Abstract

Squeezed vacuum states enable optical measurements below the quantum limit and hence are a valuable resource for applications in quantum metrology and also quantum communication. However, most available sources require high pump powers in the milliwatt range and large setups that hinder real-world applications. Furthermore, degenerate operation of such systems presents a challenge. Here, we use a compact crystalline whispering gallery mode resonator made of lithium niobate as a degenerate parametric oscillator. We demonstrate about 1.4 dB noise reduction below the shot-noise level for only 300 μW of pump power in degenerate single-mode operation. Furthermore, we report a record pump threshold as low as 1.35 μW. Our results show that the whispering gallery-based approach presents a promising platform for a compact and efficient source for nonclassical light.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

2017 (3)

R. Schnabel, “Squeezed states of light and their applications in laser interferometers,” Phys. Rep. 684, 1–51 (2017).
[Crossref]

F. Sedlmeir, M. R. Foreman, U. Vogl, R. Zeltner, G. Schunk, D. V. Strekalov, C. Marquardt, G. Leuchs, and H. G. L. Schwefel, “Polarization-selective out-coupling of whispering-gallery modes,” Phys. Rev. Appl. 7, 024029 (2017).
[Crossref]

M. Zhang, C. Wang, R. Cheng, A. Shams-Ansari, and M. Lončar, “Monolithic ultra-high-q lithium niobate microring resonator,” Optica 4, 1536–1537 (2017).
[Crossref]

2016 (6)

A. Brieussel, Y. Shen, G. Campbell, G. Guccione, J. Janousek, B. Hage, B. C. Buchler, N. Treps, C. Fabre, F. Z. Fang, X. Y. Li, T. Symul, and P. K. Lam, “Squeezed light from a diamond-turned monolithic cavity,” Opt. Express 24, 4042–4056 (2016).
[Crossref]

G. Schunk, U. Vogl, F. Sedlmeir, D. V. Strekalov, A. Otterpohl, V. Averchenko, H. G. L. Schwefel, G. Leuchs, and C. Marquardt, “Frequency tuning of single photons from a whispering-gallery mode resonator to MHz-wide transitions,” J. Mod. Opt. 63, 2058–2073 (2016).
[Crossref]

A. Dutt, S. Miller, K. Luke, J. Cardenas, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “Tunable squeezing using coupled ring resonators on a silicon nitride chip,” Opt. Lett. 41, 223–226 (2016).
[Crossref]

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
[Crossref]

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

U. L. Andersen, T. Gehring, C. Marquardt, and G. Leuchs, “30 years of squeezed light generation,” Phys. Scripta 91, 053001 (2016).
[Crossref]

2015 (4)

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[Crossref]

U. B. Hoff, B. M. Nielsen, and U. L. Andersen, “Integrated source of broadband quadrature squeezed light,” Opt. Express 23, 12013–12036(2015).
[Crossref]

A. Dutt, K. Luke, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” Phys. Rev. Appl. 3, 044005 (2015).
[Crossref]

V. Peano, H. G. L. Schwefel, C. Marquardt, and F. Marquardt, “Intracavity squeezing can enhance quantum-limited optomechanical position detection through deamplification,” Phys. Rev. Lett. 115, 243603(2015).
[Crossref]

2014 (1)

2013 (1)

M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 4, 1818 (2013).
[Crossref]

2011 (2)

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

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

2010 (7)

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]

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]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

T. J. Kippenberg, “Second-harmonic generation in microresonators through natural phase matching,” Physics 3, 32 (2010).
[Crossref]

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]

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-q crystalline microresonators,” Phys. Rev. A 82, 031804 (2010).
[Crossref]

2009 (2)

D. V. Strekalov, A. A. Savchenkov, A. B. Matsko, and N. Yu, “Efficient upconversion of subterahertz radiation in a high-q whispering gallery resonator,” Opt. Lett. 34, 713–715 (2009).
[Crossref]

C. Navarrete-Benlloch, G. J. de Valcárcel, and E. Roldán, “Generating highly squeezed hybrid Laguerre-Gauss modes in large-Fresnel-number degenerate optical parametric oscillators,” Phys. Rev. A 79, 043820 (2009).
[Crossref]

2006 (1)

2005 (1)

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[Crossref]

2004 (1)

2003 (2)

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. A 68, 012314 (2003).
[Crossref]

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[Crossref]

1999 (1)

1992 (1)

E. S. Polzik, J. Carri, and H. J. Kimble, “Atomic spectroscopy with squeezed light for sensitivity beyond the vacuum-state limit,” Appl. Phys. B 55, 279–290 (1992).
[Crossref]

1986 (1)

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

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]

1984 (1)

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[Crossref]

1980 (2)

P. Drummond, K. McNeil, and D. Walls, “Non-equilibrium transitions in sub/second harmonic generation,” Opt. Acta 27, 321–335 (1980).
[Crossref]

T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[Crossref]

Aiello, A.

