Abstract

Traditional active laser power stabilization schemes are fundamentally limited by quantum shot noise on the in-loop photodetector. One way to overcome this limitation is to implement a nondemolition sensing scheme where laser power fluctuations are transferred to motion of a micro-oscillator, which can be sensed with a high signal-to-noise ratio. In this Letter, we analyze the power stability achievable in a nondemolition scheme limited by quantum and thermal noise. Under the assumption of realistic experimental parameters, we show that generation of a strong bright squeezed quantum state of light should be possible.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. G. M. Harry, LIGO Scientific Collaboration, Classical Quantum Gravity 27, 084006 (2010).
    [Crossref]
  2. P. Kwee, B. Willke, and K. Danzmann, Opt. Lett. 34, 2912 (2009).
    [Crossref]
  3. H. Vahlbruch, D. Wilken, M. Mehmet, and B. Willke, Phys. Rev. Lett. 121, 173601 (2018).
    [Crossref]
  4. P. Kwee, B. Willke, and K. Danzmann, Opt. Lett. 33, 1509 (2008).
    [Crossref]
  5. Y. Yamamoto, N. Imoto, and S. Machida, Phys. Rev. A 33, 3243 (1986).
    [Crossref]
  6. K. Jacobs, P. Tombesi, M. J. Collett, and D. F. Walls, Phys. Rev. A 49, 1961 (1994).
    [Crossref]
  7. S. L. Danilishin and F. Y. Khalili, Living Rev. Relativity 15, 5 (2012).
    [Crossref]
  8. C. M. Caves and B. L. Schumaker, Phys. Rev. A 31, 3068 (1985).
    [Crossref]
  9. B. L. Schumaker and C. M. Caves, Phys. Rev. A 31, 3093 (1985).
    [Crossref]
  10. H. Kimble, Y. Levin, A. Matsko, K. Thorne, and S. Vyatchanin, Phys. Rev. D 65, 022002 (2001).
    [Crossref]
  11. H. M. Wiseman and G. J. Milburn, Phys. Rev. A 49, 1350 (1994).
    [Crossref]
  12. T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
    [Crossref]
  13. P. R. Saulson, Phys. Rev. D 42, 2437 (1990).
    [Crossref]
  14. K. Yamamoto, D. Friedrich, T. Westphal, S. Goßler, K. Danzmann, K. Somiya, S. L. Danilishin, and R. Schnabel, Phys. Rev. A 81, 033849 (2010).
    [Crossref]
  15. R. Singh, G. D. Cole, J. Cripe, and T. Corbitt, Phys. Rev. Lett. 117, 213604 (2016).
    [Crossref]
  16. G. D. Cole, Proc. SPIE 8458, 845807 (2012).
    [Crossref]

2018 (1)

H. Vahlbruch, D. Wilken, M. Mehmet, and B. Willke, Phys. Rev. Lett. 121, 173601 (2018).
[Crossref]

2016 (1)

R. Singh, G. D. Cole, J. Cripe, and T. Corbitt, Phys. Rev. Lett. 117, 213604 (2016).
[Crossref]

2012 (2)

G. D. Cole, Proc. SPIE 8458, 845807 (2012).
[Crossref]

S. L. Danilishin and F. Y. Khalili, Living Rev. Relativity 15, 5 (2012).
[Crossref]

2010 (2)

G. M. Harry, LIGO Scientific Collaboration, Classical Quantum Gravity 27, 084006 (2010).
[Crossref]

K. Yamamoto, D. Friedrich, T. Westphal, S. Goßler, K. Danzmann, K. Somiya, S. L. Danilishin, and R. Schnabel, Phys. Rev. A 81, 033849 (2010).
[Crossref]

2009 (1)

2008 (1)

2006 (1)

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[Crossref]

2001 (1)

H. Kimble, Y. Levin, A. Matsko, K. Thorne, and S. Vyatchanin, Phys. Rev. D 65, 022002 (2001).
[Crossref]

1994 (2)

H. M. Wiseman and G. J. Milburn, Phys. Rev. A 49, 1350 (1994).
[Crossref]

K. Jacobs, P. Tombesi, M. J. Collett, and D. F. Walls, Phys. Rev. A 49, 1961 (1994).
[Crossref]

1990 (1)

P. R. Saulson, Phys. Rev. D 42, 2437 (1990).
[Crossref]

1986 (1)

Y. Yamamoto, N. Imoto, and S. Machida, Phys. Rev. A 33, 3243 (1986).
[Crossref]

1985 (2)

C. M. Caves and B. L. Schumaker, Phys. Rev. A 31, 3068 (1985).
[Crossref]

B. L. Schumaker and C. M. Caves, Phys. Rev. A 31, 3093 (1985).
[Crossref]

Caves, C. M.

