Abstract

An integrated silicon nitride resonator is proposed as an ultra-compact source of bright single-mode quadrature squeezed light at 850 nm. Optical properties of the device are investigated and tailored through numerical simulations, with particular attention paid to loss associated with interfacing the device. An asymmetric double layer stack waveguide geometry with inverse vertical tapers is proposed for efficient and robust fibre-chip coupling, yielding a simulated total loss of −0.75 dB/facet. We assess the feasibility of the device through a full quantum noise analysis and derive the output squeezing spectrum for intra-cavity pump self-phase modulation. Subject to standard material loss and detection efficiencies, we find that the device holds promises for generating substantial quantum noise squeezing over a bandwidth exceeding 1 GHz. In the low-propagation loss regime, approximately -6 dB squeezing is predicted for a pump power of only 75 mW.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Squeezed quadrature fluctuations in a gravitational wave detector using squeezed light

S. Dwyer, L. Barsotti, S. S. Y. Chua, M. Evans, M. Factourovich, D. Gustafson, T. Isogai, K. Kawabe, A. Khalaidovski, P. K. Lam, M. Landry, N. Mavalvala, D. E. McClelland, G. D. Meadors, C. M. Mow-Lowry, R. Schnabel, R. M. S. Schofield, N. Smith-Lefebvre, M. Stefszky, C. Vorvick, and D. Sigg
Opt. Express 21(16) 19047-19060 (2013)

Detection of squeezed light with glass-integrated technology embedded into a homodyne detector setup

Carmen Porto, Davide Rusca, Simone Cialdi, Andrea Crespi, Roberto Osellame, Dario Tamascelli, Stefano Olivares, and Matteo G. A. Paris
J. Opt. Soc. Am. B 35(7) 1596-1602 (2018)

Femtosecond quadrature-squeezed light generation in CdSe at 1.55??µm

G.-M. Schucan, A. M. Fox, and J. F. Ryan
Opt. Lett. 23(9) 712-714 (1998)

References

  • View by:
  • |
  • |
  • |

  1. R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
    [Crossref] [PubMed]
  2. R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691–694 (1986).
    [Crossref] [PubMed]
  3. D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature 488, 476–480 (2012).
    [Crossref] [PubMed]
  4. T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3, 031012 (2013).
  5. A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
    [Crossref] [PubMed]
  6. L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
    [Crossref] [PubMed]
  7. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
    [Crossref]
  8. M. Xiao, L.-A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
    [Crossref] [PubMed]
  9. U. B. Hoff, G. I. Harris, L. S. Madsen, H. Kerdoncuff, M. Lassen, B. M. Nielsen, W. P. Bowen, and U. L. Andersen, “Quantum-enhanced micromechanical displacement sensitivity,” Opt. Lett. 38, 1413–1415 (2013).
    [Crossref] [PubMed]
  10. The LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot noise limit,” Nature Phys. 7, 962–965 (2011).
    [Crossref]
  11. K. Bergman and H. A. Haus, “Squeezing in fibers with optical pulses,” Opt. Lett. 16, 663–665 (1991).
    [Crossref] [PubMed]
  12. J. Heersink, V. Joss, G. Leuchs, and U. L. Andersen, “Efficient polarization squeezing in optical fibers,” Opt. Lett. 30, 1192–1194 (2005).
    [Crossref] [PubMed]
  13. P. Kürz, R. Paschotta, K. Fiedler, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
    [Crossref]
  14. G. Breitenbach, T. Müller, S. F. Pereira, J.-Ph. Poizat, S. Schiller, and J. Mlynek, “Squeezed vacuum from a monolithic optical parametric oscillator,” J. Opt. Soc. Am. B 12, 2304–2309 (1995).
    [Crossref]
  15. T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
    [Crossref] [PubMed]
  16. J. U. Fürst, 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]
  17. A. Dutt, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” arXiv p. 1309.6371 (2013).
  18. N. Daldosso, M. Melchiorri, F. Riboli, M. Girardini, G. Pucker, M. Crivellari, P. Bellutti, A. Lui, and L. Pavesi, “Comparison among various Si3N4 waveguide geometries grown within a CMOS fabrication pilot line,” J. Light-wave Technol. 22, 1734–1740 (2004).
    [Crossref]
  19. A. Gondarenko, J. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express 17, 11366–11370 (2009).
    [Crossref] [PubMed]
  20. J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Planar waveguides with less than 0.1 dB/m propagation loss fabricated with wafer bonding,” Opt. Express 19, 24090–24101 (2011).
    [Crossref] [PubMed]
  21. D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nature Photon. 7, 597–607 (2013).
    [Crossref]
  22. M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nature Photon. 2, 737 (2008).
    [Crossref]
  23. 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,” Nature Photon. 4, 37–40 (2009).
    [Crossref]
  24. Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. 36, 3398–3400 (2011).
    [Crossref] [PubMed]
  25. L. G. Helt, M. Liscidini, A. Farsi, S. Clemmen, V. Venkataraman, J. S. Levy, M. Lipson, A. L. Gaeta, and J. E. Sipe, “Quantum optics of spontaneous four-wave mixing in a silicon nitride microring resonator,” in “CLEO: 2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011, 2011), OSA Technical Digest (CD). Paper QWA4.
    [Crossref]
  26. R. Ghodssi and P. Lin, eds., MEMS Materials and Processes Handbook (Springer, 2011).
    [Crossref]
  27. K. Ikeda, R. E. Saperstein, N. Alic, and Y. Fainman, “Thermal and Kerr nonlinear properties of plasme-deposited silicon nitride/silicon dioxide waveguides,” Opt. Express 16, 12987–12994 (2008).
    [Crossref] [PubMed]
  28. H.-A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, 2004).
  29. A. Sizmann and G. Leuchs, “The optical Kerr effect and quantum optics in fibers,” Prog. Opt. 39, 373–469 (1999).
    [Crossref]
  30. L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nature Photon. 4, 41–45 (2009).
    [Crossref]
  31. T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nature Photon. 6, 480–487 (2012).
    [Crossref]
  32. M. Jack, M. Collet, and D. Walls, “Enhanced squeezing due to the influence of two instabilities,” Phys. Rev. A 51, 3318–3327 (1995).
    [Crossref] [PubMed]
  33. D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1995).
  34. C. W. Gardiner and P. Zoller, Quantum Noise (Springer-Verlag, 2000), second enlarged ed.
    [Crossref]
  35. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Effective mode area and its optimization in silicon-nanocrystal waveguides,” Opt. Lett. 37, 2295–2297 (2012).
    [Crossref] [PubMed]
  36. T. Chen, H. Lee, J. Li, and K. J. Vahala, “A general design algorithm for low optical loss adiabatic connections in waveguides,” Opt. Express 20, 22819–22829 (2012).
    [Crossref] [PubMed]
  37. W. Bogaerts and S. K. Selvaraja, “Compact single-mode silicon hybrid rib/strip waveguides with adiabatic bends,” IEEE Photonics J. 3, 422–432 (2011).
    [Crossref]
  38. C. Pollock and M. Lipson, Integrated Photonics (Kluwer Academic Publishers, 2010).
  39. J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: Adiabaticity criteria,” IEE Proc. J 138, 343–354 (1991).
  40. F. Ladouceur and J. D. Love, Silica-based Buried Channel Waveguides and Devices (Chapman & Hall, 1996).
  41. S. Reynaud, C. Fabre, E. Giacobino, and A. Heidmann, “Photon noise reduction by passive optical bistable systems,” Phys Rev A 40, 1440–1446 (1889).
    [Crossref]
  42. M. G. A. Paris, F. Illuminati, A. Serafini, and S. De Siena, “Purity of Gaussian states: Measurement schemes and time evolution in noisy channels,” Phys. Rev. Lett. 68, 012314 (2003).
  43. A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
    [Crossref]
  44. M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys. Rev. A 81, 013814 (2010).
    [Crossref]
  45. H. Yonezawa, K. Nagashima, and A. Furusawa, “Generation of squeezed light with a monolithic optical parametric oscillator: Simultaneous achievement of phase matching and cavity resonance by temperature control,” Opt. Express 18, 20143–20150 (2010).
    [Crossref] [PubMed]
  46. S. Ast, A. Samblowski, M. Mehmet, S. Steinlechner, T. Eberle, and R. Schnabel, “Continuous-wave nonclassical light with gigahertz squeezing bandwidth,” Opt. Lett 37, 2367–2369 (2012).
    [Crossref] [PubMed]
  47. S. Ast, M. Mehmet, and R. Schnabel, “High-bandwidth squeezed light at 1550 nm from a compact monolithic PPKTP cavity,” Opt. Express 21, 13572–13579 (2013).
    [Crossref] [PubMed]
  48. N. J. Cerf, M. Lévy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63, 052311 (2001).
    [Crossref]
  49. R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102, 130501 (2009).
    [Crossref] [PubMed]
  50. A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
    [Crossref] [PubMed]

