Abstract

We demonstrate a large-scale tunable-coupling ring resonator array, suitable for high-dimensional classical and quantum transforms, in a CMOS-compatible silicon photonics platform. The device consists of a waveguide coupled to 15 ring-based dispersive elements with programmable linewidths and resonance frequencies. The ability to control both quality factor and frequency of each ring provides an unprecedented 30 degrees of freedom in dispersion control on a single spatial channel. This programmable dispersion control system has a range of applications, including mode-locked lasers, quantum key distribution, and photon-pair generation. We also propose a novel application enabled by this circuit – high-speed quantum communications using temporal-mode-based quantum data locking – and discuss the utility of the system for performing the high-dimensional unitary optical transformations necessary for a quantum data locking demonstration.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]

2016 (5)

M. Pant and D. Englund, “High-dimensional unitary transformations and boson sampling on temporal modes using dispersive optics,” Phys. Rev. A 93, 043803 (2016).
[Crossref]

J. C. Mak, A. Bois, and J. K. Poon, “Programmable multiring butterworth filters with automated resonance and coupling tuning,” IEEE J. Sel. Topics Quantum Electron. 22, 232–240 (2016).
[Crossref]

D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: Experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
[Crossref]

Y. Liu, Z. Cao, C. Wu, D. Fukuda, L. You, J. Zhong, T. Numata, S. Chen, W. Zhang, S.-C. Shi, C.-Y. Lu, Z. Wang, X. Ma, J. Fan, Q. Zhang, and J.-W. Pan, “Experimental quantum data locking,” Phys. Rev. A 94, 020301 (2016).
[Crossref]

R. Adamczak, R. Latała, Z. Puchała, and K. Życzkowski, “Asymptotic entropic uncertainty relations,” J. Math. Phys. 57, 032204 (2016).
[Crossref]

2015 (6)

C. Lupo, “Quantum data locking for secure communication against an eavesdropper with time-limited storage,” Entropy 17, 3194–3204 (2015).
[Crossref]

J. C. Mak, W. D. Sacher, T. Xue, J. C. Mikkelsen, Z. Yong, and J. K. Poon, “Automatic resonance alignment of high-order microring filters,” IEEE J. Quant. Electron. 51, 1–11 (2015).
[Crossref]

C. Lupo and S. Lloyd, “Quantum data locking for high-rate private communication,” New J. Phys. 17, 033022 (2015).
[Crossref]

D. Bunandar, Z. Zhang, J. H. Shapiro, and D. R. Englund, “Practical high-dimensional quantum key distribution with decoy states,” Phys. Rev. A 91, 022336 (2015).
[Crossref]

H. Jayatilleka, K. Murray, M. Á. Guillén-Torres, M. Caverley, R. Hu, N. A. Jaeger, L. Chrostowski, and S. Shekhar, “Wavelength tuning and stabilization of microring-based filters using silicon in-resonator photoconductive heaters,” Opt. Express 23, 25084–25097 (2015).
[Crossref] [PubMed]

C. M. Gentry, J. M. Shainline, M. T. Wade, M. J. Stevens, S. D. Dyer, X. Zeng, F. Pavanello, T. Gerrits, S. W. Nam, R. P. Mirin, and M. A. Popović, “Quantum-correlated photon pairs generated in a commercial 45 nm complementary metal-oxide semiconductor microelectronic chip,” Optica 2, 1065–1071 (2015).
[Crossref]

2014 (5)

N. C. Harris, Y. Ma, J. Mower, T. Baehr-Jones, D. Englund, M. Hochberg, and C. Galland, “Efficient, compact and low loss thermo-optic phase shifter in silicon,” Opt. Express 22, 10487–10493 (2014).
[Crossref] [PubMed]

C. Lupo, M. M. Wilde, and S. Lloyd, “Robust quantum data locking from phase modulation,” Phys. Rev. A 90, 022326 (2014).
[Crossref]

S. Guha, P. Hayden, H. Krovi, S. Lloyd, C. Lupo, J. H. Shapiro, M. Takeoka, and M. M. Wilde, “Quantum enigma machines and the locking capacity of a quantum channel,” Phys. Rev. X 4, 011016 (2014).

