Abstract

We analyze the performance of optomechanical cooling of a mechanical resonator in the presence of a degenerate optical parametric amplifier within the optomechanical cavity, which squeezes the cavity light. We demonstrate that this allows to significantly enhance the cooling efficiency via the coherent suppression of Stokes scattering. The enhanced cooling occurs also far from the resolved sideband regime, and we show that this cooling scheme can be more efficient than schemes realized by injecting a squeezed field into the optomechanical cavity.

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

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References

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  1. W. P. Bowen and G. J. Milburn, Quantum Optomechanics (Taylor & Francis, 2015).
  2. 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(24), 243603 (2015).
    [Crossref]
  3. M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the Standard Sensitivity-Bandwidth Limit of Cavity-Enhanced Interferometers with Internal Squeezed-Light Generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
    [Crossref]
  4. The LIGO Scientific Collaboration, “Enhancing the sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photonics 7(8), 613–619 (2013).
    [Crossref]
  5. J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Observation of strong radiation pressure forces from squeezed light on a mechanical oscillator,” Nat. Phys. 12(7), 683–687 (2016).
    [Crossref]
  6. K. Jähne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, and P. Zoller, “Cavity-assisted squeezing of a mechanical oscillator,” Phys. Rev. A 79(6), 063819 (2009).
    [Crossref]
  7. M. Asjad, S. Zippilli, and D. Vitali, “Mechanical Einstein-Podolsky-Rosen entanglement with a finite-bandwidth squeezed reservoir,” Phys. Rev. A 93(6), 062307 (2016).
    [Crossref]
  8. S. Huang and G. S. Agarwal, “Normal-mode splitting in a coupled system of a nanomechanical oscillator and a parametric amplifier cavity,” Phys. Rev. A 80(3), 033807 (2009).
    [Crossref]
  9. X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed Optomechanics with Phase-Matched Amplification and Dissipation,” Phys. Rev. Lett. 114(9), 093602 (2015).
    [Crossref]
  10. S. Huang and G. S. Agarwal, “Enhancement of cavity cooling of a micromechanical mirror using parametric interactions,” Phys. Rev. A 79(1), 013821 (2009).
    [Crossref]
  11. M. Asjad, S. Zippilli, and D. Vitali, “Suppression of Stokes scattering and improved optomechanical cooling with squeezed light,” Phys. Rev. A 94(5), 051801 (2016).
    [Crossref]
  12. J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Sideband cooling beyond the quantum backaction limit with squeezed light,” Nature 541(7636), 191–195 (2017).
    [Crossref]
  13. H.-K. Lau and A. A. Clerk, “Ground state cooling and high-fidelity quantum transduction via parametrically-driven bad-cavity optomechanics,” ArXiv190412984 Quant-Ph (2019).
  14. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
    [Crossref]
  15. N. Kralj, M. Rossi, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. D. Giuseppe, and D. Vitali, “Enhancement of three-mode optomechanical interaction by feedback-controlled light,” Quantum Sci. Technol. 2(3), 034014 (2017).
    [Crossref]
  16. M. Rossi, N. Kralj, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. Di Giuseppe, and D. Vitali, “Enhancing Sideband Cooling by Feedback-Controlled Light,” Phys. Rev. Lett. 119(12), 123603 (2017).
    [Crossref]
  17. S. Zippilli, N. Kralj, M. Rossi, G. Di Giuseppe, and D. Vitali, “Cavity optomechanics with feedback-controlled in-loop light,” Phys. Rev. A 98(2), 023828 (2018).
    [Crossref]
  18. J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-$Q$Q crystalline microresonators,” Phys. Rev. A 82(3), 031804 (2010).
    [Crossref]
  19. 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(15), 153901 (2010).
    [Crossref]
  20. 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(1), 1818 (2013).
    [Crossref]
  21. 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(11), 113901 (2011).
    [Crossref]
  22. A. Otterpohl, F. Sedlmeir, U. Vogl, T. Dirmeier, G. Shafiee, G. Schunk, D. V. Strekalov, H. G. L. Schwefel, T. Gehring, U. L. Andersen, G. Leuchs, and C. Marquardt, “Squeezed vacuum states from a whispering gallery mode resonator,” ArXiv190507955 Quant-Ph (2019).
  23. G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
    [Crossref]
  24. 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(11), 110801 (2016).
    [Crossref]
  25. S. Begley, M. Vogt, G. K. Gulati, H. Takahashi, and M. Keller, “Optimized Multi-Ion Cavity Coupling,” Phys. Rev. Lett. 116(22), 223001 (2016).
    [Crossref]
  26. A. Neuzner, M. Körber, O. Morin, S. Ritter, and G. Rempe, “Interference and dynamics of light from a distance-controlled atom pair in an optical cavity,” Nat. Photonics 10(5), 303–306 (2016).
    [Crossref]
  27. S. Fernàndez-Vidal, S. Zippilli, and G. Morigi, “Nonlinear optics with two trapped atoms,” Phys. Rev. A 76(5), 053829 (2007).
    [Crossref]
  28. H. Habibian, S. Zippilli, and G. Morigi, “Quantum light by atomic arrays in optical resonators,” Phys. Rev. A 84(3), 033829 (2011).
    [Crossref]

2018 (1)

S. Zippilli, N. Kralj, M. Rossi, G. Di Giuseppe, and D. Vitali, “Cavity optomechanics with feedback-controlled in-loop light,” Phys. Rev. A 98(2), 023828 (2018).
[Crossref]

2017 (4)

N. Kralj, M. Rossi, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. D. Giuseppe, and D. Vitali, “Enhancement of three-mode optomechanical interaction by feedback-controlled light,” Quantum Sci. Technol. 2(3), 034014 (2017).
[Crossref]

M. Rossi, N. Kralj, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. Di Giuseppe, and D. Vitali, “Enhancing Sideband Cooling by Feedback-Controlled Light,” Phys. Rev. Lett. 119(12), 123603 (2017).
[Crossref]

J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Sideband cooling beyond the quantum backaction limit with squeezed light,” Nature 541(7636), 191–195 (2017).
[Crossref]