2013 (6)

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3, 031012 (2013).

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
[Crossref] [PubMed]

U. B. Hoff, G. I. Harris, L. S. Madsen, H. Kerdoncuff, M. Lassen, B. M. Nielsen, W. P. Bowen, and U. L. Andersen, “Quantum-enhanced micromechanical displacement sensitivity,” Opt. Lett. 38, 1413–1415 (2013).
[Crossref] [PubMed]

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nature Photon. 7, 597–607 (2013).
[Crossref]

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
[Crossref]

S. Ast, M. Mehmet, and R. Schnabel, “High-bandwidth squeezed light at 1550 nm from a compact monolithic PPKTP cavity,” Opt. Express 21, 13572–13579 (2013).
[Crossref] [PubMed]

2012 (7)

S. Ast, A. Samblowski, M. Mehmet, S. Steinlechner, T. Eberle, and R. Schnabel, “Continuous-wave nonclassical light with gigahertz squeezing bandwidth,” Opt. Lett 37, 2367–2369 (2012).
[Crossref] [PubMed]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[Crossref] [PubMed]

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nature Photon. 6, 480–487 (2012).
[Crossref]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Effective mode area and its optimization in silicon-nanocrystal waveguides,” Opt. Lett. 37, 2295–2297 (2012).
[Crossref] [PubMed]

T. Chen, H. Lee, J. Li, and K. J. Vahala, “A general design algorithm for low optical loss adiabatic connections in waveguides,” Opt. Express 20, 22819–22829 (2012).
[Crossref] [PubMed]

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

D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature 488, 476–480 (2012).
[Crossref] [PubMed]

2011 (5)

The LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot noise limit,” Nature Phys. 7, 962–965 (2011).
[Crossref]

J. U. Fürst, 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]

W. Bogaerts and S. K. Selvaraja, “Compact single-mode silicon hybrid rib/strip waveguides with adiabatic bends,” IEEE Photonics J. 3, 422–432 (2011).
[Crossref]

J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Planar waveguides with less than 0.1 dB/m propagation loss fabricated with wafer bonding,” Opt. Express 19, 24090–24101 (2011).
[Crossref] [PubMed]

Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. 36, 3398–3400 (2011).
[Crossref] [PubMed]

2010 (3)

M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys. Rev. A 81, 013814 (2010).
[Crossref]

H. Yonezawa, K. Nagashima, and A. Furusawa, “Generation of squeezed light with a monolithic optical parametric oscillator: Simultaneous achievement of phase matching and cavity resonance by temperature control,” Opt. Express 18, 20143–20150 (2010).
[Crossref] [PubMed]

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[Crossref] [PubMed]

2009 (4)

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,” Nature Photon. 4, 37–40 (2009).
[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,” Nature Photon. 4, 41–45 (2009).
[Crossref]

A. Gondarenko, J. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express 17, 11366–11370 (2009).
[Crossref] [PubMed]

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102, 130501 (2009).
[Crossref] [PubMed]

2008 (2)

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nature Photon. 2, 737 (2008).
[Crossref]

K. Ikeda, R. E. Saperstein, N. Alic, and Y. Fainman, “Thermal and Kerr nonlinear properties of plasme-deposited silicon nitride/silicon dioxide waveguides,” Opt. Express 16, 12987–12994 (2008).
[Crossref] [PubMed]

2005 (1)

2004 (1)

N. Daldosso, M. Melchiorri, F. Riboli, M. Girardini, G. Pucker, M. Crivellari, P. Bellutti, A. Lui, and L. Pavesi, “Comparison among various Si3N4 waveguide geometries grown within a CMOS fabrication pilot line,” J. Light-wave Technol. 22, 1734–1740 (2004).
[Crossref]

2003 (1)

M. G. A. Paris, F. Illuminati, A. Serafini, and S. De Siena, “Purity of Gaussian states: Measurement schemes and time evolution in noisy channels,” Phys. Rev. Lett. 68, 012314 (2003).

2001 (1)

N. J. Cerf, M. Lévy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63, 052311 (2001).
[Crossref]

1999 (1)

A. Sizmann and G. Leuchs, “The optical Kerr effect and quantum optics in fibers,” Prog. Opt. 39, 373–469 (1999).
[Crossref]

1995 (2)

1993 (1)

P. Kürz, R. Paschotta, K. Fiedler, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[Crossref]

1991 (2)

K. Bergman and H. A. Haus, “Squeezing in fibers with optical pulses,” Opt. Lett. 16, 663–665 (1991).
[Crossref] [PubMed]

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: Adiabaticity criteria,” IEE Proc. J 138, 343–354 (1991).