C. Lupo and S. Lloyd, “Quantum-locked key distribution at nearly the classical capacity rate,” Phys. Rev. Lett. 113, 160502 (2014).
[Crossref] [PubMed]

E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. R. Watts, “An ultralow power athermal silicon modulator,” Nat. Commun. 5, 5008 (2014).
[Crossref] [PubMed]

2013 (4)

J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87, 062322 (2013).
[Crossref]

M. R. Watts, J. Sun, C. DeRose, D. C. Trotter, R. W. Young, and G. N. Nielson, “Adiabatic thermo-optic mach–zehnder switch,” Opt. Lett. 38, 733–735 (2013).
[Crossref] [PubMed]

O. Fawzi, P. Hayden, and P. Sen, “From low-distortion norm embeddings to explicit uncertainty relations and efficient information locking,” J. ACM 60, 44 (2013).
[Crossref]

F. Dupuis, J. Florjanczyk, P. Hayden, and D. Leung, “The locking-decoding frontier for generic dynamics,” Proc. R. Soc. A 46920130289 (2013).
[Crossref] [PubMed]

2010 (1)

2007 (1)

N. Litchinitser, M. Sumetsky, and P. Westbrook, “Fiber-based tunable dispersion compensation,” J. Opt. Fiber. Commun. Rep. 4, 41–85 (2007).
[Crossref]

2006 (1)

2005 (2)

2004 (3)

J. E. Heebner, P. Chak, S. Pereira, J. E. Sipe, and R. W. Boyd, “Distributed and localized feedback in microresonator sequences for linear and nonlinear optics,” J. Opt. Soc. Am. B 21, 1818–1832 (2004).
[Crossref]

D. P. DiVincenzo, M. Horodecki, D. W. Leung, J. A. Smolin, and B. M. Terhal, “Locking classical correlations in quantum states,” Phys. Rev. Lett. 92, 067902 (2004).
[Crossref] [PubMed]

P. Hayden, D. Leung, P. W. Shor, and A. Winter, “Randomizing quantum states: Constructions and applications,” Commun. Math. Phys. 250, 371–391 (2004).
[Crossref]

2002 (2)

K. Inoue, E. Waks, and Y. Yamamoto, “Differential phase shift quantum key distribution,” Phys. Rev. Lett. 89, 037902 (2002).
[Crossref] [PubMed]

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Tech. Lett. 14, 483–485 (2002).
[Crossref]

2000 (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36, 321–322 (2000).
[Crossref]

1999 (2)

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Tech. Lett. 11, 1623–1625 (1999).
[Crossref]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[Crossref]

1998 (1)

M. Powell, “Direct search algorithms for optimization calculations,” Acta Numer. 7, 287–336 (1998).
[Crossref]

1991 (1)

1989 (1)

S. Ryu, Y. Horiuchi, and K. Mochizuki, “Novel chromatic dispersion measurement method over continuous gigahertz tuning range,” J. Lightwave Technol. 7, 1177–1180 (1989).
[Crossref]

1949 (1)

C. E. Shannon, “Communication theory of secrecy systems,” Bell Syst. Tech. J. 28, 656–715 (1949).
[Crossref]

Adamczak, R.

R. Adamczak, R. Latała, Z. Puchała, and K. Życzkowski, “Asymptotic entropic uncertainty relations,” J. Math. Phys. 57, 032204 (2016).
[Crossref]

Allman, M. S.

D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: Experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
[Crossref]

Alloatti, L.

J. Notaros, F. Pavanello, M. T. Wade, C. Gentry, A. Atabaki, L. Alloatti, R. J. Ram, and M. Popovic, “Ultra-efficient CMOS fiber-to-chip grating couplers,” in “Optical Fiber Communication Conference,” OSA Technical Digest (Optical Society of America, 2016), paper M2I.5.

Atabaki, A.

J. Notaros, F. Pavanello, M. T. Wade, C. Gentry, A. Atabaki, L. Alloatti, R. J. Ram, and M. Popovic, “Ultra-efficient CMOS fiber-to-chip grating couplers,” in “Optical Fiber Communication Conference,” OSA Technical Digest (Optical Society of America, 2016), paper M2I.5.

Ayazi, A.

T. Baehr-Jones, R. Ding, A. Ayazi, T. Pinguet, M. Streshinsky, N. Harris, J. Li, L. He, M. Gould, Y. Zhang, A. E.-J. Lim, T.-Y. Liow, S. H.-G. Teo, G.-Q. Lo, and M. Hochberg, “A 25 Gb/s silicon photonics platform,” arXiv:1203.0767 (2012).

Baehr-Jones, T.