M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the Standard Sensitivity-Bandwidth Limit of Cavity-Enhanced Interferometers with Internal Squeezed-Light Generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
[Crossref]

2016 (6)

J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Observation of strong radiation pressure forces from squeezed light on a mechanical oscillator,” Nat. Phys. 12(7), 683–687 (2016).
[Crossref]

M. Asjad, S. Zippilli, and D. Vitali, “Mechanical Einstein-Podolsky-Rosen entanglement with a finite-bandwidth squeezed reservoir,” Phys. Rev. A 93(6), 062307 (2016).
[Crossref]

M. Asjad, S. Zippilli, and D. Vitali, “Suppression of Stokes scattering and improved optomechanical cooling with squeezed light,” Phys. Rev. A 94(5), 051801 (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(11), 110801 (2016).
[Crossref]

S. Begley, M. Vogt, G. K. Gulati, H. Takahashi, and M. Keller, “Optimized Multi-Ion Cavity Coupling,” Phys. Rev. Lett. 116(22), 223001 (2016).
[Crossref]

A. Neuzner, M. Körber, O. Morin, S. Ritter, and G. Rempe, “Interference and dynamics of light from a distance-controlled atom pair in an optical cavity,” Nat. Photonics 10(5), 303–306 (2016).
[Crossref]

2015 (2)

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(24), 243603 (2015).
[Crossref]

X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed Optomechanics with Phase-Matched Amplification and Dissipation,” Phys. Rev. Lett. 114(9), 093602 (2015).
[Crossref]

2014 (1)

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

2013 (2)

The LIGO Scientific Collaboration, “Enhancing the sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photonics 7(8), 613–619 (2013).
[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(1), 1818 (2013).
[Crossref]

2011 (2)

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(11), 113901 (2011).
[Crossref]

H. Habibian, S. Zippilli, and G. Morigi, “Quantum light by atomic arrays in optical resonators,” Phys. Rev. A 84(3), 033829 (2011).
[Crossref]

2010 (2)

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-$Q$Q crystalline microresonators,” Phys. Rev. A 82(3), 031804 (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(15), 153901 (2010).
[Crossref]

2009 (4)

K. Jähne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, and P. Zoller, “Cavity-assisted squeezing of a mechanical oscillator,” Phys. Rev. A 79(6), 063819 (2009).
[Crossref]

S. Huang and G. S. Agarwal, “Enhancement of cavity cooling of a micromechanical mirror using parametric interactions,” Phys. Rev. A 79(1), 013821 (2009).
[Crossref]

S. Huang and G. S. Agarwal, “Normal-mode splitting in a coupled system of a nanomechanical oscillator and a parametric amplifier cavity,” Phys. Rev. A 80(3), 033807 (2009).
[Crossref]

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
[Crossref]

2007 (1)

S. Fernàndez-Vidal, S. Zippilli, and G. Morigi, “Nonlinear optics with two trapped atoms,” Phys. Rev. A 76(5), 053829 (2007).
[Crossref]

Agarwal, G. S.

S. Huang and G. S. Agarwal, “Normal-mode splitting in a coupled system of a nanomechanical oscillator and a parametric amplifier cavity,” Phys. Rev. A 80(3), 033807 (2009).
[Crossref]

S. Huang and G. S. Agarwal, “Enhancement of cavity cooling of a micromechanical mirror using parametric interactions,” Phys. Rev. A 79(1), 013821 (2009).
[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(1), 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(11), 113901 (2011).
[Crossref]

Andersen, U. L.

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(11), 113901 (2011).
[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(15), 153901 (2010).
[Crossref]

A. Otterpohl, F. Sedlmeir, U. Vogl, T. Dirmeier, G. Shafiee, G. Schunk, D. V. Strekalov, H. G. L. Schwefel, T. Gehring, U. L. Andersen, G. Leuchs, and C. Marquardt, “Squeezed vacuum states from a whispering gallery mode resonator,” ArXiv190507955 Quant-Ph (2019).

Anetsberger, G.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
[Crossref]

Arcizet, O.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
[Crossref]

Asjad, M.

M. Asjad, S. Zippilli, and D. Vitali, “Suppression of Stokes scattering and improved optomechanical cooling with squeezed light,” Phys. Rev. A 94(5), 051801 (2016).
[Crossref]

M. Asjad, S. Zippilli, and D. Vitali, “Mechanical Einstein-Podolsky-Rosen entanglement with a finite-bandwidth squeezed reservoir,” Phys. Rev. A 93(6), 062307 (2016).
[Crossref]

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

Ast, S.

M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the Standard Sensitivity-Bandwidth Limit of Cavity-Enhanced Interferometers with Internal Squeezed-Light Generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
[Crossref]

Aumentado, J.

J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Sideband cooling beyond the quantum backaction limit with squeezed light,” Nature 541(7636), 191–195 (2017).
[Crossref]

J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Observation of strong radiation pressure forces from squeezed light on a mechanical oscillator,” Nat. Phys. 12(7), 683–687 (2016).
[Crossref]

Begley, S.

S. Begley, M. Vogt, G. K. Gulati, H. Takahashi, and M. Keller, “Optimized Multi-Ion Cavity Coupling,” Phys. Rev. Lett. 116(22), 223001 (2016).
[Crossref]

Borrielli, A.

N. Kralj, M. Rossi, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. D. Giuseppe, and D. Vitali, “Enhancement of three-mode optomechanical interaction by feedback-controlled light,” Quantum Sci. Technol. 2(3), 034014 (2017).
[Crossref]

M. Rossi, N. Kralj, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. Di Giuseppe, and D. Vitali, “Enhancing Sideband Cooling by Feedback-Controlled Light,” Phys. Rev. Lett. 119(12), 123603 (2017).
[Crossref]

Bowen, W. P.

W. P. Bowen and G. J. Milburn, Quantum Optomechanics (Taylor & Francis, 2015).

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(1), 1818 (2013).
[Crossref]

Chen, Y.

M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the Standard Sensitivity-Bandwidth Limit of Cavity-Enhanced Interferometers with Internal Squeezed-Light Generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
[Crossref]

Clark, J. B.

