). [CrossRef] [PubMed]

2. M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, “Secure self-calibrating quantum random-bit generator,” Phys. Rev. A **75**, 032334 (2007). [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. Photonics **4**, 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. A **83**, 023820 (2011). [CrossRef]

6. 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. Express **19**, 20665–20672 (2011) [CrossRef] [PubMed]

7. 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]

8. 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. Express **19**, 25173–25180 (2011). [CrossRef]

9. 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]

10. 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]

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

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

13. C. D. Nabors, S. T. Yang, T. Day, and R. L. Byer, “Coherence properties of a doubly-resonant monolithic optical parametric oscillator,” J. Opt. Soc. Am. B **7**, 815–820 (1990). [CrossRef]

14. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO_{3},” J. Opt. Soc. Am. B **12**, 2102–2116 (1995). [CrossRef]

## 2. Theory

13. C. D. Nabors, S. T. Yang, T. Day, and R. L. Byer, “Coherence properties of a doubly-resonant monolithic optical parametric oscillator,” J. Opt. Soc. Am. B **7**, 815–820 (1990). [CrossRef]

*π*for the signal phase [15].

*θ*). Maximum amplification occurs both at

_{s}*θ*= 0 and

_{s}*θ*=

_{s}*π*, where the energy flows from the pump into the signal, and maximum deamplification at

*θ*=

_{s}*π*/2 where the energy flows from the signal to the pump. Equivalently, this period of

*π*exists in the phase dependence of quantum fluctuations in a squeezed state produced by degenerate parametric down conversion [9

9. 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]

*g*>

_{max}*g*=

_{th}*δ*, where

_{E}*δ*is the electric field round-trip loss [15]), depending on the zero-point fluctuations of the signal modes, the OPO will stably oscillate with the phase of either

_{E}*θ*= 0 or

_{s}*θ*=

_{s}*π*. This above-threshold phase state is inherited from the vacuum fluctuations [9

9. 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]

16. N. Leindecker, A. Marandi, R. L. Byer, and K. L. Vodopyanov, “Broadband degenerate OPO for mid-infrared frequency comb generation,” Opt. Express **19**, 6296–6302 (2011). [CrossRef] [PubMed]

17. 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. B **27**, 876–882 (2010). [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. Express **20**, 7255–7262 (2012). [CrossRef] [PubMed]

## 3. Experimental setup

_{2}and M

_{3}), and six flat mirrors, five of which are gold coated with approximately 99% reflection (M

_{4}–M

_{8}). A single dielectric mirror (M

_{1}) is used to introduce the pump, which has 90% transmission for the pump and more than 99% reflection in the 2.8 – 4

*μ*m. This mirror has a ‘chirped’ design of dielectric layers to compensate the dispersion of the nonlinear crystal.

*μ*m is provided by 1-mm long MgO-doped periodically poled lithium niobate (MgO:PPLN) crystal. The poling period is 34.8

*μ*m for broadband type-0 (e=e+e) phase matching at a temperature of 32°C. The crystal is cut such that the mid-IR beam propagates perpendicular to the poling domains when the beam enters at the Brewster angle. The beam waist for the signal in the crystal is ∼10

*μ*m. The mirrors M

_{2}and M

_{3}are set to 5-degree angle of incidence to compensate the astigmatism caused by the Brewster angled crystal and allow stable resonances in the 6-m long cavity. The output is extracted with a pellicle beam splitter (OC) having ∼8% reflection over a broad bandwidth. The filters are AR coated Ge substrates to block the pump and transmit the mid-IR signal.

_{4}. Three of these resonances occur separated by ∼1.5

*μ*m of roundtrip cavity length, corresponding to half of the signal central wavelength [16

16. N. Leindecker, A. Marandi, R. L. Byer, and K. L. Vodopyanov, “Broadband degenerate OPO for mid-infrared frequency comb generation,” Opt. Express **19**, 6296–6302 (2011). [CrossRef] [PubMed]

16. N. Leindecker, A. Marandi, R. L. Byer, and K. L. Vodopyanov, “Broadband degenerate OPO for mid-infrared frequency comb generation,” Opt. Express **19**, 6296–6302 (2011). [CrossRef] [PubMed]

## 4. Results and discussions

*μ*m and the pump centered at 1.56

*μ*m. Complementary stable fringe patterns at the output of the interferometer were obtained as depicted in Fig. 3(b) when the beams in the arms are slightly angled vertically. Blocking and unblocking the pump resulted in random toggling between these two patterns (Media 1).