1987 (1)

M. Xiao, L.-A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
[Crossref] [PubMed]

1986 (1)

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691–694 (1986).
[Crossref] [PubMed]

1985 (1)

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

1981 (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
[Crossref]

1889 (1)

S. Reynaud, C. Fabre, E. Giacobino, and A. Heidmann, “Photon noise reduction by passive optical bistable systems,” Phys Rev A 40, 1440–1446 (1889).
[Crossref]

Agrawal, G. P.

Aiello, A.

J. U. Fürst, 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]

Alegre, T. P. M.

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[Crossref] [PubMed]

Alic, N.

Andersen, U. L.

U. B. Hoff, G. I. Harris, L. S. Madsen, H. Kerdoncuff, M. Lassen, B. M. Nielsen, W. P. Bowen, and U. L. Andersen, “Quantum-enhanced micromechanical displacement sensitivity,” Opt. Lett. 38, 1413–1415 (2013).
[Crossref] [PubMed]

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

J. U. Fürst, 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. Heersink, V. Joss, G. Leuchs, and U. L. Andersen, “Efficient polarization squeezing in optical fibers,” Opt. Lett. 30, 1192–1194 (2005).
[Crossref] [PubMed]

Aspelmeyer, M.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
[Crossref] [PubMed]

Ast, S.

S. Ast, M. Mehmet, and R. Schnabel, “High-bandwidth squeezed light at 1550 nm from a compact monolithic PPKTP cavity,” Opt. Express 21, 13572–13579 (2013).
[Crossref] [PubMed]

S. Ast, A. Samblowski, M. Mehmet, S. Steinlechner, T. Eberle, and R. Schnabel, “Continuous-wave nonclassical light with gigahertz squeezing bandwidth,” Opt. Lett 37, 2367–2369 (2012).
[Crossref] [PubMed]

Bachor, H.-A.

H.-A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, 2004).

Baets, R.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
[Crossref]

Barton, J. S.

Bauchrowitz, J.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[Crossref] [PubMed]

Bauters, J. F.

Bellutti, P.

N. Daldosso, M. Melchiorri, F. Riboli, M. Girardini, G. Pucker, M. Crivellari, P. Bellutti, A. Lui, and L. Pavesi, “Comparison among various Si3N4 waveguide geometries grown within a CMOS fabrication pilot line,” J. Light-wave Technol. 22, 1734–1740 (2004).
[Crossref]

Bergman, K.

Black, R. J.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: Adiabaticity criteria,” IEE Proc. J 138, 343–354 (1991).

Blumenthal, D. J.

Bogaerts, W.

W. Bogaerts and S. K. Selvaraja, “Compact single-mode silicon hybrid rib/strip waveguides with adiabatic bends,” IEEE Photonics J. 3, 422–432 (2011).
[Crossref]

Botter, T.

D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature 488, 476–480 (2012).
[Crossref] [PubMed]

Bowen, W. P.

Bowers, J. E.

Brahms, N.

D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature 488, 476–480 (2012).
[Crossref] [PubMed]

Breitenbach, G.

Brooks, D. W. C.

D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature 488, 476–480 (2012).
[Crossref] [PubMed]

Bruinink, C. M.

Caves, C. M.

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
[Crossref]

Cerf, N. J.

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102, 130501 (2009).
[Crossref] [PubMed]

N. J. Cerf, M. Lévy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63, 052311 (2001).
[Crossref]

Chan, J.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
[Crossref] [PubMed]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[Crossref] [PubMed]

Chen, T.

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,” Nature Photon. 4, 41–45 (2009).
[Crossref]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nature Photon. 2, 737 (2008).
[Crossref]

Claes, T.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
[Crossref]

Clemmen, S.

L. G. Helt, M. Liscidini, A. Farsi, S. Clemmen, V. Venkataraman, J. S. Levy, M. Lipson, A. L. Gaeta, and J. E. Sipe, “Quantum optics of spontaneous four-wave mixing in a silicon nitride microring resonator,” in “CLEO: 2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011, 2011), OSA Technical Digest (CD). Paper QWA4.
[Crossref]

Collet, M.

M. Jack, M. Collet, and D. Walls, “Enhanced squeezing due to the influence of two instabilities,” Phys. Rev. A 51, 3318–3327 (1995).
[Crossref] [PubMed]

Crivellari, M.

N. Daldosso, M. Melchiorri, F. Riboli, M. Girardini, G. Pucker, M. Crivellari, P. Bellutti, A. Lui, and L. Pavesi, “Comparison among various Si3N4 waveguide geometries grown within a CMOS fabrication pilot line,” J. Light-wave Technol. 22, 1734–1740 (2004).
[Crossref]

Daldosso, N.

N. Daldosso, M. Melchiorri, F. Riboli, M. Girardini, G. Pucker, M. Crivellari, P. Bellutti, A. Lui, and L. Pavesi, “Comparison among various Si3N4 waveguide geometries grown within a CMOS fabrication pilot line,” J. Light-wave Technol. 22, 1734–1740 (2004).
[Crossref]

Danzmann, K.

M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys. Rev. A 81, 013814 (2010).
[Crossref]

De Siena, S.

M. G. A. Paris, F. Illuminati, A. Serafini, and S. De Siena, “Purity of Gaussian states: Measurement schemes and time evolution in noisy channels,” Phys. Rev. Lett. 68, 012314 (2003).

Deshpande, P.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
[Crossref]

DeVoe, R. G.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691–694 (1986).
[Crossref] [PubMed]

Dhakal, A.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
[Crossref]

Du-Bois, B.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
[Crossref]

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,” Nature Photon. 4, 41–45 (2009).
[Crossref]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nature Photon. 2, 737 (2008).
[Crossref]

Dutt, A.

A. Dutt, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” arXiv p. 1309.6371 (2013).

Eberle, T.

S. Ast, A. Samblowski, M. Mehmet, S. Steinlechner, T. Eberle, and R. Schnabel, “Continuous-wave nonclassical light with gigahertz squeezing bandwidth,” Opt. Lett 37, 2367–2369 (2012).
[Crossref] [PubMed]

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[Crossref] [PubMed]

Elser, D.

J. U. Fürst, 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]

Fabre, C.

S. Reynaud, C. Fabre, E. Giacobino, and A. Heidmann, “Photon noise reduction by passive optical bistable systems,” Phys Rev A 40, 1440–1446 (1889).
[Crossref]

Fainman, Y.

Farsi, A.

