K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A 72, 043819 (2005).

[CrossRef]

M. Cerdonio, L. Conti, A. Heidmann, and M. Pinard, “Thermoelastic effects at low temperatures and quantum limits in displacement measurements,” Phys. Rev. D 63, 082003 (2001).

[CrossRef]

Y. T. Liu and K. S. Thorne, “Thermoelastic noise and homogeneous thermal noise in finite sized gravitationalwave test masses,” Phys. Rev. D 62, 122002 (2000).

[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, “Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae,” Phys. Lett. A 264, 1–10 (1999).

[CrossRef]

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]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).

[CrossRef]

J. A. Giordmaine and R. C. Miller, “Tunable Coherent Parametric Oscillation in LiNbO3 at Optical Frequencies,” Phys. Rev. Lett. 14, 973–976 (1965).

[CrossRef]

S. P. Tewari and G. S. Agarwal, “Control of phase matching and nonlinear generation in dense media by resonant fields,” Phys. Rev. Lett. 17 1811–1814 (1986).

V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, “Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae,” Phys. Lett. A 264, 1–10 (1999).

[CrossRef]

M. Cerdonio, L. Conti, A. Heidmann, and M. Pinard, “Thermoelastic effects at low temperatures and quantum limits in displacement measurements,” Phys. Rev. D 63, 082003 (2001).

[CrossRef]

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]

M. Cerdonio, L. Conti, A. Heidmann, and M. Pinard, “Thermoelastic effects at low temperatures and quantum limits in displacement measurements,” Phys. Rev. D 63, 082003 (2001).

[CrossRef]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).

[CrossRef]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).

[CrossRef]

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]

J. A. Giordmaine and R. C. Miller, “Tunable Coherent Parametric Oscillation in LiNbO3 at Optical Frequencies,” Phys. Rev. Lett. 14, 973–976 (1965).

[CrossRef]

K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A 72, 043819 (2005).

[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, “Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae,” Phys. Lett. A 264, 1–10 (1999).

[CrossRef]

K. McKenzie, M. B. Gray, S. Goβler, P. K. Lam, and D. E. McClelland, “Squeezed State Generation for Interferometric Gravitational-Wave Detection,” Class. Quant. Grav. 23, S245–S250 (2006).

K. McKenzie, M. B. Gray, S. Goβler, P. K. Lam, and D. E. McClelland, “Squeezed State Generation for Interferometric Gravitational-Wave Detection,” Class. Quant. Grav. 23, S245–S250 (2006).

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).

[CrossRef]

M. Cerdonio, L. Conti, A. Heidmann, and M. Pinard, “Thermoelastic effects at low temperatures and quantum limits in displacement measurements,” Phys. Rev. D 63, 082003 (2001).

[CrossRef]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).

[CrossRef]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).

[CrossRef]

K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A 72, 043819 (2005).

[CrossRef]

K. McKenzie, M. B. Gray, S. Goβler, P. K. Lam, and D. E. McClelland, “Squeezed State Generation for Interferometric Gravitational-Wave Detection,” Class. Quant. Grav. 23, S245–S250 (2006).

Y. T. Liu and K. S. Thorne, “Thermoelastic noise and homogeneous thermal noise in finite sized gravitationalwave test masses,” Phys. Rev. D 62, 122002 (2000).

[CrossRef]

K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A 72, 043819 (2005).

[CrossRef]

K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A 72, 043819 (2005).

[CrossRef]

K. McKenzie, M. B. Gray, S. Goβler, P. K. Lam, and D. E. McClelland, “Squeezed State Generation for Interferometric Gravitational-Wave Detection,” Class. Quant. Grav. 23, S245–S250 (2006).

K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A 72, 043819 (2005).

[CrossRef]

K. McKenzie, M. B. Gray, S. Goβler, P. K. Lam, and D. E. McClelland, “Squeezed State Generation for Interferometric Gravitational-Wave Detection,” Class. Quant. Grav. 23, S245–S250 (2006).