J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Sideband cooling beyond the quantum backaction limit with squeezed light,” Nature 541(7636), 191–195 (2017).
[Crossref]

J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Observation of strong radiation pressure forces from squeezed light on a mechanical oscillator,” Nat. Phys. 12(7), 683–687 (2016).
[Crossref]

Clerk, A. A.

H.-K. Lau and A. A. Clerk, “Ground state cooling and high-fidelity quantum transduction via parametrically-driven bad-cavity optomechanics,” ArXiv190412984 Quant-Ph (2019).

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(11), 110801 (2016).
[Crossref]

Di Giuseppe, G.

S. Zippilli, N. Kralj, M. Rossi, G. Di Giuseppe, and D. Vitali, “Cavity optomechanics with feedback-controlled in-loop light,” Phys. Rev. A 98(2), 023828 (2018).
[Crossref]

M. Rossi, N. Kralj, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. Di Giuseppe, and D. Vitali, “Enhancing Sideband Cooling by Feedback-Controlled Light,” Phys. Rev. Lett. 119(12), 123603 (2017).
[Crossref]

Dirmeier, T.

A. Otterpohl, F. Sedlmeir, U. Vogl, T. Dirmeier, G. Shafiee, G. Schunk, D. V. Strekalov, H. G. L. Schwefel, T. Gehring, U. L. Andersen, G. Leuchs, and C. Marquardt, “Squeezed vacuum states from a whispering gallery mode resonator,” ArXiv190507955 Quant-Ph (2019).

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(11), 113901 (2011).
[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(15), 153901 (2010).
[Crossref]

Fernàndez-Vidal, S.

S. Fernàndez-Vidal, S. Zippilli, and G. Morigi, “Nonlinear optics with two trapped atoms,” Phys. Rev. A 76(5), 053829 (2007).
[Crossref]

Förtsch, M.

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(1), 1818 (2013).
[Crossref]

Fürst, J. U.

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(1), 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(11), 113901 (2011).
[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(15), 153901 (2010).
[Crossref]

Gehring, T.

A. Otterpohl, F. Sedlmeir, U. Vogl, T. Dirmeier, G. Shafiee, G. Schunk, D. V. Strekalov, H. G. L. Schwefel, T. Gehring, U. L. Andersen, G. Leuchs, and C. Marquardt, “Squeezed vacuum states from a whispering gallery mode resonator,” ArXiv190507955 Quant-Ph (2019).

Genes, C.

K. Jähne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, and P. Zoller, “Cavity-assisted squeezing of a mechanical oscillator,” Phys. Rev. A 79(6), 063819 (2009).
[Crossref]

Giuseppe, G. D.

N. Kralj, M. Rossi, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. D. Giuseppe, and D. Vitali, “Enhancement of three-mode optomechanical interaction by feedback-controlled light,” Quantum Sci. Technol. 2(3), 034014 (2017).
[Crossref]

Gulati, G. K.

S. Begley, M. Vogt, G. K. Gulati, H. Takahashi, and M. Keller, “Optimized Multi-Ion Cavity Coupling,” Phys. Rev. Lett. 116(22), 223001 (2016).
[Crossref]

Habibian, H.

H. Habibian, S. Zippilli, and G. Morigi, “Quantum light by atomic arrays in optical resonators,” Phys. Rev. A 84(3), 033829 (2011).
[Crossref]

Hammerer, K.

K. Jähne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, and P. Zoller, “Cavity-assisted squeezing of a mechanical oscillator,” Phys. Rev. A 79(6), 063819 (2009).
[Crossref]

Hofer, J.

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-$Q$Q crystalline microresonators,” Phys. Rev. A 82(3), 031804 (2010).
[Crossref]

Huang, S.

S. Huang and G. S. Agarwal, “Normal-mode splitting in a coupled system of a nanomechanical oscillator and a parametric amplifier cavity,” Phys. Rev. A 80(3), 033807 (2009).
[Crossref]

S. Huang and G. S. Agarwal, “Enhancement of cavity cooling of a micromechanical mirror using parametric interactions,” Phys. Rev. A 79(1), 013821 (2009).
[Crossref]

Jähne, K.

K. Jähne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, and P. Zoller, “Cavity-assisted squeezing of a mechanical oscillator,” Phys. Rev. A 79(6), 063819 (2009).
[Crossref]

Jing, H.

X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed Optomechanics with Phase-Matched Amplification and Dissipation,” Phys. Rev. Lett. 114(9), 093602 (2015).
[Crossref]

Johansson, J. R.

X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed Optomechanics with Phase-Matched Amplification and Dissipation,” Phys. Rev. Lett. 114(9), 093602 (2015).
[Crossref]

Keller, M.

S. Begley, M. Vogt, G. K. Gulati, H. Takahashi, and M. Keller, “Optimized Multi-Ion Cavity Coupling,” Phys. Rev. Lett. 116(22), 223001 (2016).
[Crossref]

Kippenberg, T. J.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-$Q$Q crystalline microresonators,” Phys. Rev. A 82(3), 031804 (2010).
[Crossref]

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
[Crossref]

Kleybolte, L.

M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the Standard Sensitivity-Bandwidth Limit of Cavity-Enhanced Interferometers with Internal Squeezed-Light Generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
[Crossref]

Körber, M.

A. Neuzner, M. Körber, O. Morin, S. Ritter, and G. Rempe, “Interference and dynamics of light from a distance-controlled atom pair in an optical cavity,” Nat. Photonics 10(5), 303–306 (2016).
[Crossref]

Korobko, M.

M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the Standard Sensitivity-Bandwidth Limit of Cavity-Enhanced Interferometers with Internal Squeezed-Light Generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
[Crossref]

Kotthaus, J. P.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
[Crossref]

Kralj, N.

S. Zippilli, N. Kralj, M. Rossi, G. Di Giuseppe, and D. Vitali, “Cavity optomechanics with feedback-controlled in-loop light,” Phys. Rev. A 98(2), 023828 (2018).
[Crossref]

M. Rossi, N. Kralj, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. Di Giuseppe, and D. Vitali, “Enhancing Sideband Cooling by Feedback-Controlled Light,” Phys. Rev. Lett. 119(12), 123603 (2017).
[Crossref]

N. Kralj, M. Rossi, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. D. Giuseppe, and D. Vitali, “Enhancement of three-mode optomechanical interaction by feedback-controlled light,” Quantum Sci. Technol. 2(3), 034014 (2017).
[Crossref]

Lassen, M.