L. G. Helt, M. Liscidini, A. Farsi, S. Clemmen, V. Venkataraman, J. S. Levy, M. Lipson, A. L. Gaeta, and J. E. Sipe, “Quantum optics of spontaneous four-wave mixing in a silicon nitride microring resonator,” in “CLEO: 2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011, 2011), OSA Technical Digest (CD). Paper QWA4.
[Crossref]

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,” Nature Photon. 4, 41–45 (2009).
[Crossref]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nature Photon. 2, 737 (2008).
[Crossref]

Fiedler, K.

P. Kürz, R. Paschotta, K. Fiedler, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[Crossref]

Filip, R.

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

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,” Nature Photon. 4, 37–40 (2009).
[Crossref]

Fürst, J. U.

J. U. Fürst, 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, A.

Gaeta, A. L.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nature Photon. 7, 597–607 (2013).
[Crossref]

Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. 36, 3398–3400 (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,” Nature Photon. 4, 37–40 (2009).
[Crossref]

L. G. Helt, M. Liscidini, A. Farsi, S. Clemmen, V. Venkataraman, J. S. Levy, M. Lipson, A. L. Gaeta, and J. E. Sipe, “Quantum optics of spontaneous four-wave mixing in a silicon nitride microring resonator,” in “CLEO: 2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011, 2011), OSA Technical Digest (CD). Paper QWA4.
[Crossref]

A. Dutt, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” arXiv p. 1309.6371 (2013).

García-Patrón, R.

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102, 130501 (2009).
[Crossref] [PubMed]

Gardiner, C. W.

C. W. Gardiner and P. Zoller, Quantum Noise (Springer-Verlag, 2000), second enlarged ed.
[Crossref]

Gavartin, E.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nature Photon. 6, 480–487 (2012).
[Crossref]

Giacobino, E.

S. Reynaud, C. Fabre, E. Giacobino, and A. Heidmann, “Photon noise reduction by passive optical bistable systems,” Phys Rev A 40, 1440–1446 (1889).
[Crossref]

Girardini, M.

N. Daldosso, M. Melchiorri, F. Riboli, M. Girardini, G. Pucker, M. Crivellari, P. Bellutti, A. Lui, and L. Pavesi, “Comparison among various Si3N4 waveguide geometries grown within a CMOS fabrication pilot line,” J. Light-wave Technol. 22, 1734–1740 (2004).
[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,” Nature Photon. 4, 37–40 (2009).
[Crossref]

A. Gondarenko, J. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express 17, 11366–11370 (2009).
[Crossref] [PubMed]

Gonthier, F.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: Adiabaticity criteria,” IEE Proc. J 138, 343–354 (1991).

Gorodetsky, M. L.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nature Photon. 6, 480–487 (2012).
[Crossref]

Gröblacher, S.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
[Crossref] [PubMed]

Händchen, V.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[Crossref] [PubMed]

Harris, G. I.

Hartinger, K.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nature Photon. 6, 480–487 (2012).
[Crossref]

Haus, H. A.

Heck, M. J. R.

Heersink, J.

Heideman, R. G.

Heidmann, A.

S. Reynaud, C. Fabre, E. Giacobino, and A. Heidmann, “Photon noise reduction by passive optical bistable systems,” Phys Rev A 40, 1440–1446 (1889).
[Crossref]

Helin, P.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
[Crossref]

Helt, L. G.

L. G. Helt, M. Liscidini, A. Farsi, S. Clemmen, V. Venkataraman, J. S. Levy, M. Lipson, A. L. Gaeta, and J. E. Sipe, “Quantum optics of spontaneous four-wave mixing in a silicon nitride microring resonator,” in “CLEO: 2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011, 2011), OSA Technical Digest (CD). Paper QWA4.
[Crossref]

Henry, W. M.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: Adiabaticity criteria,” IEE Proc. J 138, 343–354 (1991).

Herr, T.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nature Photon. 6, 480–487 (2012).
[Crossref]

Hill, J. T.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
[Crossref] [PubMed]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[Crossref] [PubMed]

Hoff, U. B.

Hollberg, L. W.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Holzwarth, R.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nature Photon. 6, 480–487 (2012).
[Crossref]

Ikeda, K.

Illuminati, F.

M. G. A. Paris, F. Illuminati, A. Serafini, and S. De Siena, “Purity of Gaussian states: Measurement schemes and time evolution in noisy channels,” Phys. Rev. Lett. 68, 012314 (2003).

Jack, M.

M. Jack, M. Collet, and D. Walls, “Enhanced squeezing due to the influence of two instabilities,” Phys. Rev. A 51, 3318–3327 (1995).
[Crossref] [PubMed]

Jansen, R.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
[Crossref]

John, D. D.

Joss, V.

Kampel, N. S.

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3, 031012 (2013).

Kerdoncuff, H.

Kimble, H. J.

M. Xiao, L.-A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
[Crossref] [PubMed]

Kippenberg, T. J.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nature Photon. 6, 480–487 (2012).
[Crossref]

Krause, A.

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[Crossref] [PubMed]

Kürz, P.

P. Kürz, R. Paschotta, K. Fiedler, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[Crossref]

Lacroix, S.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: Adiabaticity criteria,” IEE Proc. J 138, 343–354 (1991).

Ladouceur, F.

F. Ladouceur and J. D. Love, Silica-based Buried Channel Waveguides and Devices (Chapman & Hall, 1996).

Lassen, M.

U. B. Hoff, G. I. Harris, L. S. Madsen, H. Kerdoncuff, M. Lassen, B. M. Nielsen, W. P. Bowen, and U. L. Andersen, “Quantum-enhanced micromechanical displacement sensitivity,” Opt. Lett. 38, 1413–1415 (2013).
[Crossref] [PubMed]

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

Lastzka, N.

M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys. Rev. A 81, 013814 (2010).
[Crossref]

Lee, H.

Leinse, A.

Leuchs, G.

J. U. Fürst, 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. Heersink, V. Joss, G. Leuchs, and U. L. Andersen, “Efficient polarization squeezing in optical fibers,” Opt. Lett. 30, 1192–1194 (2005).
[Crossref] [PubMed]

A. Sizmann and G. Leuchs, “The optical Kerr effect and quantum optics in fibers,” Prog. Opt. 39, 373–469 (1999).
[Crossref]

Levenson, M. D.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691–694 (1986).
[Crossref] [PubMed]

Levy, J.

Levy, J. S.

Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. 36, 3398–3400 (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,” Nature Photon. 4, 37–40 (2009).
[Crossref]

L. G. Helt, M. Liscidini, A. Farsi, S. Clemmen, V. Venkataraman, J. S. Levy, M. Lipson, A. L. Gaeta, and J. E. Sipe, “Quantum optics of spontaneous four-wave mixing in a silicon nitride microring resonator,” in “CLEO: 2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011, 2011), OSA Technical Digest (CD). Paper QWA4.
[Crossref]

Lévy, M.

N. J. Cerf, M. Lévy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63, 052311 (2001).
[Crossref]

Leyssens, K.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
[Crossref]

Li, J.