K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A 72, 043819 (2005).

[CrossRef]

For Example: D. F. Walls and G. J. Milburn, Quantum Optics, Springer-Verlag, Berlin, 1st ed. (1994).

J. A. Giordmaine and R. C. Miller, “Tunable Coherent Parametric Oscillation in LiNbO3 at Optical Frequencies,” Phys. Rev. Lett. 14, 973–976 (1965).

[CrossRef]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).

[CrossRef]

M. Cerdonio, L. Conti, A. Heidmann, and M. Pinard, “Thermoelastic effects at low temperatures and quantum limits in displacement measurements,” Phys. Rev. D 63, 082003 (2001).

[CrossRef]

A.E. Siegman, Lasers, University Science Books (1986).

S. P. Tewari and G. S. Agarwal, “Control of phase matching and nonlinear generation in dense media by resonant fields,” Phys. Rev. Lett. 17 1811–1814 (1986).

Y. T. Liu and K. S. Thorne, “Thermoelastic noise and homogeneous thermal noise in finite sized gravitationalwave test masses,” Phys. Rev. D 62, 122002 (2000).

[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, “Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae,” Phys. Lett. A 264, 1–10 (1999).

[CrossRef]

For Example: D. F. Walls and G. J. Milburn, Quantum Optics, Springer-Verlag, Berlin, 1st ed. (1994).

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).

[CrossRef]

A. Yariv, Optical Electonics in Modern Communications, Fifth Edition, Oxford University Press (1997).

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).

[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, “Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae,” Phys. Lett. A 264, 1–10 (1999).

[CrossRef]

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]

K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A 72, 043819 (2005).

[CrossRef]

Y. T. Liu and K. S. Thorne, “Thermoelastic noise and homogeneous thermal noise in finite sized gravitationalwave test masses,” Phys. Rev. D 62, 122002 (2000).

[CrossRef]

M. Cerdonio, L. Conti, A. Heidmann, and M. Pinard, “Thermoelastic effects at low temperatures and quantum limits in displacement measurements,” Phys. Rev. D 63, 082003 (2001).

[CrossRef]

J. A. Giordmaine and R. C. Miller, “Tunable Coherent Parametric Oscillation in LiNbO3 at Optical Frequencies,” Phys. Rev. Lett. 14, 973–976 (1965).

[CrossRef]

The SHG is a custom Diabolo model developed by Innolight GmbH.

S. P. Tewari and G. S. Agarwal, “Control of phase matching and nonlinear generation in dense media by resonant fields,” Phys. Rev. Lett. 17 1811–1814 (1986).

A.E. Siegman, Lasers, University Science Books (1986).

A. Yariv, Optical Electonics in Modern Communications, Fifth Edition, Oxford University Press (1997).

For Example: D. F. Walls and G. J. Milburn, Quantum Optics, Springer-Verlag, Berlin, 1st ed. (1994).

We define doubly resonant to be resonant at both the fundamental and harmonic frequencies.

Assuming there is no differential phase shift on reflection between the harmonic and fundamental frequencies on the mirror coatings. In general, there will be a differential phase shift on reflection on the mirror coatings and on transmission through anti-reflective (AR) coatings. In our system we experimentally determine that the sum of the differential phase shifts per round trip of the cavity is close to an integer multiple times p. When the differential phase shift is significantly large we compensate for the dispersion by inserting a dichroic AR coated BK7 substrate placed in the cavity. This substrate is angled such that the dispersion on transmission through the substrate compensates for the differential phase shift on the mirror coatings and AR coatings, see [7].

K. McKenzie, M. B. Gray, S. Goβler, P. K. Lam, and D. E. McClelland, “Squeezed State Generation for Interferometric Gravitational-Wave Detection,” Class. Quant. Grav. 23, S245–S250 (2006).