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(15), 153901 (2010).
[Crossref]

Lau, H.-K.

H.-K. Lau and A. A. Clerk, “Ground state cooling and high-fidelity quantum transduction via parametrically-driven bad-cavity optomechanics,” ArXiv190412984 Quant-Ph (2019).

Lecocq, F.

J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Sideband cooling beyond the quantum backaction limit with squeezed light,” Nature 541(7636), 191–195 (2017).
[Crossref]

J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Observation of strong radiation pressure forces from squeezed light on a mechanical oscillator,” Nat. Phys. 12(7), 683–687 (2016).
[Crossref]

Leuchs, G.

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(1), 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(11), 113901 (2011).
[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(15), 153901 (2010).
[Crossref]

A. Otterpohl, F. Sedlmeir, U. Vogl, T. Dirmeier, G. Shafiee, G. Schunk, D. V. Strekalov, H. G. L. Schwefel, T. Gehring, U. L. Andersen, G. Leuchs, and C. Marquardt, “Squeezed vacuum states from a whispering gallery mode resonator,” ArXiv190507955 Quant-Ph (2019).

Lü, X.-Y.

X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed Optomechanics with Phase-Matched Amplification and Dissipation,” Phys. Rev. Lett. 114(9), 093602 (2015).
[Crossref]

Marquardt, C.

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(24), 243603 (2015).
[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(1), 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(11), 113901 (2011).
[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(15), 153901 (2010).
[Crossref]

A. Otterpohl, F. Sedlmeir, U. Vogl, T. Dirmeier, G. Shafiee, G. Schunk, D. V. Strekalov, H. G. L. Schwefel, T. Gehring, U. L. Andersen, G. Leuchs, and C. Marquardt, “Squeezed vacuum states from a whispering gallery mode resonator,” ArXiv190507955 Quant-Ph (2019).

Marquardt, F.

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(24), 243603 (2015).
[Crossref]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

Mehmet, M.

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(11), 110801 (2016).
[Crossref]

Miao, H.

M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the Standard Sensitivity-Bandwidth Limit of Cavity-Enhanced Interferometers with Internal Squeezed-Light Generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
[Crossref]

Milburn, G. J.

W. P. Bowen and G. J. Milburn, Quantum Optomechanics (Taylor & Francis, 2015).

Morigi, G.

H. Habibian, S. Zippilli, and G. Morigi, “Quantum light by atomic arrays in optical resonators,” Phys. Rev. A 84(3), 033829 (2011).
[Crossref]

S. Fernàndez-Vidal, S. Zippilli, and G. Morigi, “Nonlinear optics with two trapped atoms,” Phys. Rev. A 76(5), 053829 (2007).
[Crossref]

Morin, O.

A. Neuzner, M. Körber, O. Morin, S. Ritter, and G. Rempe, “Interference and dynamics of light from a distance-controlled atom pair in an optical cavity,” Nat. Photonics 10(5), 303–306 (2016).
[Crossref]

Natali, R.

N. Kralj, M. Rossi, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. D. Giuseppe, and D. Vitali, “Enhancement of three-mode optomechanical interaction by feedback-controlled light,” Quantum Sci. Technol. 2(3), 034014 (2017).
[Crossref]

M. Rossi, N. Kralj, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. Di Giuseppe, and D. Vitali, “Enhancing Sideband Cooling by Feedback-Controlled Light,” Phys. Rev. Lett. 119(12), 123603 (2017).
[Crossref]

Neuzner, A.

A. Neuzner, M. Körber, O. Morin, S. Ritter, and G. Rempe, “Interference and dynamics of light from a distance-controlled atom pair in an optical cavity,” Nat. Photonics 10(5), 303–306 (2016).
[Crossref]

Nori, F.

X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed Optomechanics with Phase-Matched Amplification and Dissipation,” Phys. Rev. Lett. 114(9), 093602 (2015).
[Crossref]

Otterpohl, A.

A. Otterpohl, F. Sedlmeir, U. Vogl, T. Dirmeier, G. Shafiee, G. Schunk, D. V. Strekalov, H. G. L. Schwefel, T. Gehring, U. L. Andersen, G. Leuchs, and C. Marquardt, “Squeezed vacuum states from a whispering gallery mode resonator,” ArXiv190507955 Quant-Ph (2019).

Pandraud, G.

M. Rossi, N. Kralj, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. Di Giuseppe, and D. Vitali, “Enhancing Sideband Cooling by Feedback-Controlled Light,” Phys. Rev. Lett. 119(12), 123603 (2017).
[Crossref]

N. Kralj, M. Rossi, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. D. Giuseppe, and D. Vitali, “Enhancement of three-mode optomechanical interaction by feedback-controlled light,” Quantum Sci. Technol. 2(3), 034014 (2017).
[Crossref]

Peano, V.

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(24), 243603 (2015).
[Crossref]

Polzik, E. S.

K. Jähne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, and P. Zoller, “Cavity-assisted squeezing of a mechanical oscillator,” Phys. Rev. A 79(6), 063819 (2009).
[Crossref]

Rempe, G.

A. Neuzner, M. Körber, O. Morin, S. Ritter, and G. Rempe, “Interference and dynamics of light from a distance-controlled atom pair in an optical cavity,” Nat. Photonics 10(5), 303–306 (2016).
[Crossref]

Ritter, S.

A. Neuzner, M. Körber, O. Morin, S. Ritter, and G. Rempe, “Interference and dynamics of light from a distance-controlled atom pair in an optical cavity,” Nat. Photonics 10(5), 303–306 (2016).
[Crossref]

Rivière, R.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
[Crossref]

Rossi, M.