Lipson, M.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nature Photon. 7, 597–607 (2013).
[Crossref]

Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. 36, 3398–3400 (2011).
[Crossref] [PubMed]

A. Gondarenko, J. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express 17, 11366–11370 (2009).
[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,” Nature Photon. 4, 37–40 (2009).
[Crossref]

L. G. Helt, M. Liscidini, A. Farsi, S. Clemmen, V. Venkataraman, J. S. Levy, M. Lipson, A. L. Gaeta, and J. E. Sipe, “Quantum optics of spontaneous four-wave mixing in a silicon nitride microring resonator,” in “CLEO: 2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011, 2011), OSA Technical Digest (CD). Paper QWA4.
[Crossref]

C. Pollock and M. Lipson, Integrated Photonics (Kluwer Academic Publishers, 2010).

A. Dutt, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” arXiv p. 1309.6371 (2013).

Liscidini, M.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nature Photon. 2, 737 (2008).
[Crossref]

L. G. Helt, M. Liscidini, A. Farsi, S. Clemmen, V. Venkataraman, J. S. Levy, M. Lipson, A. L. Gaeta, and J. E. Sipe, “Quantum optics of spontaneous four-wave mixing in a silicon nitride microring resonator,” in “CLEO: 2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011, 2011), OSA Technical Digest (CD). Paper QWA4.
[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,” Nature Photon. 4, 41–45 (2009).
[Crossref]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nature Photon. 2, 737 (2008).
[Crossref]

Love, J. D.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: Adiabaticity criteria,” IEE Proc. J 138, 343–354 (1991).

F. Ladouceur and J. D. Love, Silica-based Buried Channel Waveguides and Devices (Chapman & Hall, 1996).

Lui, A.

N. Daldosso, M. Melchiorri, F. Riboli, M. Girardini, G. Pucker, M. Crivellari, P. Bellutti, A. Lui, and L. Pavesi, “Comparison among various Si3N4 waveguide geometries grown within a CMOS fabrication pilot line,” J. Light-wave Technol. 22, 1734–1740 (2004).
[Crossref]

Madsen, L. S.

U. B. Hoff, G. I. Harris, L. S. Madsen, H. Kerdoncuff, M. Lassen, B. M. Nielsen, W. P. Bowen, and U. L. Andersen, “Quantum-enhanced micromechanical displacement sensitivity,” Opt. Lett. 38, 1413–1415 (2013).
[Crossref] [PubMed]

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

Manipatruni, S.

A. Dutt, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” arXiv p. 1309.6371 (2013).

Marquardt, Ch.

J. U. Fürst, 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]

Mehmet, M.

S. Ast, M. Mehmet, and R. Schnabel, “High-bandwidth squeezed light at 1550 nm from a compact monolithic PPKTP cavity,” Opt. Express 21, 13572–13579 (2013).
[Crossref] [PubMed]

S. Ast, A. Samblowski, M. Mehmet, S. Steinlechner, T. Eberle, and R. Schnabel, “Continuous-wave nonclassical light with gigahertz squeezing bandwidth,” Opt. Lett 37, 2367–2369 (2012).
[Crossref] [PubMed]

M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys. Rev. A 81, 013814 (2010).
[Crossref]

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[Crossref] [PubMed]

Melchiorri, M.

N. Daldosso, M. Melchiorri, F. Riboli, M. Girardini, G. Pucker, M. Crivellari, P. Bellutti, A. Lui, and L. Pavesi, “Comparison among various Si3N4 waveguide geometries grown within a CMOS fabrication pilot line,” J. Light-wave Technol. 22, 1734–1740 (2004).
[Crossref]

Mertz, J. C.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Milburn, G. J.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1995).

Mlynek, J.

G. Breitenbach, T. Müller, S. F. Pereira, J.-Ph. Poizat, S. Schiller, and J. Mlynek, “Squeezed vacuum from a monolithic optical parametric oscillator,” J. Opt. Soc. Am. B 12, 2304–2309 (1995).
[Crossref]

P. Kürz, R. Paschotta, K. Fiedler, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[Crossref]

Morandotti, R.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nature Photon. 7, 597–607 (2013).
[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,” Nature Photon. 4, 41–45 (2009).
[Crossref]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nature Photon. 2, 737 (2008).
[Crossref]

Moss, D. J.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nature Photon. 7, 597–607 (2013).
[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,” Nature Photon. 4, 41–45 (2009).
[Crossref]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nature Photon. 2, 737 (2008).
[Crossref]

Müller, T.

Müller-Ebhardt, H.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[Crossref] [PubMed]

Nagashima, K.

Neutens, P.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
[Crossref]

Nielsen, B. M.

Nussenzveig, P.

A. Dutt, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” arXiv p. 1309.6371 (2013).

Okawachi, Y.

Painter, O.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
[Crossref] [PubMed]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[Crossref] [PubMed]

Paris, M. G. A.

M. G. A. Paris, F. Illuminati, A. Serafini, and S. De Siena, “Purity of Gaussian states: Measurement schemes and time evolution in noisy channels,” Phys. Rev. Lett. 68, 012314 (2003).

Paschotta, R.

P. Kürz, R. Paschotta, K. Fiedler, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[Crossref]

Pavesi, L.

N. Daldosso, M. Melchiorri, F. Riboli, M. Girardini, G. Pucker, M. Crivellari, P. Bellutti, A. Lui, and L. Pavesi, “Comparison among various Si3N4 waveguide geometries grown within a CMOS fabrication pilot line,” J. Light-wave Technol. 22, 1734–1740 (2004).
[Crossref]

Pereira, S. F.

Perlmutter, S. H.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691–694 (1986).
[Crossref] [PubMed]

Peterson, R. W.

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3, 031012 (2013).

Peyskens, F.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
[Crossref]

Poizat, J.-Ph.

Pollock, C.

C. Pollock and M. Lipson, Integrated Photonics (Kluwer Academic Publishers, 2010).

Premaratne, M.

Pucker, G.

N. Daldosso, M. Melchiorri, F. Riboli, M. Girardini, G. Pucker, M. Crivellari, P. Bellutti, A. Lui, and L. Pavesi, “Comparison among various Si3N4 waveguide geometries grown within a CMOS fabrication pilot line,” J. Light-wave Technol. 22, 1734–1740 (2004).
[Crossref]

Purdy, T. P.

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3, 031012 (2013).

D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature 488, 476–480 (2012).
[Crossref] [PubMed]

Ralph, T. C.

H.-A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, 2004).

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,” Nature Photon. 4, 41–45 (2009).
[Crossref]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nature Photon. 2, 737 (2008).
[Crossref]

Regal, C. A.

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3, 031012 (2013).

Reynaud, S.