N. C. Harris, Y. Ma, J. Mower, T. Baehr-Jones, D. Englund, M. Hochberg, and C. Galland, “Efficient, compact and low loss thermo-optic phase shifter in silicon,” Opt. Express 22, 10487–10493 (2014).
[Crossref] [PubMed]

T. Baehr-Jones, R. Ding, A. Ayazi, T. Pinguet, M. Streshinsky, N. Harris, J. Li, L. He, M. Gould, Y. Zhang, A. E.-J. Lim, T.-Y. Liow, S. H.-G. Teo, G.-Q. Lo, and M. Hochberg, “A 25 Gb/s silicon photonics platform,” arXiv:1203.0767 (2012).

Biberman, A.

E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. R. Watts, “An ultralow power athermal silicon modulator,” Nat. Commun. 5, 5008 (2014).
[Crossref] [PubMed]

Bois, A.

J. C. Mak, A. Bois, and J. K. Poon, “Programmable multiring butterworth filters with automated resonance and coupling tuning,” IEEE J. Sel. Topics Quantum Electron. 22, 232–240 (2016).
[Crossref]

Boyd, R. W.

Bruce, A.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Tech. Lett. 11, 1623–1625 (1999).
[Crossref]

Bunandar, D.

D. Bunandar, Z. Zhang, J. H. Shapiro, and D. R. Englund, “Practical high-dimensional quantum key distribution with decoy states,” Phys. Rev. A 91, 022336 (2015).
[Crossref]

Cao, Z.

Y. Liu, Z. Cao, C. Wu, D. Fukuda, L. You, J. Zhong, T. Numata, S. Chen, W. Zhang, S.-C. Shi, C.-Y. Lu, Z. Wang, X. Ma, J. Fan, Q. Zhang, and J.-W. Pan, “Experimental quantum data locking,” Phys. Rev. A 94, 020301 (2016).
[Crossref]

Cappuzzo, M.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Tech. Lett. 11, 1623–1625 (1999).
[Crossref]

Caverley, M.

Chak, P.

Cheben, P.

J. H. Schmid, P. Cheben, M. Rahim, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, M.-J. Picard, M. Poulin, and M. Guy, “Subwavelength gratings for broadband and polarization independent fiber-chip coupling with −0.4 dB efficiency,” in “Optical Fiber Communication Conference,” OSA Technical Digest (Optical Society of America, 2016), paper M2I.4.

Chen, S.

Y. Liu, Z. Cao, C. Wu, D. Fukuda, L. You, J. Zhong, T. Numata, S. Chen, W. Zhang, S.-C. Shi, C.-Y. Lu, Z. Wang, X. Ma, J. Fan, Q. Zhang, and J.-W. Pan, “Experimental quantum data locking,” Phys. Rev. A 94, 020301 (2016).
[Crossref]

Chrostowski, L.

DeRose, C.

DeRose, G. A.

Desjardins, P.

J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87, 062322 (2013).
[Crossref]

Ding, R.

T. Baehr-Jones, R. Ding, A. Ayazi, T. Pinguet, M. Streshinsky, N. Harris, J. Li, L. He, M. Gould, Y. Zhang, A. E.-J. Lim, T.-Y. Liow, S. H.-G. Teo, G.-Q. Lo, and M. Hochberg, “A 25 Gb/s silicon photonics platform,” arXiv:1203.0767 (2012).

DiVincenzo, D. P.

D. P. DiVincenzo, M. Horodecki, D. W. Leung, J. A. Smolin, and B. M. Terhal, “Locking classical correlations in quantum states,” Phys. Rev. Lett. 92, 067902 (2004).
[Crossref] [PubMed]

Dupuis, F.

F. Dupuis, J. Florjanczyk, P. Hayden, and D. Leung, “The locking-decoding frontier for generic dynamics,” Proc. R. Soc. A 46920130289 (2013).
[Crossref] [PubMed]

Dyer, S. D.

Englund, D.

M. Pant and D. Englund, “High-dimensional unitary transformations and boson sampling on temporal modes using dispersive optics,” Phys. Rev. A 93, 043803 (2016).
[Crossref]

N. C. Harris, Y. Ma, J. Mower, T. Baehr-Jones, D. Englund, M. Hochberg, and C. Galland, “Efficient, compact and low loss thermo-optic phase shifter in silicon,” Opt. Express 22, 10487–10493 (2014).
[Crossref] [PubMed]

J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87, 062322 (2013).
[Crossref]

Englund, D. R.

D. Bunandar, Z. Zhang, J. H. Shapiro, and D. R. Englund, “Practical high-dimensional quantum key distribution with decoy states,” Phys. Rev. A 91, 022336 (2015).
[Crossref]

Fan, J.