M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 4, 1818 (2013).
[Crossref]

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

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

Andersen, U. L.

U. L. Andersen, T. Gehring, C. Marquardt, and G. Leuchs, “30 years of squeezed light generation,” Phys. Scripta 91, 053001 (2016).
[Crossref]

U. B. Hoff, B. M. Nielsen, and U. L. Andersen, “Integrated source of broadband quadrature squeezed light,” Opt. Express 23, 12013–12036(2015).
[Crossref]

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

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

Averchenko, V.

G. Schunk, U. Vogl, F. Sedlmeir, D. V. Strekalov, A. Otterpohl, V. Averchenko, H. G. L. Schwefel, G. Leuchs, and C. Marquardt, “Frequency tuning of single photons from a whispering-gallery mode resonator to MHz-wide transitions,” J. Mod. Opt. 63, 2058–2073 (2016).
[Crossref]

Bachor, H.-A.

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[Crossref]

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]

Bowen, W. P.

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[Crossref]

Braunstein, S. L.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[Crossref]

Brieussel, A.

Buchler, B. C.

Campbell, G.

Cardenas, J.

Carri, J.

E. S. Polzik, J. Carri, and H. J. Kimble, “Atomic spectroscopy with squeezed light for sensitivity beyond the vacuum-state limit,” Appl. Phys. B 55, 279–290 (1992).
[Crossref]

Chekhova, M. V.

M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 4, 1818 (2013).
[Crossref]

Cheng, R.

Collett, M. J.

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[Crossref]

Couillaud, B.

T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[Crossref]

Danzmann, K.

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

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. A 68, 012314 (2003).
[Crossref]

de Valcárcel, G. J.

C. Navarrete-Benlloch, G. J. de Valcárcel, and E. Roldán, “Generating highly squeezed hybrid Laguerre-Gauss modes in large-Fresnel-number degenerate optical parametric oscillators,” Phys. Rev. A 79, 043820 (2009).
[Crossref]

Drummond, P.

P. Drummond, K. McNeil, and D. Walls, “Non-equilibrium transitions in sub/second harmonic generation,” Opt. Acta 27, 321–335 (1980).
[Crossref]

Duhme, J.

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[Crossref]

Dutt, A.

A. Dutt, S. Miller, K. Luke, J. Cardenas, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “Tunable squeezing using coupled ring resonators on a silicon nitride chip,” Opt. Lett. 41, 223–226 (2016).
[Crossref]

A. Dutt, K. Luke, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” Phys. Rev. Appl. 3, 044005 (2015).
[Crossref]

Eberle, T.

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]

Elser, D.

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

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G. Schunk, U. Vogl, F. Sedlmeir, D. V. Strekalov, A. Otterpohl, V. Averchenko, H. G. L. Schwefel, G. Leuchs, and C. Marquardt, “Frequency tuning of single photons from a whispering-gallery mode resonator to MHz-wide transitions,” J. Mod. Opt. 63, 2058–2073 (2016).
[Crossref]

G. Schunk, J. U. Fürst, M. Förtsch, D. V. Strekalov, U. Vogl, F. Sedlmeir, H. G. L. Schwefel, G. Leuchs, and C. Marquardt, “Identifying modes of large whispering-gallery mode resonators from the spectrum and emission pattern,” Opt. Express 22, 30795–30806 (2014).
[Crossref]

M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 4, 1818 (2013).
[Crossref]

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

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
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J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
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A. Dutt, K. Luke, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” Phys. Rev. Appl. 3, 044005 (2015).
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U. L. Andersen, T. Gehring, C. Marquardt, and G. Leuchs, “30 years of squeezed light generation,” Phys. Scripta 91, 053001 (2016).
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V. Peano, H. G. L. Schwefel, C. Marquardt, and F. Marquardt, “Intracavity squeezing can enhance quantum-limited optomechanical position detection through deamplification,” Phys. Rev. Lett. 115, 243603(2015).
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G. Schunk, J. U. Fürst, M. Förtsch, D. V. Strekalov, U. Vogl, F. Sedlmeir, H. G. L. Schwefel, G. Leuchs, and C. Marquardt, “Identifying modes of large whispering-gallery mode resonators from the spectrum and emission pattern,” Opt. Express 22, 30795–30806 (2014).
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J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett. 106, 113901 (2011).
[Crossref]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
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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).
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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).
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A. Dutt, K. Luke, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” Phys. Rev. Appl. 3, 044005 (2015).
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T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
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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. A 68, 012314 (2003).
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V. Peano, H. G. L. Schwefel, C. Marquardt, and F. Marquardt, “Intracavity squeezing can enhance quantum-limited optomechanical position detection through deamplification,” Phys. Rev. Lett. 115, 243603(2015).
[Crossref]

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Schliesser, A.