S. Reynaud, C. Fabre, E. Giacobino, and A. Heidmann, “Photon noise reduction by passive optical bistable systems,” Phys Rev A 40, 1440–1446 (1889).
[Crossref]

Riboli, F.

N. Daldosso, M. Melchiorri, F. Riboli, M. Girardini, G. Pucker, M. Crivellari, P. Bellutti, A. Lui, and L. Pavesi, “Comparison among various Si3N4 waveguide geometries grown within a CMOS fabrication pilot line,” J. Light-wave Technol. 22, 1734–1740 (2004).
[Crossref]

Riemensberger, J.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nature Photon. 6, 480–487 (2012).
[Crossref]

Rottenberg, X.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
[Crossref]

Rukhlenko, I. D.

Safavi-Naeini, A. H.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
[Crossref] [PubMed]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[Crossref] [PubMed]

Saha, K.

Samblowski, A.

S. Ast, A. Samblowski, M. Mehmet, S. Steinlechner, T. Eberle, and R. Schnabel, “Continuous-wave nonclassical light with gigahertz squeezing bandwidth,” Opt. Lett 37, 2367–2369 (2012).
[Crossref] [PubMed]

Saperstein, R. E.

Schiller, S.

Schnabel, R.

S. Ast, M. Mehmet, and R. Schnabel, “High-bandwidth squeezed light at 1550 nm from a compact monolithic PPKTP cavity,” Opt. Express 21, 13572–13579 (2013).
[Crossref] [PubMed]

S. Ast, A. Samblowski, M. Mehmet, S. Steinlechner, T. Eberle, and R. Schnabel, “Continuous-wave nonclassical light with gigahertz squeezing bandwidth,” Opt. Lett 37, 2367–2369 (2012).
[Crossref] [PubMed]

M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys. Rev. A 81, 013814 (2010).
[Crossref]

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[Crossref] [PubMed]

Schreppler, S.

D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature 488, 476–480 (2012).
[Crossref] [PubMed]

Selvaraja, S.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
[Crossref]

Selvaraja, S. K.

W. Bogaerts and S. K. Selvaraja, “Compact single-mode silicon hybrid rib/strip waveguides with adiabatic bends,” IEEE Photonics J. 3, 422–432 (2011).
[Crossref]

Serafini, A.

M. G. A. Paris, F. Illuminati, A. Serafini, and S. De Siena, “Purity of Gaussian states: Measurement schemes and time evolution in noisy channels,” Phys. Rev. Lett. 68, 012314 (2003).

Severi, S.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
[Crossref]

Shelby, R. M.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691–694 (1986).
[Crossref] [PubMed]

Sipe, J. E.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nature Photon. 2, 737 (2008).
[Crossref]

L. G. Helt, M. Liscidini, A. Farsi, S. Clemmen, V. Venkataraman, J. S. Levy, M. Lipson, A. L. Gaeta, and J. E. Sipe, “Quantum optics of spontaneous four-wave mixing in a silicon nitride microring resonator,” in “CLEO: 2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011, 2011), OSA Technical Digest (CD). Paper QWA4.
[Crossref]

Sizmann, A.

A. Sizmann and G. Leuchs, “The optical Kerr effect and quantum optics in fibers,” Prog. Opt. 39, 373–469 (1999).
[Crossref]

Slusher, R. E.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Stamper-Kurn, D. M.

D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature 488, 476–480 (2012).
[Crossref] [PubMed]

Steinlechner, S.

S. Ast, A. Samblowski, M. Mehmet, S. Steinlechner, T. Eberle, and R. Schnabel, “Continuous-wave nonclassical light with gigahertz squeezing bandwidth,” Opt. Lett 37, 2367–2369 (2012).
[Crossref] [PubMed]

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[Crossref] [PubMed]

Stewart, W. J.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: Adiabaticity criteria,” IEE Proc. J 138, 343–354 (1991).

Strekalov, D. V.

J. U. Fürst, 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]

Subramanian, A. Z.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
[Crossref]

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,” Nature Photon. 4, 37–40 (2009).
[Crossref]

Usenko, V. C.

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

Vahala, K. J.

Vahlbruch, H.

M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys. Rev. A 81, 013814 (2010).
[Crossref]

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[Crossref] [PubMed]

Valley, J. F.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Van Assche, G.

N. J. Cerf, M. Lévy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63, 052311 (2001).
[Crossref]

Van Dorpe, P.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
[Crossref]

Venkataraman, V.

L. G. Helt, M. Liscidini, A. Farsi, S. Clemmen, V. Venkataraman, J. S. Levy, M. Lipson, A. L. Gaeta, and J. E. Sipe, “Quantum optics of spontaneous four-wave mixing in a silicon nitride microring resonator,” in “CLEO: 2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011, 2011), OSA Technical Digest (CD). Paper QWA4.
[Crossref]

Walls, D.

M. Jack, M. Collet, and D. Walls, “Enhanced squeezing due to the influence of two instabilities,” Phys. Rev. A 51, 3318–3327 (1995).
[Crossref] [PubMed]

Walls, D. F.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691–694 (1986).
[Crossref] [PubMed]

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1995).

Wang, C. Y.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nature Photon. 6, 480–487 (2012).
[Crossref]

Wen, Y. H.

Wu, L.-A.

M. Xiao, L.-A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
[Crossref] [PubMed]

Xiao, M.

M. Xiao, L.-A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
[Crossref] [PubMed]

Yang, Z.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nature Photon. 2, 737 (2008).
[Crossref]

Yonezawa, H.

Yu, P.-L.

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3, 031012 (2013).

Yurke, B.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Zoller, P.

C. W. Gardiner and P. Zoller, Quantum Noise (Springer-Verlag, 2000), second enlarged ed.
[Crossref]

Europhys. Lett. (1)

P. Kürz, R. Paschotta, K. Fiedler, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[Crossref]

IEE Proc. J (1)

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: Adiabaticity criteria,” IEE Proc. J 138, 343–354 (1991).