Y. Liu, Z. Cao, C. Wu, D. Fukuda, L. You, J. Zhong, T. Numata, S. Chen, W. Zhang, S.-C. Shi, C.-Y. Lu, Z. Wang, X. Ma, J. Fan, Q. Zhang, and J.-W. Pan, “Experimental quantum data locking,” Phys. Rev. A 94, 020301 (2016).
[Crossref]

Fan, L.

Fawzi, O.

O. Fawzi, P. Hayden, and P. Sen, “From low-distortion norm embeddings to explicit uncertainty relations and efficient information locking,” J. ACM 60, 44 (2013).
[Crossref]

Florjanczyk, J.

F. Dupuis, J. Florjanczyk, P. Hayden, and D. Leung, “The locking-decoding frontier for generic dynamics,” Proc. R. Soc. A 46920130289 (2013).
[Crossref] [PubMed]

Fujimoto, J. G.

Fukuda, D.

Y. Liu, Z. Cao, C. Wu, D. Fukuda, L. You, J. Zhong, T. Numata, S. Chen, W. Zhang, S.-C. Shi, C.-Y. Lu, Z. Wang, X. Ma, J. Fan, Q. Zhang, and J.-W. Pan, “Experimental quantum data locking,” Phys. Rev. A 94, 020301 (2016).
[Crossref]

Galland, C.

Gentry, C.

J. Notaros, F. Pavanello, M. T. Wade, C. Gentry, A. Atabaki, L. Alloatti, R. J. Ram, and M. Popovic, “Ultra-efficient CMOS fiber-to-chip grating couplers,” in “Optical Fiber Communication Conference,” OSA Technical Digest (Optical Society of America, 2016), paper M2I.5.

Gentry, C. M.

Gerrits, T.

Gomez, L.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Tech. Lett. 11, 1623–1625 (1999).
[Crossref]

Gould, M.

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Guy, M.

J. H. Schmid, P. Cheben, M. Rahim, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, M.-J. Picard, M. Poulin, and M. Guy, “Subwavelength gratings for broadband and polarization independent fiber-chip coupling with −0.4 dB efficiency,” in “Optical Fiber Communication Conference,” OSA Technical Digest (Optical Society of America, 2016), paper M2I.4.

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T. Baehr-Jones, R. Ding, A. Ayazi, T. Pinguet, M. Streshinsky, N. Harris, J. Li, L. He, M. Gould, Y. Zhang, A. E.-J. Lim, T.-Y. Liow, S. H.-G. Teo, G.-Q. Lo, and M. Hochberg, “A 25 Gb/s silicon photonics platform,” arXiv:1203.0767 (2012).

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Haus, H. A.

Hayden, P.

S. Guha, P. Hayden, H. Krovi, S. Lloyd, C. Lupo, J. H. Shapiro, M. Takeoka, and M. M. Wilde, “Quantum enigma machines and the locking capacity of a quantum channel,” Phys. Rev. X 4, 011016 (2014).

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T. Baehr-Jones, R. Ding, A. Ayazi, T. Pinguet, M. Streshinsky, N. Harris, J. Li, L. He, M. Gould, Y. Zhang, A. E.-J. Lim, T.-Y. Liow, S. H.-G. Teo, G.-Q. Lo, and M. Hochberg, “A 25 Gb/s silicon photonics platform,” arXiv:1203.0767 (2012).

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Hochberg, M.

N. C. Harris, Y. Ma, J. Mower, T. Baehr-Jones, D. Englund, M. Hochberg, and C. Galland, “Efficient, compact and low loss thermo-optic phase shifter in silicon,” Opt. Express 22, 10487–10493 (2014).
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S. Ryu, Y. Horiuchi, and K. Mochizuki, “Novel chromatic dispersion measurement method over continuous gigahertz tuning range,” J. Lightwave Technol. 7, 1177–1180 (1989).
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D. P. DiVincenzo, M. Horodecki, D. W. Leung, J. A. Smolin, and B. M. Terhal, “Locking classical correlations in quantum states,” Phys. Rev. Lett. 92, 067902 (2004).
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E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. R. Watts, “An ultralow power athermal silicon modulator,” Nat. Commun. 5, 5008 (2014).
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D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: Experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
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Khan, M. H.

Krovi, H.

S. Guha, P. Hayden, H. Krovi, S. Lloyd, C. Lupo, J. H. Shapiro, M. Takeoka, and M. M. Wilde, “Quantum enigma machines and the locking capacity of a quantum channel,” Phys. Rev. X 4, 011016 (2014).

