Abstract

The measurement of very small light forces has wide applications in many fields of physics. A common measurement method for small force detection is the determination of changes in the dynamic behavior of mechanical oscillators, either in amplitude or in frequency. The detection of slowly varying forces mostly requires long period oscillators, such as a torsion pendulum. We demonstrate the application of a macroscopic, low-noise, torsion balance oscillator for the detection of radiation pressure forces at the femto-Newton level. The system is “precooled” (removing excess seimic noise) to be only thermal noise limited. The demonstrated force sensitivity reaches the thermal limit.

© 2008 Optical Society of America

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References

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    [CrossRef] [PubMed]

2008 (1)

F. Mueller, S. Heugel, and L. J. Wang, Appl. Phys. Lett. 92, 044101 (2008).
[CrossRef]

2007 (2)

L. Haiberger, M. Weingran, and S. Schiller, Rev. Sci. Instrum. 78, 025101 (2007).
[CrossRef] [PubMed]

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, Phys. Rev. Lett. 99, 160801 (2007).
[CrossRef] [PubMed]

2006 (1)

D. Kleckner and D. Bouwmeester, Nature 444, 75 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

C. H. Metzger and K. Karrai, Nature 432, 1002 (2004).
[CrossRef] [PubMed]

1996 (1)

A. B. Matsko, E. A. Zubova, and S. P. Vyatchanin, Opt. Commun. 131, 107 (1996).
[CrossRef]

1991 (2)

P. Lorrain, Opt. Lasers Eng. 15, 197 (1991).
[CrossRef]

D. Rugar and P. Gruetter, Phys. Rev. Lett. 67, 699 (1991).
[CrossRef] [PubMed]

1990 (2)

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

Y. T. Chen and A. Cook, Class. Quantum Grav. 7, 1225 (1990).
[CrossRef]

1985 (1)

R. C. Ritter and G. T. Gillies, Phys. Rev. A 31, 995 (1985).
[CrossRef] [PubMed]

1964 (1)

P. G. Roll, R. Krotkov, and R. H. Dicke, Ann. Phys. (N.Y.) 26, 442 (1964).
[CrossRef]

1953 (1)

C. W. McCombie, Rep. Prog. Phys. 16, 266 (1953).
[CrossRef]

1928 (1)

H. Nyquist, Phys. Rev. 32, 110 (1928).
[CrossRef]

Ann. Phys. (N.Y.) (1)

P. G. Roll, R. Krotkov, and R. H. Dicke, Ann. Phys. (N.Y.) 26, 442 (1964).
[CrossRef]

Appl. Phys. Lett. (1)

F. Mueller, S. Heugel, and L. J. Wang, Appl. Phys. Lett. 92, 044101 (2008).
[CrossRef]

Class. Quantum Grav. (1)

Y. T. Chen and A. Cook, Class. Quantum Grav. 7, 1225 (1990).
[CrossRef]

Nature (2)

C. H. Metzger and K. Karrai, Nature 432, 1002 (2004).
[CrossRef] [PubMed]

D. Kleckner and D. Bouwmeester, Nature 444, 75 (2006).
[CrossRef] [PubMed]

Opt. Commun. (1)

A. B. Matsko, E. A. Zubova, and S. P. Vyatchanin, Opt. Commun. 131, 107 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

P. Lorrain, Opt. Lasers Eng. 15, 197 (1991).
[CrossRef]

Phys. Rev. (1)

H. Nyquist, Phys. Rev. 32, 110 (1928).
[CrossRef]

Phys. Rev. A (1)

R. C. Ritter and G. T. Gillies, Phys. Rev. A 31, 995 (1985).
[CrossRef] [PubMed]

Phys. Rev. D (1)

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

Phys. Rev. Lett. (2)

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, Phys. Rev. Lett. 99, 160801 (2007).
[CrossRef] [PubMed]

D. Rugar and P. Gruetter, Phys. Rev. Lett. 67, 699 (1991).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

C. W. McCombie, Rep. Prog. Phys. 16, 266 (1953).
[CrossRef]

Rev. Sci. Instrum. (1)

L. Haiberger, M. Weingran, and S. Schiller, Rev. Sci. Instrum. 78, 025101 (2007).
[CrossRef] [PubMed]

Other (1)

V. B. Braginsky and A. B. Manukin, Measurement of Weak Forces in Physics Experiments (U. Chicago Press, 1977).

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Figures (3)

Fig. 1
Fig. 1

(a) Experimental setup. The oscillator’s angular position is measured by pointing Laser 1 to the center of the oscillator and detecting the reflected light beam. Two capacitive feedback electrodes on the left side are used for dynamic position control. Laser 2 exerts a radiation pressure force on one arm of the balance. This force can be used for calibrating the angular deflection as well as in the high-precision force detection measurements. (b) Closed-loop feedback system enables full control over the oscillator’s dynamic behavior. The detection light beam is amplitude modulated and detected using a low-noise position detector in combination with a high-sensitivity lock-in amplifier (LIA). The digital computer control (PC) generates a real-time control signal applied to the feedback electrodes.

Fig. 2
Fig. 2

Light pressure detection. The critically damped oscillator responds to a modulated light beam of 2.5 mW in amplitude at a frequency of 0.1 Hz . The impact of the light beam is clearly visible in the temporal response of the oscillator.

Fig. 3
Fig. 3

High-sensitivity light force measurement. A 30 mHz modulated laser beam of 50 μ W in amplitude is sent to the torsion balance. In the calculated force spectral density of the total measurement (lower curve), this influence is clearly seen. For comparison, an earlier measurement is shown (black curve) when the oscillator is under the influence of a strong seismic disturbance (details in the text).

Equations (5)

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φ ̈ + 2 γ φ ̇ + ω 0 2 φ = α t h ( t ) .
P t h ( ω ) = 8 k B T I γ ω 0 4 ( ω 0 2 ω 2 ) 2 + ( 2 γ ω ) 2 .
P t h ( ω ω 0 ) = 8 k B T I γ ,
F min L 1 P t h ( ω ω 0 ) Δ f = L 1 8 k B T I γ τ 1 ,
F L = 2 P 0 c ,

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