C. M. Caves and B. L. Schumaker, Phys. Rev. A 31, 3068 (1985).
[Crossref]

B. L. Schumaker and C. M. Caves, Phys. Rev. A 31, 3093 (1985).
[Crossref]

Chen, Y.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[Crossref]

Cole, G. D.

R. Singh, G. D. Cole, J. Cripe, and T. Corbitt, Phys. Rev. Lett. 117, 213604 (2016).
[Crossref]

G. D. Cole, Proc. SPIE 8458, 845807 (2012).
[Crossref]

Collett, M. J.

K. Jacobs, P. Tombesi, M. J. Collett, and D. F. Walls, Phys. Rev. A 49, 1961 (1994).
[Crossref]

Corbitt, T.

R. Singh, G. D. Cole, J. Cripe, and T. Corbitt, Phys. Rev. Lett. 117, 213604 (2016).
[Crossref]

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[Crossref]

Cripe, J.

R. Singh, G. D. Cole, J. Cripe, and T. Corbitt, Phys. Rev. Lett. 117, 213604 (2016).
[Crossref]

Danilishin, S. L.

S. L. Danilishin and F. Y. Khalili, Living Rev. Relativity 15, 5 (2012).
[Crossref]

K. Yamamoto, D. Friedrich, T. Westphal, S. Goßler, K. Danzmann, K. Somiya, S. L. Danilishin, and R. Schnabel, Phys. Rev. A 81, 033849 (2010).
[Crossref]

Danzmann, K.

K. Yamamoto, D. Friedrich, T. Westphal, S. Goßler, K. Danzmann, K. Somiya, S. L. Danilishin, and R. Schnabel, Phys. Rev. A 81, 033849 (2010).
[Crossref]

P. Kwee, B. Willke, and K. Danzmann, Opt. Lett. 34, 2912 (2009).
[Crossref]

P. Kwee, B. Willke, and K. Danzmann, Opt. Lett. 33, 1509 (2008).
[Crossref]

Friedrich, D.

K. Yamamoto, D. Friedrich, T. Westphal, S. Goßler, K. Danzmann, K. Somiya, S. L. Danilishin, and R. Schnabel, Phys. Rev. A 81, 033849 (2010).
[Crossref]

Goßler, S.

K. Yamamoto, D. Friedrich, T. Westphal, S. Goßler, K. Danzmann, K. Somiya, S. L. Danilishin, and R. Schnabel, Phys. Rev. A 81, 033849 (2010).
[Crossref]

Harry, G. M.

G. M. Harry, LIGO Scientific Collaboration, Classical Quantum Gravity 27, 084006 (2010).
[Crossref]

Imoto, N.

Y. Yamamoto, N. Imoto, and S. Machida, Phys. Rev. A 33, 3243 (1986).
[Crossref]

Jacobs, K.

K. Jacobs, P. Tombesi, M. J. Collett, and D. F. Walls, Phys. Rev. A 49, 1961 (1994).
[Crossref]

Khalili, F.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[Crossref]

Khalili, F. Y.

S. L. Danilishin and F. Y. Khalili, Living Rev. Relativity 15, 5 (2012).
[Crossref]

Kimble, H.

H. Kimble, Y. Levin, A. Matsko, K. Thorne, and S. Vyatchanin, Phys. Rev. D 65, 022002 (2001).
[Crossref]

Kwee, P.

Levin, Y.

H. Kimble, Y. Levin, A. Matsko, K. Thorne, and S. Vyatchanin, Phys. Rev. D 65, 022002 (2001).
[Crossref]

Machida, S.

Y. Yamamoto, N. Imoto, and S. Machida, Phys. Rev. A 33, 3243 (1986).
[Crossref]

Matsko, A.

H. Kimble, Y. Levin, A. Matsko, K. Thorne, and S. Vyatchanin, Phys. Rev. D 65, 022002 (2001).
[Crossref]

Mavalvala, N.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[Crossref]

Mehmet, M.

H. Vahlbruch, D. Wilken, M. Mehmet, and B. Willke, Phys. Rev. Lett. 121, 173601 (2018).
[Crossref]

Milburn, G. J.

H. M. Wiseman and G. J. Milburn, Phys. Rev. A 49, 1350 (1994).
[Crossref]

Ottaway, D.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[Crossref]

Saulson, P. R.