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J. H. Schmid, P. Cheben, M. Rahim, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, M.-J. Picard, M. Poulin, and M. Guy, “Subwavelength gratings for broadband and polarization independent fiber-chip coupling with −0.4 dB efficiency,” in “Optical Fiber Communication Conference,” OSA Technical Digest (Optical Society of America, 2016), paper M2I.4.

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F. Dupuis, J. Florjanczyk, P. Hayden, and D. Leung, “The locking-decoding frontier for generic dynamics,” Proc. R. Soc. A 46920130289 (2013).
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D. P. DiVincenzo, M. Horodecki, D. W. Leung, J. A. Smolin, and B. M. Terhal, “Locking classical correlations in quantum states,” Phys. Rev. Lett. 92, 067902 (2004).
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T. Baehr-Jones, R. Ding, A. Ayazi, T. Pinguet, M. Streshinsky, N. Harris, J. Li, L. He, M. Gould, Y. Zhang, A. E.-J. Lim, T.-Y. Liow, S. H.-G. Teo, G.-Q. Lo, and M. Hochberg, “A 25 Gb/s silicon photonics platform,” arXiv:1203.0767 (2012).

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T. Baehr-Jones, R. Ding, A. Ayazi, T. Pinguet, M. Streshinsky, N. Harris, J. Li, L. He, M. Gould, Y. Zhang, A. E.-J. Lim, T.-Y. Liow, S. H.-G. Teo, G.-Q. Lo, and M. Hochberg, “A 25 Gb/s silicon photonics platform,” arXiv:1203.0767 (2012).

Liow, T.-Y.

T. Baehr-Jones, R. Ding, A. Ayazi, T. Pinguet, M. Streshinsky, N. Harris, J. Li, L. He, M. Gould, Y. Zhang, A. E.-J. Lim, T.-Y. Liow, S. H.-G. Teo, G.-Q. Lo, and M. Hochberg, “A 25 Gb/s silicon photonics platform,” arXiv:1203.0767 (2012).

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Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
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N. Litchinitser, M. Sumetsky, and P. Westbrook, “Fiber-based tunable dispersion compensation,” J. Opt. Fiber. Commun. Rep. 4, 41–85 (2007).
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D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: Experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
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Y. Liu, Z. Cao, C. Wu, D. Fukuda, L. You, J. Zhong, T. Numata, S. Chen, W. Zhang, S.-C. Shi, C.-Y. Lu, Z. Wang, X. Ma, J. Fan, Q. Zhang, and J.-W. Pan, “Experimental quantum data locking,” Phys. Rev. A 94, 020301 (2016).
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D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: Experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
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D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: Experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
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C. Lupo and S. Lloyd, “Quantum-locked key distribution at nearly the classical capacity rate,” Phys. Rev. Lett. 113, 160502 (2014).
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S. Guha, P. Hayden, H. Krovi, S. Lloyd, C. Lupo, J. H. Shapiro, M. Takeoka, and M. M. Wilde, “Quantum enigma machines and the locking capacity of a quantum channel,” Phys. Rev. X 4, 011016 (2014).

C. Lupo, M. M. Wilde, and S. Lloyd, “Robust quantum data locking from phase modulation,” Phys. Rev. A 90, 022326 (2014).
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Y. Liu, Z. Cao, C. Wu, D. Fukuda, L. You, J. Zhong, T. Numata, S. Chen, W. Zhang, S.-C. Shi, C.-Y. Lu, Z. Wang, X. Ma, J. Fan, Q. Zhang, and J.-W. Pan, “Experimental quantum data locking,” Phys. Rev. A 94, 020301 (2016).
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Madsen, C.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Tech. Lett. 11, 1623–1625 (1999).
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J. C. Mak, A. Bois, and J. K. Poon, “Programmable multiring butterworth filters with automated resonance and coupling tuning,” IEEE J. Sel. Topics Quantum Electron. 22, 232–240 (2016).
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J. C. Mak, W. D. Sacher, T. Xue, J. C. Mikkelsen, Z. Yong, and J. K. Poon, “Automatic resonance alignment of high-order microring filters,” IEEE J. Quant. Electron. 51, 1–11 (2015).
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J. C. Mak, W. D. Sacher, T. Xue, J. C. Mikkelsen, Z. Yong, and J. K. Poon, “Automatic resonance alignment of high-order microring filters,” IEEE J. Quant. Electron. 51, 1–11 (2015).
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Mochizuki, K.