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[Crossref]

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[Crossref]

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).
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F. Sedlmeir, M. R. Foreman, U. Vogl, R. Zeltner, G. Schunk, D. V. Strekalov, C. Marquardt, G. Leuchs, and H. G. L. Schwefel, “Polarization-selective out-coupling of whispering-gallery modes,” Phys. Rev. Appl. 7, 024029 (2017).
[Crossref]

G. Schunk, U. Vogl, F. Sedlmeir, D. V. Strekalov, A. Otterpohl, V. Averchenko, H. G. L. Schwefel, G. Leuchs, and C. Marquardt, “Frequency tuning of single photons from a whispering-gallery mode resonator to MHz-wide transitions,” J. Mod. Opt. 63, 2058–2073 (2016).
[Crossref]

G. Schunk, J. U. Fürst, M. Förtsch, D. V. Strekalov, U. Vogl, F. Sedlmeir, H. G. L. Schwefel, G. Leuchs, and C. Marquardt, “Identifying modes of large whispering-gallery mode resonators from the spectrum and emission pattern,” Opt. Express 22, 30795–30806 (2014).
[Crossref]

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F. Sedlmeir, M. R. Foreman, U. Vogl, R. Zeltner, G. Schunk, D. V. Strekalov, C. Marquardt, G. Leuchs, and H. G. L. Schwefel, “Polarization-selective out-coupling of whispering-gallery modes,” Phys. Rev. Appl. 7, 024029 (2017).
[Crossref]

G. Schunk, U. Vogl, F. Sedlmeir, D. V. Strekalov, A. Otterpohl, V. Averchenko, H. G. L. Schwefel, G. Leuchs, and C. Marquardt, “Frequency tuning of single photons from a whispering-gallery mode resonator to MHz-wide transitions,” J. Mod. Opt. 63, 2058–2073 (2016).
[Crossref]

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
[Crossref]

V. Peano, H. G. L. Schwefel, C. Marquardt, and F. Marquardt, “Intracavity squeezing can enhance quantum-limited optomechanical position detection through deamplification,” Phys. Rev. Lett. 115, 243603(2015).
[Crossref]

G. Schunk, J. U. Fürst, M. Förtsch, D. V. Strekalov, U. Vogl, F. Sedlmeir, H. G. L. Schwefel, G. Leuchs, and C. Marquardt, “Identifying modes of large whispering-gallery mode resonators from the spectrum and emission pattern,” Opt. Express 22, 30795–30806 (2014).
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F. Sedlmeir, M. R. Foreman, U. Vogl, R. Zeltner, G. Schunk, D. V. Strekalov, C. Marquardt, G. Leuchs, and H. G. L. Schwefel, “Polarization-selective out-coupling of whispering-gallery modes,” Phys. Rev. Appl. 7, 024029 (2017).
[Crossref]

G. Schunk, U. Vogl, F. Sedlmeir, D. V. Strekalov, A. Otterpohl, V. Averchenko, H. G. L. Schwefel, G. Leuchs, and C. Marquardt, “Frequency tuning of single photons from a whispering-gallery mode resonator to MHz-wide transitions,” J. Mod. Opt. 63, 2058–2073 (2016).
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G. Schunk, J. U. Fürst, M. Förtsch, D. V. Strekalov, U. Vogl, F. Sedlmeir, H. G. L. Schwefel, G. Leuchs, and C. Marquardt, “Identifying modes of large whispering-gallery mode resonators from the spectrum and emission pattern,” Opt. Express 22, 30795–30806 (2014).
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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. A 68, 012314 (2003).
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M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 4, 1818 (2013).
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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).
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[Crossref]

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

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
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H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
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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).
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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).
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F. Sedlmeir, M. R. Foreman, U. Vogl, R. Zeltner, G. Schunk, D. V. Strekalov, C. Marquardt, G. Leuchs, and H. G. L. Schwefel, “Polarization-selective out-coupling of whispering-gallery modes,” Phys. Rev. Appl. 7, 024029 (2017).
[Crossref]