S. Zippilli, N. Kralj, M. Rossi, G. Di Giuseppe, and D. Vitali, “Cavity optomechanics with feedback-controlled in-loop light,” Phys. Rev. A 98(2), 023828 (2018).
[Crossref]

M. Rossi, N. Kralj, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. Di Giuseppe, and D. Vitali, “Enhancing Sideband Cooling by Feedback-Controlled Light,” Phys. Rev. Lett. 119(12), 123603 (2017).
[Crossref]

N. Kralj, M. Rossi, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. D. Giuseppe, and D. Vitali, “Enhancement of three-mode optomechanical interaction by feedback-controlled light,” Quantum Sci. Technol. 2(3), 034014 (2017).
[Crossref]

Schliesser, A.

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-$Q$Q crystalline microresonators,” Phys. Rev. A 82(3), 031804 (2010).
[Crossref]

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
[Crossref]

Schnabel, R.

M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the Standard Sensitivity-Bandwidth Limit of Cavity-Enhanced Interferometers with Internal Squeezed-Light Generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
[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(11), 110801 (2016).
[Crossref]

Schunk, G.

A. Otterpohl, F. Sedlmeir, U. Vogl, T. Dirmeier, G. Shafiee, G. Schunk, D. V. Strekalov, H. G. L. Schwefel, T. Gehring, U. L. Andersen, G. Leuchs, and C. Marquardt, “Squeezed vacuum states from a whispering gallery mode resonator,” ArXiv190507955 Quant-Ph (2019).

Schwefel, H. G. L.

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(24), 243603 (2015).
[Crossref]

A. Otterpohl, F. Sedlmeir, U. Vogl, T. Dirmeier, G. Shafiee, G. Schunk, D. V. Strekalov, H. G. L. Schwefel, T. Gehring, U. L. Andersen, G. Leuchs, and C. Marquardt, “Squeezed vacuum states from a whispering gallery mode resonator,” ArXiv190507955 Quant-Ph (2019).

Sedlmeir, F.

A. Otterpohl, F. Sedlmeir, U. Vogl, T. Dirmeier, G. Shafiee, G. Schunk, D. V. Strekalov, H. G. L. Schwefel, T. Gehring, U. L. Andersen, G. Leuchs, and C. Marquardt, “Squeezed vacuum states from a whispering gallery mode resonator,” ArXiv190507955 Quant-Ph (2019).

Serra, E.

M. Rossi, N. Kralj, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. Di Giuseppe, and D. Vitali, “Enhancing Sideband Cooling by Feedback-Controlled Light,” Phys. Rev. Lett. 119(12), 123603 (2017).
[Crossref]

N. Kralj, M. Rossi, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. D. Giuseppe, and D. Vitali, “Enhancement of three-mode optomechanical interaction by feedback-controlled light,” Quantum Sci. Technol. 2(3), 034014 (2017).
[Crossref]

Shafiee, G.

A. Otterpohl, F. Sedlmeir, U. Vogl, T. Dirmeier, G. Shafiee, G. Schunk, D. V. Strekalov, H. G. L. Schwefel, T. Gehring, U. L. Andersen, G. Leuchs, and C. Marquardt, “Squeezed vacuum states from a whispering gallery mode resonator,” ArXiv190507955 Quant-Ph (2019).

Silberhorn, C.

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(1), 1818 (2013).
[Crossref]

Simmonds, R. W.

J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Sideband cooling beyond the quantum backaction limit with squeezed light,” Nature 541(7636), 191–195 (2017).
[Crossref]

J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Observation of strong radiation pressure forces from squeezed light on a mechanical oscillator,” Nat. Phys. 12(7), 683–687 (2016).
[Crossref]

Strekalov, D.

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(1), 1818 (2013).
[Crossref]

Strekalov, D. V.

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(11), 113901 (2011).
[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(15), 153901 (2010).
[Crossref]

A. Otterpohl, F. Sedlmeir, U. Vogl, T. Dirmeier, G. Shafiee, G. Schunk, D. V. Strekalov, H. G. L. Schwefel, T. Gehring, U. L. Andersen, G. Leuchs, and C. Marquardt, “Squeezed vacuum states from a whispering gallery mode resonator,” ArXiv190507955 Quant-Ph (2019).

Takahashi, H.

S. Begley, M. Vogt, G. K. Gulati, H. Takahashi, and M. Keller, “Optimized Multi-Ion Cavity Coupling,” Phys. Rev. Lett. 116(22), 223001 (2016).
[Crossref]

Teufel, J. D.

J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Sideband cooling beyond the quantum backaction limit with squeezed light,” Nature 541(7636), 191–195 (2017).
[Crossref]

J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Observation of strong radiation pressure forces from squeezed light on a mechanical oscillator,” Nat. Phys. 12(7), 683–687 (2016).
[Crossref]

Unterreithmeier, Q. P.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
[Crossref]

Vahlbruch, H.

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(11), 110801 (2016).
[Crossref]

Vitali, D.

S. Zippilli, N. Kralj, M. Rossi, G. Di Giuseppe, and D. Vitali, “Cavity optomechanics with feedback-controlled in-loop light,” Phys. Rev. A 98(2), 023828 (2018).
[Crossref]

M. Rossi, N. Kralj, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. Di Giuseppe, and D. Vitali, “Enhancing Sideband Cooling by Feedback-Controlled Light,” Phys. Rev. Lett. 119(12), 123603 (2017).
[Crossref]

N. Kralj, M. Rossi, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. D. Giuseppe, and D. Vitali, “Enhancement of three-mode optomechanical interaction by feedback-controlled light,” Quantum Sci. Technol. 2(3), 034014 (2017).
[Crossref]

M. Asjad, S. Zippilli, and D. Vitali, “Suppression of Stokes scattering and improved optomechanical cooling with squeezed light,” Phys. Rev. A 94(5), 051801 (2016).
[Crossref]

M. Asjad, S. Zippilli, and D. Vitali, “Mechanical Einstein-Podolsky-Rosen entanglement with a finite-bandwidth squeezed reservoir,” Phys. Rev. A 93(6), 062307 (2016).
[Crossref]

Vogl, U.

A. Otterpohl, F. Sedlmeir, U. Vogl, T. Dirmeier, G. Shafiee, G. Schunk, D. V. Strekalov, H. G. L. Schwefel, T. Gehring, U. L. Andersen, G. Leuchs, and C. Marquardt, “Squeezed vacuum states from a whispering gallery mode resonator,” ArXiv190507955 Quant-Ph (2019).