S. Ryu, Y. Horiuchi, and K. Mochizuki, “Novel chromatic dispersion measurement method over continuous gigahertz tuning range,” J. Lightwave Technol. 7, 1177–1180 (1989).
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N. C. Harris, Y. Ma, J. Mower, T. Baehr-Jones, D. Englund, M. Hochberg, and C. Galland, “Efficient, compact and low loss thermo-optic phase shifter in silicon,” Opt. Express 22, 10487–10493 (2014).
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Y. Liu, Z. Cao, C. Wu, D. Fukuda, L. You, J. Zhong, T. Numata, S. Chen, W. Zhang, S.-C. Shi, C.-Y. Lu, Z. Wang, X. Ma, J. Fan, Q. Zhang, and J.-W. Pan, “Experimental quantum data locking,” Phys. Rev. A 94, 020301 (2016).
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Painchaud, Y.

J. H. Schmid, P. Cheben, M. Rahim, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, M.-J. Picard, M. Poulin, and M. Guy, “Subwavelength gratings for broadband and polarization independent fiber-chip coupling with −0.4 dB efficiency,” in “Optical Fiber Communication Conference,” OSA Technical Digest (Optical Society of America, 2016), paper M2I.4.

Pan, J.-W.

Y. Liu, Z. Cao, C. Wu, D. Fukuda, L. You, J. Zhong, T. Numata, S. Chen, W. Zhang, S.-C. Shi, C.-Y. Lu, Z. Wang, X. Ma, J. Fan, Q. Zhang, and J.-W. Pan, “Experimental quantum data locking,” Phys. Rev. A 94, 020301 (2016).
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Picard, M.-J.

J. H. Schmid, P. Cheben, M. Rahim, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, M.-J. Picard, M. Poulin, and M. Guy, “Subwavelength gratings for broadband and polarization independent fiber-chip coupling with −0.4 dB efficiency,” in “Optical Fiber Communication Conference,” OSA Technical Digest (Optical Society of America, 2016), paper M2I.4.

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T. Baehr-Jones, R. Ding, A. Ayazi, T. Pinguet, M. Streshinsky, N. Harris, J. Li, L. He, M. Gould, Y. Zhang, A. E.-J. Lim, T.-Y. Liow, S. H.-G. Teo, G.-Q. Lo, and M. Hochberg, “A 25 Gb/s silicon photonics platform,” arXiv:1203.0767 (2012).

Poon, J. K.

J. C. Mak, A. Bois, and J. K. Poon, “Programmable multiring butterworth filters with automated resonance and coupling tuning,” IEEE J. Sel. Topics Quantum Electron. 22, 232–240 (2016).
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J. C. Mak, W. D. Sacher, T. Xue, J. C. Mikkelsen, Z. Yong, and J. K. Poon, “Automatic resonance alignment of high-order microring filters,” IEEE J. Quant. Electron. 51, 1–11 (2015).
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J. Notaros, F. Pavanello, M. T. Wade, C. Gentry, A. Atabaki, L. Alloatti, R. J. Ram, and M. Popovic, “Ultra-efficient CMOS fiber-to-chip grating couplers,” in “Optical Fiber Communication Conference,” OSA Technical Digest (Optical Society of America, 2016), paper M2I.5.

Popovic, M. A.

Poulin, M.

J. H. Schmid, P. Cheben, M. Rahim, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, M.-J. Picard, M. Poulin, and M. Guy, “Subwavelength gratings for broadband and polarization independent fiber-chip coupling with −0.4 dB efficiency,” in “Optical Fiber Communication Conference,” OSA Technical Digest (Optical Society of America, 2016), paper M2I.4.

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Rahim, M.

J. H. Schmid, P. Cheben, M. Rahim, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, M.-J. Picard, M. Poulin, and M. Guy, “Subwavelength gratings for broadband and polarization independent fiber-chip coupling with −0.4 dB efficiency,” in “Optical Fiber Communication Conference,” OSA Technical Digest (Optical Society of America, 2016), paper M2I.4.

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J. Notaros, F. Pavanello, M. T. Wade, C. Gentry, A. Atabaki, L. Alloatti, R. J. Ram, and M. Popovic, “Ultra-efficient CMOS fiber-to-chip grating couplers,” in “Optical Fiber Communication Conference,” OSA Technical Digest (Optical Society of America, 2016), paper M2I.5.