P. R. Saulson, Phys. Rev. D 42, 2437 (1990).
[Crossref]

Schnabel, R.

K. Yamamoto, D. Friedrich, T. Westphal, S. Goßler, K. Danzmann, K. Somiya, S. L. Danilishin, and R. Schnabel, Phys. Rev. A 81, 033849 (2010).
[Crossref]

Schumaker, B. L.

C. M. Caves and B. L. Schumaker, Phys. Rev. A 31, 3068 (1985).
[Crossref]

B. L. Schumaker and C. M. Caves, Phys. Rev. A 31, 3093 (1985).
[Crossref]

Singh, R.

R. Singh, G. D. Cole, J. Cripe, and T. Corbitt, Phys. Rev. Lett. 117, 213604 (2016).
[Crossref]

Somiya, K.

K. Yamamoto, D. Friedrich, T. Westphal, S. Goßler, K. Danzmann, K. Somiya, S. L. Danilishin, and R. Schnabel, Phys. Rev. A 81, 033849 (2010).
[Crossref]

Thorne, K.

H. Kimble, Y. Levin, A. Matsko, K. Thorne, and S. Vyatchanin, Phys. Rev. D 65, 022002 (2001).
[Crossref]

Tombesi, P.

K. Jacobs, P. Tombesi, M. J. Collett, and D. F. Walls, Phys. Rev. A 49, 1961 (1994).
[Crossref]

Vahlbruch, H.

H. Vahlbruch, D. Wilken, M. Mehmet, and B. Willke, Phys. Rev. Lett. 121, 173601 (2018).
[Crossref]

Vyatchanin, S.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[Crossref]

H. Kimble, Y. Levin, A. Matsko, K. Thorne, and S. Vyatchanin, Phys. Rev. D 65, 022002 (2001).
[Crossref]

Walls, D. F.

K. Jacobs, P. Tombesi, M. J. Collett, and D. F. Walls, Phys. Rev. A 49, 1961 (1994).
[Crossref]

Westphal, T.

K. Yamamoto, D. Friedrich, T. Westphal, S. Goßler, K. Danzmann, K. Somiya, S. L. Danilishin, and R. Schnabel, Phys. Rev. A 81, 033849 (2010).
[Crossref]

Whitcomb, S.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[Crossref]

Wilken, D.

H. Vahlbruch, D. Wilken, M. Mehmet, and B. Willke, Phys. Rev. Lett. 121, 173601 (2018).
[Crossref]

Willke, B.

Wiseman, H. M.

H. M. Wiseman and G. J. Milburn, Phys. Rev. A 49, 1350 (1994).
[Crossref]

Yamamoto, K.

K. Yamamoto, D. Friedrich, T. Westphal, S. Goßler, K. Danzmann, K. Somiya, S. L. Danilishin, and R. Schnabel, Phys. Rev. A 81, 033849 (2010).
[Crossref]

Yamamoto, Y.

Y. Yamamoto, N. Imoto, and S. Machida, Phys. Rev. A 33, 3243 (1986).
[Crossref]

Classical Quantum Gravity (1)

G. M. Harry, LIGO Scientific Collaboration, Classical Quantum Gravity 27, 084006 (2010).
[Crossref]

Living Rev. Relativity (1)

S. L. Danilishin and F. Y. Khalili, Living Rev. Relativity 15, 5 (2012).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (7)

K. Yamamoto, D. Friedrich, T. Westphal, S. Goßler, K. Danzmann, K. Somiya, S. L. Danilishin, and R. Schnabel, Phys. Rev. A 81, 033849 (2010).
[Crossref]

C. M. Caves and B. L. Schumaker, Phys. Rev. A 31, 3068 (1985).
[Crossref]

B. L. Schumaker and C. M. Caves, Phys. Rev. A 31, 3093 (1985).
[Crossref]

Y. Yamamoto, N. Imoto, and S. Machida, Phys. Rev. A 33, 3243 (1986).
[Crossref]

K. Jacobs, P. Tombesi, M. J. Collett, and D. F. Walls, Phys. Rev. A 49, 1961 (1994).
[Crossref]

H. M. Wiseman and G. J. Milburn, Phys. Rev. A 49, 1350 (1994).
[Crossref]

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[Crossref]

Phys. Rev. D (2)

P. R. Saulson, Phys. Rev. D 42, 2437 (1990).
[Crossref]

H. Kimble, Y. Levin, A. Matsko, K. Thorne, and S. Vyatchanin, Phys. Rev. D 65, 022002 (2001).
[Crossref]

Phys. Rev. Lett. (2)