Vogt, M.

S. Begley, M. Vogt, G. K. Gulati, H. Takahashi, and M. Keller, “Optimized Multi-Ion Cavity Coupling,” Phys. Rev. Lett. 116(22), 223001 (2016).
[Crossref]

Wallquist, M.

K. Jähne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, and P. Zoller, “Cavity-assisted squeezing of a mechanical oscillator,” Phys. Rev. A 79(6), 063819 (2009).
[Crossref]

Weig, E. M.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
[Crossref]

Wittmann, C.

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(1), 1818 (2013).
[Crossref]

Wu, Y.

X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed Optomechanics with Phase-Matched Amplification and Dissipation,” Phys. Rev. Lett. 114(9), 093602 (2015).
[Crossref]

Zhang, J.

X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed Optomechanics with Phase-Matched Amplification and Dissipation,” Phys. Rev. Lett. 114(9), 093602 (2015).
[Crossref]

Zippilli, S.

S. Zippilli, N. Kralj, M. Rossi, G. Di Giuseppe, and D. Vitali, “Cavity optomechanics with feedback-controlled in-loop light,” Phys. Rev. A 98(2), 023828 (2018).
[Crossref]

M. Rossi, N. Kralj, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. Di Giuseppe, and D. Vitali, “Enhancing Sideband Cooling by Feedback-Controlled Light,” Phys. Rev. Lett. 119(12), 123603 (2017).
[Crossref]

N. Kralj, M. Rossi, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. D. Giuseppe, and D. Vitali, “Enhancement of three-mode optomechanical interaction by feedback-controlled light,” Quantum Sci. Technol. 2(3), 034014 (2017).
[Crossref]

M. Asjad, S. Zippilli, and D. Vitali, “Suppression of Stokes scattering and improved optomechanical cooling with squeezed light,” Phys. Rev. A 94(5), 051801 (2016).
[Crossref]

M. Asjad, S. Zippilli, and D. Vitali, “Mechanical Einstein-Podolsky-Rosen entanglement with a finite-bandwidth squeezed reservoir,” Phys. Rev. A 93(6), 062307 (2016).
[Crossref]

H. Habibian, S. Zippilli, and G. Morigi, “Quantum light by atomic arrays in optical resonators,” Phys. Rev. A 84(3), 033829 (2011).
[Crossref]

S. Fernàndez-Vidal, S. Zippilli, and G. Morigi, “Nonlinear optics with two trapped atoms,” Phys. Rev. A 76(5), 053829 (2007).
[Crossref]

Zoller, P.

K. Jähne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, and P. Zoller, “Cavity-assisted squeezing of a mechanical oscillator,” Phys. Rev. A 79(6), 063819 (2009).
[Crossref]

Nat. Commun. (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(1), 1818 (2013).
[Crossref]

Nat. Photonics (2)

A. Neuzner, M. Körber, O. Morin, S. Ritter, and G. Rempe, “Interference and dynamics of light from a distance-controlled atom pair in an optical cavity,” Nat. Photonics 10(5), 303–306 (2016).
[Crossref]

The LIGO Scientific Collaboration, “Enhancing the sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photonics 7(8), 613–619 (2013).
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Nat. Phys. (2)

J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Observation of strong radiation pressure forces from squeezed light on a mechanical oscillator,” Nat. Phys. 12(7), 683–687 (2016).
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G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
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Nature (1)

J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Sideband cooling beyond the quantum backaction limit with squeezed light,” Nature 541(7636), 191–195 (2017).
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Phys. Rev. A (9)

S. Zippilli, N. Kralj, M. Rossi, G. Di Giuseppe, and D. Vitali, “Cavity optomechanics with feedback-controlled in-loop light,” Phys. Rev. A 98(2), 023828 (2018).
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J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-$Q$Q crystalline microresonators,” Phys. Rev. A 82(3), 031804 (2010).
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M. Asjad, S. Zippilli, and D. Vitali, “Mechanical Einstein-Podolsky-Rosen entanglement with a finite-bandwidth squeezed reservoir,” Phys. Rev. A 93(6), 062307 (2016).
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S. Huang and G. S. Agarwal, “Normal-mode splitting in a coupled system of a nanomechanical oscillator and a parametric amplifier cavity,” Phys. Rev. A 80(3), 033807 (2009).
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S. Huang and G. S. Agarwal, “Enhancement of cavity cooling of a micromechanical mirror using parametric interactions,” Phys. Rev. A 79(1), 013821 (2009).
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M. Asjad, S. Zippilli, and D. Vitali, “Suppression of Stokes scattering and improved optomechanical cooling with squeezed light,” Phys. Rev. A 94(5), 051801 (2016).
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S. Fernàndez-Vidal, S. Zippilli, and G. Morigi, “Nonlinear optics with two trapped atoms,” Phys. Rev. A 76(5), 053829 (2007).
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H. Habibian, S. Zippilli, and G. Morigi, “Quantum light by atomic arrays in optical resonators,” Phys. Rev. A 84(3), 033829 (2011).
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Phys. Rev. Lett. (8)

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(11), 110801 (2016).
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S. Begley, M. Vogt, G. K. Gulati, H. Takahashi, and M. Keller, “Optimized Multi-Ion Cavity Coupling,” Phys. Rev. Lett. 116(22), 223001 (2016).
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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(11), 113901 (2011).
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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(24), 243603 (2015).
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M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the Standard Sensitivity-Bandwidth Limit of Cavity-Enhanced Interferometers with Internal Squeezed-Light Generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
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X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed Optomechanics with Phase-Matched Amplification and Dissipation,” Phys. Rev. Lett. 114(9), 093602 (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(15), 153901 (2010).
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M. Rossi, N. Kralj, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. Di Giuseppe, and D. Vitali, “Enhancing Sideband Cooling by Feedback-Controlled Light,” Phys. Rev. Lett. 119(12), 123603 (2017).
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Quantum Sci. Technol. (1)

N. Kralj, M. Rossi, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. D. Giuseppe, and D. Vitali, “Enhancement of three-mode optomechanical interaction by feedback-controlled light,” Quantum Sci. Technol. 2(3), 034014 (2017).
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Rev. Mod. Phys. (1)

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
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Other (3)

W. P. Bowen and G. J. Milburn, Quantum Optomechanics (Taylor & Francis, 2015).

H.-K. Lau and A. A. Clerk, “Ground state cooling and high-fidelity quantum transduction via parametrically-driven bad-cavity optomechanics,” ArXiv190412984 Quant-Ph (2019).