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S. Ryu, Y. Horiuchi, and K. Mochizuki, “Novel chromatic dispersion measurement method over continuous gigahertz tuning range,” J. Lightwave Technol. 7, 1177–1180 (1989).
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J. C. Mak, W. D. Sacher, T. Xue, J. C. Mikkelsen, Z. Yong, and J. K. Poon, “Automatic resonance alignment of high-order microring filters,” IEEE J. Quant. Electron. 51, 1–11 (2015).
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Schmid, J. H.

J. H. Schmid, P. Cheben, M. Rahim, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, M.-J. Picard, M. Poulin, and M. Guy, “Subwavelength gratings for broadband and polarization independent fiber-chip coupling with −0.4 dB efficiency,” in “Optical Fiber Communication Conference,” OSA Technical Digest (Optical Society of America, 2016), paper M2I.4.

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Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
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C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Tech. Lett. 11, 1623–1625 (1999).
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O. Fawzi, P. Hayden, and P. Sen, “From low-distortion norm embeddings to explicit uncertainty relations and efficient information locking,” J. ACM 60, 44 (2013).
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J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87, 062322 (2013).
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Shen, H.

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Y. Liu, Z. Cao, C. Wu, D. Fukuda, L. You, J. Zhong, T. Numata, S. Chen, W. Zhang, S.-C. Shi, C.-Y. Lu, Z. Wang, X. Ma, J. Fan, Q. Zhang, and J.-W. Pan, “Experimental quantum data locking,” Phys. Rev. A 94, 020301 (2016).
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P. Hayden, D. Leung, P. W. Shor, and A. Winter, “Randomizing quantum states: Constructions and applications,” Commun. Math. Phys. 250, 371–391 (2004).
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Smolin, J. A.

D. P. DiVincenzo, M. Horodecki, D. W. Leung, J. A. Smolin, and B. M. Terhal, “Locking classical correlations in quantum states,” Phys. Rev. Lett. 92, 067902 (2004).
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E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. R. Watts, “An ultralow power athermal silicon modulator,” Nat. Commun. 5, 5008 (2014).
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Streshinsky, M.

T. Baehr-Jones, R. Ding, A. Ayazi, T. Pinguet, M. Streshinsky, N. Harris, J. Li, L. He, M. Gould, Y. Zhang, A. E.-J. Lim, T.-Y. Liow, S. H.-G. Teo, G.-Q. Lo, and M. Hochberg, “A 25 Gb/s silicon photonics platform,” arXiv:1203.0767 (2012).

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N. Litchinitser, M. Sumetsky, and P. Westbrook, “Fiber-based tunable dispersion compensation,” J. Opt. Fiber. Commun. Rep. 4, 41–85 (2007).
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E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. R. Watts, “An ultralow power athermal silicon modulator,” Nat. Commun. 5, 5008 (2014).
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T. Baehr-Jones, R. Ding, A. Ayazi, T. Pinguet, M. Streshinsky, N. Harris, J. Li, L. He, M. Gould, Y. Zhang, A. E.-J. Lim, T.-Y. Liow, S. H.-G. Teo, G.-Q. Lo, and M. Hochberg, “A 25 Gb/s silicon photonics platform,” arXiv:1203.0767 (2012).

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E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. R. Watts, “An ultralow power athermal silicon modulator,” Nat. Commun. 5, 5008 (2014).
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Optica (1)

Phys. Rev. A (6)

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[Crossref]

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[Crossref]

C. Lupo, M. M. Wilde, and S. Lloyd, “Robust quantum data locking from phase modulation,” Phys. Rev. A 90, 022326 (2014).
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[Crossref]

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Other (4)

S. Lloyd, “Quantum enigma machines,” arXiv:1307.0380 (2013).

T. Baehr-Jones, R. Ding, A. Ayazi, T. Pinguet, M. Streshinsky, N. Harris, J. Li, L. He, M. Gould, Y. Zhang, A. E.-J. Lim, T.-Y. Liow, S. H.-G. Teo, G.-Q. Lo, and M. Hochberg, “A 25 Gb/s silicon photonics platform,” arXiv:1203.0767 (2012).

J. Notaros, F. Pavanello, M. T. Wade, C. Gentry, A. Atabaki, L. Alloatti, R. J. Ram, and M. Popovic, “Ultra-efficient CMOS fiber-to-chip grating couplers,” in “Optical Fiber Communication Conference,” OSA Technical Digest (Optical Society of America, 2016), paper M2I.5.