IEEE Photon J. (1)

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Du-Bois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-loss singlemode PECVD silicon nitride photonic wire waveguides for 532-900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon J. 5, 2202809 (2013).
[Crossref]

IEEE Photonics J. (1)

W. Bogaerts and S. K. Selvaraja, “Compact single-mode silicon hybrid rib/strip waveguides with adiabatic bends,” IEEE Photonics J. 3, 422–432 (2011).
[Crossref]

J. Light-wave Technol. (1)

N. Daldosso, M. Melchiorri, F. Riboli, M. Girardini, G. Pucker, M. Crivellari, P. Bellutti, A. Lui, and L. Pavesi, “Comparison among various Si3N4 waveguide geometries grown within a CMOS fabrication pilot line,” J. Light-wave Technol. 22, 1734–1740 (2004).
[Crossref]

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

Nat. Commun. (1)

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

Nature (2)

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
[Crossref] [PubMed]

D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature 488, 476–480 (2012).
[Crossref] [PubMed]

Nature Photon. (5)

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nature Photon. 7, 597–607 (2013).
[Crossref]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nature Photon. 2, 737 (2008).
[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,” Nature Photon. 4, 37–40 (2009).
[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,” Nature Photon. 4, 41–45 (2009).
[Crossref]

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nature Photon. 6, 480–487 (2012).
[Crossref]

Nature Phys. (1)

The LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot noise limit,” Nature Phys. 7, 962–965 (2011).
[Crossref]

Opt. Express (6)

Opt. Lett (1)

S. Ast, A. Samblowski, M. Mehmet, S. Steinlechner, T. Eberle, and R. Schnabel, “Continuous-wave nonclassical light with gigahertz squeezing bandwidth,” Opt. Lett 37, 2367–2369 (2012).
[Crossref] [PubMed]

Opt. Lett. (5)

Phys Rev A (1)

S. Reynaud, C. Fabre, E. Giacobino, and A. Heidmann, “Photon noise reduction by passive optical bistable systems,” Phys Rev A 40, 1440–1446 (1889).
[Crossref]

Phys. Rev. A (3)

M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys. Rev. A 81, 013814 (2010).
[Crossref]

N. J. Cerf, M. Lévy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63, 052311 (2001).
[Crossref]

M. Jack, M. Collet, and D. Walls, “Enhanced squeezing due to the influence of two instabilities,” Phys. Rev. A 51, 3318–3327 (1995).
[Crossref] [PubMed]

Phys. Rev. D (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
[Crossref]

Phys. Rev. Lett. (8)

M. Xiao, L.-A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
[Crossref] [PubMed]

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691–694 (1986).
[Crossref] [PubMed]

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[Crossref] [PubMed]

J. U. Fürst, 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]

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102, 130501 (2009).
[Crossref] [PubMed]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[Crossref] [PubMed]

M. G. A. Paris, F. Illuminati, A. Serafini, and S. De Siena, “Purity of Gaussian states: Measurement schemes and time evolution in noisy channels,” Phys. Rev. Lett. 68, 012314 (2003).

Phys. Rev. X (1)

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3, 031012 (2013).

Prog. Opt. (1)

A. Sizmann and G. Leuchs, “The optical Kerr effect and quantum optics in fibers,” Prog. Opt. 39, 373–469 (1999).
[Crossref]

Other (8)

H.-A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, 2004).

C. Pollock and M. Lipson, Integrated Photonics (Kluwer Academic Publishers, 2010).

F. Ladouceur and J. D. Love, Silica-based Buried Channel Waveguides and Devices (Chapman & Hall, 1996).

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1995).

C. W. Gardiner and P. Zoller, Quantum Noise (Springer-Verlag, 2000), second enlarged ed.
[Crossref]

L. G. Helt, M. Liscidini, A. Farsi, S. Clemmen, V. Venkataraman, J. S. Levy, M. Lipson, A. L. Gaeta, and J. E. Sipe, “Quantum optics of spontaneous four-wave mixing in a silicon nitride microring resonator,” in “CLEO: 2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011, 2011), OSA Technical Digest (CD). Paper QWA4.
[Crossref]

R. Ghodssi and P. Lin, eds., MEMS Materials and Processes Handbook (Springer, 2011).
[Crossref]

A. Dutt, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” arXiv p. 1309.6371 (2013).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1 (a) Top view of the racetrack resonator geometry. (b) Cross sectional view at the bus-resonator coupling region. The thickness is t = 250nm and the width w is chosen such that the waveguide only supports a single transversal mode. The gap size g is fixed, and limited from below by the resolution of the lithographic method chosen, and the coupling rate γc is determined by the length of the coupling region Lc.
Fig. 2
Fig. 2 Real part of the pumped mode eigenvalue λ+ as a function of pump parameter and detuning. The λ+ = 0 contour (black dashed line) divides the parameter space into a stable (λ+ < 0) and an unstable (λ+ > 0) region. For detunings above the bistability condition (white dashed line) two stable regions exist and the system can be tuned between the two by changing the intracavity power. The intermediate unstable region is not accessible. By progressively detuning the drive field from the empty cavity resonance as the pump power is increased it is possible to maintain stability of the system and maximize the intra-cavity power (red dashed line). Furthermore, we observe that in terms of power the instability region is bounded from below by the condition that |ε| > γ indicating that the nonlinear scattering rate from the pumped mode should exceed the cavity dissipation rate in order for instability to occur.
Fig. 3
Fig. 3 Simulated (λ = 850nm, t = 250 nm) effective mode indices for the first three guided modes as function of waveguide width. Insets: Simulated mode profiles corresponding to each of the five encircled points. Solid black lines outline the waveguide core cross section.
Fig. 4
Fig. 4 Simulated (λ = 850nm) effective mode area as function of waveguide width for different waveguide thicknesses. Dashed lines show the nonlinear core area aNL which, according to the definition in Eq. (23), is the minimal effective mode area for a given cross section.
Fig. 5
Fig. 5 Simulated (λ = 850nm, t = 250 nm, w = 500 nm) efficiency of TE0 coupling between RTR and bus waveguide as function of coupling length Lc. (left) Simulation runs with gap sizes in the range 100−800nm. (right) Selected simulation runs plotted on linear scale. Gray dashed lines indicate the total intra cavity loss for an RTR with R = 50μm in case of −1 dB/cm (lower) and −2 dB/cm (upper) propagation loss.
Fig. 6
Fig. 6 (a) Longitudinal cross section of the proposed silicon nitride double layer stack and inverse taper for robust chip coupling. Silicon nitride is indicated in red and the surrounding oxide cladding in blue. The performance of the design depends on optimization of thin film thickness ttf, intermediate oxide layer thickness tox, and the tapering length Lt. (b) Transverse cross section of the double layer stack. The lower thin film mirrors the lithographically defined pattern of the upper main waveguide, but with the essential exception that it extends all the way to the chip facets, acting as a weakly guiding structure in connection with both in- and out-coupling.
Fig. 7
Fig. 7 Simulated (λ = 850nm, w = 500 nm) mode waist sizes along major (X) and minor (Y) axes of the lower stripe waveguide as function of film thickness (a), and corresponding overlap efficiency with an incoming symmetric Gaussian mode with a waist of 1 μm (b). (c) Simulated delineation curves for approximate taper adiabaticity. Dashed horizontal lines correspond to linear constant-slope tapers of varying taper length.
Fig. 8
Fig. 8 (λ = 850nm, α = −1dB/cm, η = 80.6%, Ω/2π = 30MHz) Relative noise power in the output field of a resonantly pumped RTR (Δp = |ε|) as function of pump parameter |ε|. Panels (a)-(d) correspond to RTR escape efficiencies of 75%, 80%, 85%, and 90% respectively. Shot noise level is indicated by the dashed contour and the solid black contour corresponds to −3dB quantum noise reduction. (e) Cross sectional views of panels (a)-(d) corresponding to an input pump power of 200 mW.
Fig. 9
Fig. 9 State purity as function of noise reduction for different RTR escape efficiencies. Dashed segments indicate that generation of the corresponding noise reduction requires a pump power in the bus waveguide exceeding 200 mW. The two panels correspond to detection efficiencies of η = 80.6% (left) and η = 100% (right).
Fig. 10
Fig. 10 State purity as function of noise reduction with device loss properties of α = −0.5 dB/cm and ηc = 95%. Dashed segments indicate that generation of the corresponding noise reduction requires a pump power in the bus waveguide exceeding 75 mW.
Fig. 11
Fig. 11 (λ = 850nm, α = −1dB/cm, |ε|/γ = 0.5) Spectrum of the squeezed and anti-squeezed quadratures assuming 80.6% (thick), 91.2% (thin), and unity (dashed) detection efficiency. Panels (a)-(d) correspond to RTR escape efficiencies of 75%, 80%, 85%, and 90% respectively.
Fig. 12
Fig. 12 Pictorial illustration of the χ(3)-mediated processes SPM, CPM, and NDFWM, in the case where a strongly pumped resonator mode at frequency ωp interacts with two weaker signal and idler sideband modes at frequency ωs and ωi, respectively.