19. 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).

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

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]

### 4.1. Estimated maximum speed

*W*, to the quantum noise level, i.e. one photon per mode (

*P*=

_{noise}*hν*Δ

*ν*[15]), which is about 1

*μW*. Here

*hν*is the photon energy at the central signal wavelength of 3.1

*μ*m, and Δ

*ν*is the OPO bandwidth at 3-dB level, estimated to be ∼10 THz (Fig. 3(a)). The intensity decay time of the OPO can be estimated using: where

*δ*is the electric-field fractional round-trip loss,

_{E}*P*is the pump power at threshold,

_{th}*P*is the pump power at the “off” state, and

_{off}*T*is the cavity roundtrip time. In the presence of the AOM, the OPO threshold measured before M

_{1}is increased to 190 mW because of pulse broadening in the AOM. The pump power at the off state is 168 mW, and intracavity power loss (2

*δ*) is estimated to be 0.27 resulting in the 1/e intensity decay time of 1.2

_{E}*μ*s. Hence the minimum turn-off time required for decaying from steady state power to quantum noise level is about 17

*μ*s corresponding to a maximum clock speed of ∼30 kbps.

## 5. Summary

*χ*

^{3}OPOs [22

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. Photonics **4**, 37–40 (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. Photonics **4**, 557–560 (2010). [CrossRef]

## Acknowledgments

## References and links

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,” Nature |

2. | M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, “Secure self-calibrating quantum random-bit generator,” Phys. Rev. A |

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. Photonics |

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. |

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. A |

6. | 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. Express |

7. | 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. |

8. | 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. Express |

9. | L. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. |

10. | 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. |

11. | W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes I,” Phys. Rev. |

12. | S. E. Harris, M. K. Oshman, and R. L. Byer, “Observation of tunable optical parametric fluorescence,” Phys. Rev. Lett. |

13. | C. D. Nabors, S. T. Yang, T. Day, and R. L. Byer, “Coherence properties of a doubly-resonant monolithic optical parametric oscillator,” J. Opt. Soc. Am. B |

14. | L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO |

15. | A. Yariv and P. Yeh, |

16. | N. Leindecker, A. Marandi, R. L. Byer, and K. L. Vodopyanov, “Broadband degenerate OPO for mid-infrared frequency comb generation,” Opt. Express |

17. | 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. B |

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. Express |

19. | 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). |

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. |

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. |

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. Photonics |

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. Photonics |

24. | X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics |

**OCIS Codes**

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: June 22, 2012

Revised Manuscript: August 1, 2012

Manuscript Accepted: August 2, 2012

Published: August 8, 2012

**Citation**

Alireza Marandi, Nick C. Leindecker, Konstantin L. Vodopyanov, and Robert L. Byer, "All-optical quantum random bit generation from intrinsically binary phase of parametric oscillators," Opt. Express **20**, 19322-19330 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-17-19322

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### References

- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes I,” Phys. Rev.124, 1646–1654 (1961). [CrossRef]
- S. E. Harris, M. K. Oshman, and R. L. Byer, “Observation of tunable optical parametric fluorescence,” Phys. Rev. Lett.18, 732–734 (1967). [CrossRef]
- C. D. Nabors, S. T. Yang, T. Day, and R. L. Byer, “Coherence properties of a doubly-resonant monolithic optical parametric oscillator,” J. Opt. Soc. Am. B7, 815–820 (1990). [CrossRef]
- L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B12, 2102–2116 (1995). [CrossRef]
- A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, 2007).
- 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]
- 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]
- 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). [CrossRef] [PubMed]
- 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).
- 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. 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]
- 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]

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