A. Otterpohl, F. Sedlmeir, U. Vogl, T. Dirmeier, G. Shafiee, G. Schunk, D. V. Strekalov, H. G. L. Schwefel, T. Gehring, U. L. Andersen, G. Leuchs, and C. Marquardt, “Squeezed vacuum states from a whispering gallery mode resonator,” ArXiv190507955 Quant-Ph (2019).

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Figures (7)

Fig. 1.
Fig. 1. Schematical description of the optomechanical system with intracavity squeezing generated by the driven nonlinear crystal.
Fig. 2.
Fig. 2. (a) Power spectrum of the radiation pressure force defined in Eq. (24) and (b)-(d) steady-state excitation number $N_{st}$ as a function of (b) the phase of the squeezing $\phi$, (c) the value of squeezing measured by the parameter ${{\cal R}}$ defined in Eq. (29), and (d) the optomechanical coupling strength $G_a$. The solid lines are evaluated by solving numerically Eq. (15). The dashed lines correspond to the analytical approximated solution evaluated with Eq. (24). The grey lines are evaluated without squeezing (${{\cal R}}=0$). The red lines are evaluated with squeezing, and with the optimal values for Stokes scattering suppression $\phi {^{({opt})}}$ and $\mathcal {R}={{\cal R}}{^{({opt})}}$ as reported in Eqs. (27) and (30). The other parameters are $n_T=1000$, $\gamma _m=0.25\times 10^{-6}\omega _m$ and $\kappa _a= \omega _m$, $G_a=0.1\omega _m$, $\Delta _a=\omega _m$.
Fig. 3.
Fig. 3. Steady state excitation number, $N_{st}$, as a function of (first column) the squeezing phase $\phi =\phi _s$, (second column) the optical detuning $\Delta _a=\Delta _a^{({s})}$, (third column) the optomechanical coupling strength $G_a=G_a^{({s})}$, and (fourth column) the value of squeezing ${{\cal R}}={{\cal R}}_s$. The red lines correspond to the model with internal OPO [see Eq. (15)], the black lines to the model with external OPO [see Eq. (20)] and the grey lines are with no squeezing. The results for the two models (red and black lines) in the third column are equal and only the red line is visible. The vertical dashed lines in plot (i) limit the region of stability of the model described by Eq. (15). Each row is evaluated for a different cavity linewidth: (first row) $\kappa _a=0.1\omega _m$, (second row) $\kappa _a=\omega _m$, (third row) $\kappa _a=10\omega _m$. Each curve is evaluated for the parameters that minimize the corresponding curves in the other plots of the same row. The plots as a function of the optical detuning and the optomechanical coupling strength (second and third columns) are evaluated under the condition of Stokes scattering suppression defined in Eqs. (27), (28), (30) and (32). The insets in the second columns show the specific values of the squeezing parameter ${{\cal R}}$ and of the squeezing phase $\phi$ and $\phi _s$ used to compute the corresponding results for $N_{st}$. The other parameters are as in Fig. 2.
Fig. 4.
Fig. 4. Steady state excitation number, $N_{st}$. The line-styles are as in Fig. 3. The parameters are the same as in the second row of Fig. 3 ($\kappa _a=\omega _m$), but with different mean thermal phonon number $n_T$. The first row corresponds to $n_T=0.1$ and the second to $n_T=10^5$.
Fig. 5.
Fig. 5. (a), (b) Steady state excitation number $N_{st}$ as a function of the squeezing phase $\phi$ ($\phi _s$) and the value of squeezing ${{\cal R}}$ (${{\cal R}}_s$), for (a) internal and (b) external OPO, and for $\kappa _a=10\omega _m$. The curves in plots (c) report the values of $N_{st}$ as a function of ${{\cal R}}={{\cal R}}_s$ along cuts of the contour plots at the specific values of $\phi$ ($\phi _s$) which correspond to the minima of $N_{st}$: the red curves correspond to the cut of the plots (a) at the value of the phase $\phi =0.62\pi$, and the black curves to the cut of the plots (b) at the value of the phase $\phi _s=0.47\pi$. These results are evaluated by minimizing the value of $N_{st}$, at each point in the $\phi -{{\cal R}}$ ($\phi _s-{{\cal R}}_s$) space, as a function of $\Delta _a$ and $G_a$ ($\Delta _a^{({s})}$ and $G_a^{({s})}$). The specific values of $\Delta _a$ and $G_a$ corresponding to plot (c) are reported in plots (d)-(e). The other parameters are equal to the ones used in the third row of Fig. 3.
Fig. 6.
Fig. 6. The same as in Fig. 5, but with $\kappa _a=100\omega _m$. The curves in (c), (d) and (e) correspond to $\phi =0.63\pi$ and $\phi _s=0.45\pi$.
Fig. 7.
Fig. 7. Effect of the OPO pump. Steady state excitation number as a function of (a) the single photon optomechanical coupling strength $g_c$ for the pump mode and (b) the single photon non-linearity $\chi _0$, for fixed values of $G_a$, $\chi$ and $g_a$. Solid blue lines are numerical results evaluated solving Eq. (10), dashed blue lines are evaluated using the analytical result in Eq. (36). The red solid and dashed red lines are for the model in Eq. (15) and the corresponding approximations in Eq. (24). The dashed vertical line limits the region of stability of the model in Eq. (10). The solid blue lines are evaluated for values of the cavity linewidth and the optical detuning, corresponding to mode $a$, modified according to the relations $\kappa _a-{\kappa _c\ \epsilon ^2}\left ( {\kappa _c^2+\Delta _c^2} \right )$ and $\Delta _a+{\Delta _c\ \epsilon ^2}/\left ( {\kappa _c^2+\Delta _c^2} \right )$, where $\kappa _a=\Delta _a=\omega _m$ are the corresponding values used for the red lines. All the results are evaluated for $g_a=10^{-6}\,\omega _m$, $\kappa _c=500\omega _m$ and $\kappa _c=\omega _m$ and for the parameters that minimize $N_{st}$ in the second row of Fig. 3. In (a) $g_c=10^{-6}\omega _m$ and in (b) $\chi _0=10^{-4}\omega _m$.