Tables (3)

Tables Icon

Table 1 Simulated (λ = 850nm, t = 250nm, and w = 500nm) bending loss for the TE0 mode in resonators with different radii of curvature, R.

Tables Icon

Table 2 Evaluation of RTR (R = 50 μm) escape efficiency and finesse in case of -1 dB/cm (left) and -2 dB/cm (right) propagation loss. Italicized values indicate that the approximations used in Eq. (24) are only partially justified.

Tables Icon

Table 3 Energy conserving operator products in the expansion of the normal ordered interaction Hamiltonian in Eq. (34)

Equations (37)

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

δ X 1 out = δ X 1 in
δ X 2 out = δ X 2 in + 2 r δ X 1 in
H SPM = ξ 2 a p 2 a p 2 ,
ξ = ω c 2 γ nl 2 n eff 2 L .
d a p d t = i [ a p , H ] γ a p + 2 γ c a p , in e i ω L t + 2 γ 0 b p ,
H = ω p a p a p + H SPM .
d A p d t = ( γ i Δ p ) A p i ξ A p A p 2 + 2 γ c A p , in + 2 γ 0 B p ,
| α p | 2 ( γ 2 + ( Δ p ξ | α p | 2 ) 2 ) = 2 γ c | α p , in | 2 .
d δ a p d t = [ M γ I ] δ a p + 2 γ c δ a in + 2 γ 0 δ b ,
M γ I = ( γ i ( 2 | ε | Δ p ) i ε i ε * γ + i ( 2 | ε | Δ p ) ) ,
λ ± = γ ± | ε | 2 ( Δ p 2 | ε | ) 2 .
i Ω δ a p ( Ω ) = [ M γ I ] δ a p ( Ω ) + 2 γ c δ a in ( Ω ) + 2 γ 0 δ b ( Ω ) ,
δ a p ( Ω ) = [ M ( γ i Ω ) I ] 1 ( 2 γ c δ a in ( Ω ) + 2 γ 0 δ b ( Ω ) ) .
δ a out ( Ω ) = δ a in ( Ω ) 2 γ c δ a p ( Ω ) .
δ a out ( Ω ) = [ M ( γ i Ω ) I ] 1 × ( [ M + ( Δ γ + i Ω ) I ] δ a in ( Ω ) + 2 γ 0 γ c δ b ( Ω ) ) ,
δ X θ ( Ω ) = δ a out ( Ω ) e i θ + δ a out ( Ω ) e i θ ,
: δ X θ ( Ω ) δ X θ ( Ω ) : = [ e 2 i θ δ a out ( Ω ) δ a out ( Ω ) + e 2 i θ δ a out ( Ω ) δ a out ( Ω ) + δ a out ( Ω ) δ a out ( Ω ) ] δ ( Ω + Ω ) .
: S θ ( Ω ) : = d Ω : δ X θ ( Ω ) δ X θ ( Ω ) : ,
S θ ( Ω ) = 1 + : S θ ( Ω ) :
S θ SPM ( Ω ) = 1 + : S θ SPM ( Ω ) : = 1 + G [ 2 γ | ε | 2 γ [ 2 | ε | Δ p ] cos 2 ( θ + ϕ ) [ γ 2 + Ω 2 Δ p 2 + 4 Δ p | ε | 3 | ε | 2 ] sin 2 ( θ + ϕ ) ] ,
G = 4 γ c | ε | [ Δ p 2 + γ 2 Ω 2 4 Δ p | ε | + 3 | ε | 2 ] 2 + 4 γ 2 Ω 2 .
S θ meas ( Ω ) = ( 1 η ) + η S θ ( Ω ) = 1 + η : S θ ( Ω ) : ,
A eff = a NL S Z d x d y / NL S z d x d y ,
2 π κ c 2 + , η esc κ c 2 κ c 2 + ,
η = 4 w 1 2 w 2 2 ( w 1 2 + w 2 2 ) 2 ,
Ω = ρ ( β 1 β 2 ) 2 π .
η c = η Fresnel · η overlap · η taper 0.96 · 0.98 · 0.90 84 % ,
I = 3 ε 0 χ ( 3 ) 1 2 d V ( r , t ) 4 ,
E ( r , t ) = i 0 i ( a i e i ( k i r ω i t ) + a i e i ( k i r ω i t ) ) where i = { p 1 , p 2 , + , }
d V e i Δ k z = A eff d x d y 0 L d z e i Δ k z = A eff L Φ ( Δ k L )
Ξ = 1 2 3 ε 0 χ ( 3 ) ( ω 2 ε 0 n 2 V ) 4 A eff L Φ ( Δ k L )
= 1 2 2 ω c 2 γ NL n 2 L Φ ( Δ k L )
= ξ Φ ( Δ k L ) where ξ = ω c 2 γ NL 2 n 2 L .
H I = 2 ξ : ( Σ i ( a i + a i ) ) 4 : 4 ! where i = { p , + , }
H I = ξ Φ ( Δ k L ) ( a p a + a + a p 2 a + a )
2 ξ ( a p a p a + a + + a p a p a a + a + a + a a )
+ ξ 2 ( a p 2 a p 2 + a + 2 a + 2 + a 2 a 2 ) .

Metrics