R. Singh, G. D. Cole, J. Cripe, and T. Corbitt, Phys. Rev. Lett. 117, 213604 (2016).
[Crossref]

H. Vahlbruch, D. Wilken, M. Mehmet, and B. Willke, Phys. Rev. Lett. 121, 173601 (2018).
[Crossref]

Proc. SPIE (1)

G. D. Cole, Proc. SPIE 8458, 845807 (2012).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1. Schematic of the stabilization scheme via radiation pressure. Power fluctuations of a strong transfer beam are transferred to motion of a micro-oscillator mirror. The micro-oscillator’s position is sensed via a Michelson interferometer with a balanced homodyne readout and a weak sensing beam. The feedback signal is amplified by a gain $\epsilon$. The convention adopted as the positive displacement direction $\hat x$ is shown by the arrow on top of the oscillator.
Fig. 2.
Fig. 2. ASD of $S_{{\rm cc}}^{\hat o}$ (upper plot) and $S_{{\rm ss}}^{\hat o}$ (lower plot) calculated for different amplification factors $\epsilon$ and for ${\bar P _{\rm t}} = 1\;{\rm W}$ and ${\bar P _{\rm s}} = 0.4\;{\rm mW}$. The ASD of a coherent state is displayed by the dashed yellow line as a reference.
Fig. 3.
Fig. 3. ASD of ${{\rm RPN}_{{\rm ool,q}}}$ for different relative power noise in the transfer and sensing beams (${{\rm RPN}_{{\rm f,s}}}$) and different sensing beam powers. For all curves, ${\bar P _{\rm t}} = 1\;{\rm W}$ and $| \epsilon |{= 10^3}$. The transfer beam relative shot noise (RSN) is depicted by the dashed yellow curve as reference.
Fig. 4.
Fig. 4. ASD of the total ${{\rm RPN}_{{\rm ool}}}$ (red curve) for ${\bar P _{\rm t}} = 4\;{\rm W}$, ${\bar P _{\rm s}} = 37\;{\rm mW}$, ${{\rm RPN}_{{\rm f,s}}}{= 10^{- 8}}\;{{\rm Hz}^{- 1/2}}$, $T = 4\;{\rm K}$, and $| \epsilon |{= 10^3}$. The transfer beam relative shot noise is shown by the dashed yellow curve, and the relative shot noise of 50 mW (stability achieved with the traditional scheme) is shown by the dashed blue curve.

Equations (15)

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a ^ c ( Ω ) = a ^ ω 0 + Ω + a ^ ω 0 Ω 2 a n d a ^ s ( Ω ) = a ^ ω 0 + Ω a ^ ω 0 Ω i 2 ,
χ m ( Ω ) = 1 m Ω 2 + m Ω 0 2 ( 1 + i ϕ ) ,
x ^ = χ m ( α ( s ^ c v ^ c ) + β t ^ c ) ,
α = 2 P ¯ s ω 0 / c a n d β = 8 P ¯ t ω 0 / c ,
h ^ s = v ^ s α x ^ / = v ^ s + K α ( s ^ c v ^ c ) K α K β t ^ c ,
t ^ c = f ^ c + ϵ ( v ^ s + K α ( s ^ c v ^ c ) ) 1 + ϵ K α K β a n d t ^ s = f ^ s .
o ^ c = t ^ c a n d o ^ s = t ^ s β x ^ / ,
o ^ c = f ^ c ϵ v ^ s + ϵ K α ( s ^ c v ^ c ) 1 + ϵ K α K β ,
o ^ s = f ^ s K β f ^ c ϵ K β v ^ s K α K β ( s ^ c v ^ c ) 1 + ϵ K α K β .
S c c o ^ = S c c f ^ + | ϵ | 2 + | ϵ K α | 2 ( S c c s ^ + 1 ) | 1 + ϵ K α K β | 2 ,
S s s o ^ = S s s f ^ + | K β | 2 ( S c c f ^ + | ϵ | 2 ) + | K α K β | ( S c c s ^ + 1 ) | 1 + ϵ K α K β | 2 .
S c c o ^ S s s o ^ | S c s o ^ | 2 = | K α K β | 1 + 2 | K α K β 1 | + 2 > 1 .
R P N j = δ P j P ¯ j = 2 ω 0 S c c j ^ P ¯ j .
x t n 2 ( Ω ) = 4 k B T Ω 0 2 m Ω Q [ ( Ω 0 2 Ω 2 ) 2 + Ω 0 4 / Q 2 ] ,
R P N o o l , t n = c Ω 0 P ¯ t k B T m Q Ω .