Equations (46)

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HOPO=iχ02(c a2c a2),
HOM= ga aa(b+b) gc cc(b+b) .
a˙=(κa+iΔ¯a)a+iga a(b+b)+χ0ca+Ea+2κaain,c˙=(κc+iΔ¯c)c+igc c(b+b)χ02a2+Ec+2κccin,b˙=(γ2+iωm)b+iga aa+igc cc+γbin,
[κa+iΔa]ast+χ0astcst+Ea=0,[κc+iΔc]cstχ02ast2+Ec=0,(γ2+iωm)bst+i(ga|cst|2+ga|ast|2)=0.
ast=Ea(κaiΔa)+Ea χ0cstκa2+Δa2χ02|cst|2,cst=Ecκc+iΔcχ02ast2κc+iΔc,bst=iga|ast|2+gc|cst|2γ2+iωm ,
δa˙=(κa+iΔa)δa+iGa(δb+δb)+χδa+ϵδc+2κaain ,δc˙=(κc+iΔc)δc+iGc(δb+δb)ϵδa+2κccin ,δb˙=(γ2+iωm)δb+i(Gaδa+Gaδa)+i(Gcδc+Gcδc)+γbin ,
Gι=gιιstfor ι=a,c
χ=χ0cst
ϵ=χ0ast
δa˙=(κa+iΔa)δa+iGa(δb+δb)+χe2iϕδa+ϵδc+2κaain,δc˙=(κc+iΔc)δc+iGce2iϕ(δb+δb)ϵδa+2κccin,δb˙=(γ2+iωm)δb+iGa(δa+δa)+iGc(e2iϕδc+e2iϕδc)+γbin .
Nst=γ nT+Γ noγ+Γ .
F=ι=a,cGι(δι+δι) ,
A±=dt eiωmtF(t) F(0)st,
Γ=AA+ ,no=A+Γ ,
δa˙=(κa+iΔa)δa+iGa(δb+δb)+χe2iϕδa+2κaain,δb˙=(γ2+iωm)δb+iGa(δa+δa)+γbin .
δas=eiϕ[cosh(s) δa+sinh(s) e2i(ϕsϕ) δa] ,
tanh(s)=ΔaΔa2χ2χ,
ϕs=ϕ+ϕ+π4,
ϕ=arctan[sinh(s) sin(2ϕs)cosh(s)+sinh(s) cos(2ϕs)] .
δas˙=(κa+iΔa(s))δas+iGa(s)(δb+δb)+2κaain(s),δb˙=(γ2+iωm)δb+iGa(s)(δas+δas)+γbin,
Δa(s)=Δa2ns+1,
Ga(s)=Ga11+2ns+2ms cos(2ϕs) ,
ns=sinh(s)2,ms=cosh(s) sinh(s)=ns(ns+1) .
Sa(ω)=2 κa |ν(ω)ζ(ω)|2 ,
ν(ω)=κa+i(Δa+ω)+χ e2iϕ ,ζ(ω)=(κaiω)2+Δa2χ2 .
Sa(s)(ω)=2 κa |1+nsκa+i(Δa(s)ω)+nsκai(Δa(s)+ω) e2iϕs|2 .
e2iϕ(opt)=κa+i(Δaωm)κa2+(Δaωm)2χ(opt)=κa2+(Δaωm)2 .
e2iϕs(opt)=(κaiΔa(s))2+ωm2[κa2+(Δa(s)ωm)2][κa2+(Δa(s)+ωm)2],ns(opt)=κa2+(Δa(s)ωm)24Δa(s)ωm .
R=χκa2+Δa2,
R(opt)=κa2+(Δaωm)2κa2+Δa2 .
Rs=χsκs ,
Rs(opt)=κa2+(Δa(s)+ωm)22Δa(s) ωmκa2+(Δa(s)ωm)2 .
Aa,|ϕ=ϕ(opt), χ=χ(opt)=2κaGa2κa2+(Δaωm)2
Aa,(s)|ϕs=ϕs(opt), ns=ns(opt)=2κaGa(s)2κa2+(Δa(s)ωm)22κaGa(s)2κa2+(Δa(s)+ωm)2 .
Δa(s)=ωmΔa=κa2+2ωm22ωm ,
A±=Ga2 Sa(ωm)+Gc2 Sc(ωm)+GaGc Sa,c(ωm),
Sc(ω)=2κcκc2+(Δcω)2,Sa,c(ω)=2κa ϵ|ζ(ω)|2Re{ν(ω) e2iϕ[κcκaζ(ω)κc2+(Δcω)2κai(Δa+ω)κc+i(Δcω)χ e2iϕκci(Δc+ω),]}
a˙=Ma+iGa(δb+δb) e+2κain
a˙(s)=M(s)a(s)+iGa(s)(δb+δb) e+2κaain(s)
M=(κaiΔaχe2iϕχe2iϕκa+iΔa)M(s)=(κaiΔa(s)00κ+iΔa(s)) .
Cin=(0100)Cin(s)=(mse2iϕsns+1nsmse2iϕs) .
U=(eiϕ cosh(s)e2iϕseiϕ sinh(s)e2iϕseiϕ sinh(s)eiϕ cosh(s)) .
M=U1 M(s) U=(κaiΔa(s)(1+2ns)2imsΔa(s)e2i(ϕsϕ)2imsΔa(s)e2i(ϕsϕ)κa+iΔa(s)(1+2ns))
Ga e=Ga(s) U1e=Ga(s) (eiϕ[cosh(s)+e2iϕs sinh(s)]eiϕ[cosh(s)+e2iϕs sinh(s)]) ,
Δa=Δa(s)(1+2ns)χ e2iϕ=2imsΔa(s)e2i(ϕsϕ) ,
tan(ϕ)=sinh(s) sin(2ϕs)cosh(s)+sinh(s) cos(2ϕs) .

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