G. Schunk, U. Vogl, F. Sedlmeir, D. V. Strekalov, A. Otterpohl, V. Averchenko, H. G. L. Schwefel, G. Leuchs, and C. Marquardt, “Frequency tuning of single photons from a whispering-gallery mode resonator to MHz-wide transitions,” J. Mod. Opt. 63, 2058–2073 (2016).
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G. Schunk, J. U. Fürst, M. Förtsch, D. V. Strekalov, U. Vogl, F. Sedlmeir, H. G. L. Schwefel, G. Leuchs, and C. Marquardt, “Identifying modes of large whispering-gallery mode resonators from the spectrum and emission pattern,” Opt. Express 22, 30795–30806 (2014).
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F. Sedlmeir, M. R. Foreman, U. Vogl, R. Zeltner, G. Schunk, D. V. Strekalov, C. Marquardt, G. Leuchs, and H. G. L. Schwefel, “Polarization-selective out-coupling of whispering-gallery modes,” Phys. Rev. Appl. 7, 024029 (2017).
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D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
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[Crossref]

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
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C. Navarrete-Benlloch, G. J. de Valcárcel, and E. Roldán, “Generating highly squeezed hybrid Laguerre-Gauss modes in large-Fresnel-number degenerate optical parametric oscillators,” Phys. Rev. A 79, 043820 (2009).
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F. Sedlmeir, M. R. Foreman, U. Vogl, R. Zeltner, G. Schunk, D. V. Strekalov, C. Marquardt, G. Leuchs, and H. G. L. Schwefel, “Polarization-selective out-coupling of whispering-gallery modes,” Phys. Rev. Appl. 7, 024029 (2017).
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J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett. 106, 113901 (2011).
[Crossref]

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

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]

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[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).
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V. Peano, H. G. L. Schwefel, C. Marquardt, and F. Marquardt, “Intracavity squeezing can enhance quantum-limited optomechanical position detection through deamplification,” Phys. Rev. Lett. 115, 243603(2015).
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J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
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U. L. Andersen, T. Gehring, C. Marquardt, and G. Leuchs, “30 years of squeezed light generation,” Phys. Scripta 91, 053001 (2016).
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Physics (1)

T. J. Kippenberg, “Second-harmonic generation in microresonators through natural phase matching,” Physics 3, 32 (2010).
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V. D. Vaidya, B. Morrison, L. G. Helt, R. Shahrokhshahi, D. H. Mahler, M. J. Collins, K. Tan, J. Lavoie, A. Repingon, M. Menotti, N. Quesada, R. C. Pooser, A. E. Lita, T. Gerrits, S. W. Nam, and Z. Vernon, “Broadband quadrature-squeezed vacuum and nonclassical photon number correlations from a nanophotonic device,” https://www.arxiv.org/abs/1904.07833 .

C. Navarrete-Benlloch, “Contributions to the quantum optics of multi-mode optical parametric oscillators,” Ph.D. thesis (Universitat de Valencia, 2011).

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Figures (4)

Fig. 1.
Fig. 1. Experimental setup. Squeezed vacuum states of light are generated via degenerate parametric downconversion of a 532 nm pump inside a crystalline WGMR. The prism couplers 1 and 2 have independent coupling rates γ1 and γ2 at the subharmonic frequency, respectively. The lock is based on the Hänsch–Couillaud scheme and is applicable to both the pump beam and the alignment beam. The homodyne detection is implemented with two polarizing beam splitters. The dashed box indicates a flip mirror for optionally detecting the intracavity pump power. BS, beam splitter; DM, dichroic mirror; EOM, electro-optic modulator; HWP, half-wave plate; PBS, polarizing beam splitter; PID, proportional-integral-derivative controller; QWP, quarter-wave plate; SHG, second harmonic generation.
Fig. 2.
Fig. 2. (a) Classical OPO behavior. Above the threshold, the intracavity pump power stays constant alongside increasing parametric power. (b) Threshold of the OPO. Parametric light output in reflection of the first prism coupler versus pump power showing the square root behavior and the oscillation threshold described by Eq. (5). The fit yielded a threshold of 1.35 μW.
Fig. 3.
Fig. 3. Noise variance of the subharmonic field. Averaging the displayed extrema yields a squeezed noise variance of 1.4dB and an antisqueezed noise variance of 2.1 dB relative to shot noise for 300 μW of incident pump power at a sideband frequency of 500 kHz. The inset shows an attenuation measurement of a squeezed state verifying the linear regime of the detector.
Fig. 4.
Fig. 4. Comparison of measured squeezing values with the theoretical model for below-threshold operation. The system was operated in the slightly undercoupled regime with 2Γ=2π×2.18MHz. Though the theoretical model is incomplete close to and above the threshold, the model is consistent with the measurement.

Equations (6)

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

Var(Xsq/asq)[f]=14ηV2γ2Γ·G(1±G)2+(2πfΓ)2,
Γ=ΓFWHM2=γ1+γ2+γint
G=4g2npΓ2,
Pth=ωp8g2Γ2Γp2γ1p.
Psignal=4Pthγ1Γγ1pΓp·(PpPth1),
G=1+(2πf/Γ)2>1.