J. H. Schmid, P. Cheben, M. Rahim, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, M.-J. Picard, M. Poulin, and M. Guy, “Subwavelength gratings for broadband and polarization independent fiber-chip coupling with −0.4 dB efficiency,” in “Optical Fiber Communication Conference,” OSA Technical Digest (Optical Society of America, 2016), paper M2I.4.

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Figures (11)

Fig. 1
Fig. 1

Schematic of (a) a ring with tunable resonance and (b) a ring with tunable coupling and resonance (a tunable-coupling ring). The resonant frequency is set using phase Φ and the coupling is set using phase Θ.

Fig. 2
Fig. 2

Simulated transmission and group delay as a function of wavelength for varying (a,c) resonance phase setting, Φ, and (b,d) coupling phase setting, Θ, for a single tunable-coupling ring with α = 0.99, L = 100μm, and neff = 2.7.

Fig. 3
Fig. 3

Schematic of the tunable-coupling ring array (TCRA) with three rings shown. The ring resonant frequencies are set using phases Φj and the couplings are set using phases Θj.

Fig. 4
Fig. 4

Simulated example transmissions and group delays for a 15-ring tunable-coupling ring array device with α = 0.99, L = 100μm, and neff = 2.7. (a,c) Arbitrary device spectrum with phase settings set to random values between 0 and 2π. (b,d) Example optimization of this device for three goal group delay functions. The goal group delays are shown as dashed lines while the optimized simulations are shown as solid lines.

Fig. 5
Fig. 5

(a) Layout of a single tunable-coupling ring. Optical micrographs of (b) the full fabricated 15-ring tunable-coupling ring array device and (c) a single tunable-coupling ring within the 15-ring array (device waveguides are traced in white on the micrographs for clarity).

Fig. 6
Fig. 6

Block diagram illustrating the experimental setup used to characterize the tunable-coupling ring array device. A modulated laser source is coupled onto the chip and the output signal is read using an off-chip photodiode. A lock-in amplifier is used to convert the photodiode signal to a phase measurement [21]. A Python interface reads the lock-in amplifier’s phase measurement and photodiode’s intensity output, controls an electrical driver circuit, and sweeps the tunable laser.

Fig. 7
Fig. 7

Passive spectrum of the 15-ring tunable-coupling ring array device.

Fig. 8
Fig. 8

Active tuning of a single ring in the tunable-coupling ring array device. Measured intensity and group delay as a function of wavelength for varying (a,c) resonance phase shifter voltage, Φ, and (b,d) coupling phase shifter voltage, Θ.

Fig. 9
Fig. 9

Optimization of the 15-ring tunable-coupling ring array device for an example goal group delay function (shown as a dashed line). The measured group delay spectra is shown in its initial state before the optimization has begun (solid red line), at an intermediate point within the optimization (solid green line), and in the final optimized state (solid blue line).

Fig. 10
Fig. 10

Schematic of a quantum enigma machine protocol. A relatively small key of ≪n bits is shared between Alice, the transmitter, and Bob, the receiver, and used to encode, and decode, the n bit message. The protocol guarantees composable security against an eavesdropper, Eve, with either a finite-coherence-time memory or no quantum memory at all.

Fig. 11
Fig. 11

Proposed quantum enigma machine protocol using the tunable-coupling ring array device. Photons are prepared in a time domain basis using a pulsed light source, locked using Alice’s TCRA, transmitted over a public channel, and unlocked using Bob’s TCRA. Alice’s and Bob’s TCRA settings for each transmission are determined using a secret pre-shared key.

Equations (6)

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

[ B 1 B 2 ] = M [ A 1 A 2 ]
M coupler = 1 2 [ κ i 1 κ 2 i 1 κ 2 κ ]
M MZI = e i ( Θ / 2 + π / 2 ) [ sin ( Θ / 2 ) cos ( Θ / 2 ) cos ( Θ / 2 ) sin ( Θ / 2 ) ]
A 2 = α e i ( β ( ω ) L + Φ ) B 2
T ( ω ) = B 1 A 1 = 1 e i Θ + 2 e i ( β ( ω ) L + Φ + Θ ) α 2 e i ( β ( ω ) L + Φ ) α + e i ( β ( ω ) L + Φ + Θ ) α .
T N ( ω ) = j = 1 n T j ( ω ) = j = 1 n 1 e i Θ j + 2 e i ( β ( ω ) L + Φ j + Θ j ) α j 2 e i ( β ( ω ) L + Φ j ) α j + e i ( β ( ω ) L + Φ j + Θ j ) α j

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