Abstract

Cavity optoelectromechanical regenerative amplification is demonstrated. An optical cavity enhances mechanical transduction, allowing sensitive measurement even for heavy oscillators. A 27.3 MHz mechanical mode of a microtoroid was linewidth narrowed to 6.6 ± 1.4 mHz, 30 times smaller than previously achieved with radiation pressure driving in such a system. These results may have applications in areas such as ultrasensitive optomechanical mass spectroscopy.

© 2012 Optical Society of America

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    [Crossref]

2011 (5)

2010 (6)

J. Lee, W. Shen, K. Payer, T. P. Burg, and S. R. Manalis, “Toward attogram mass measurements in solution with suspended nanochannel resonators,” Nano Lett. 10, 2537–2542 (2010).
[Crossref] [PubMed]

M. Hossein-Zadeh and K. J. Vahala, “An optomechanical oscillator on a slicon chip,” IEEE J. Sel. Top. Quantum Electron. 16, 276–287 (2010).
[Crossref]

Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nat. Photonics 4, 236–242 (2010).
[Crossref]

A. Mirzaei and A. A. Abidi, “The spectrum of a noisy free-running oscillator explained by random frequency pulling,” IEEE Trans. Circuits Syst., I: Regul. Pap. 57, 642–653 (2010).
[Crossref]

K. H. Lee, T. G. McRae, G. I. Harris, J. Knittel, and W. P. Bowen, “Cooling and control of a cavity optoelectromechanical system,” Phys. Rev. Lett. 104, 123604–123607 (2010).
[Crossref] [PubMed]

T. G. McRae, K. H. Lee, G. I. Harris, J. Knittel, and W. P. Bowen, “Cavity optoelectromechanical system combining strong electrical actuation with ultrasensitive transduction,” Phys. Rev. A 82, 23825–23831 (2010).
[Crossref]

2009 (4)

M. Arndt, M. Aspelmeyer, and A. Zeilinger, “How to extend quantum experiments,” Fortschr. Phys. 57, 1153–1162 (2009).
[Crossref]

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

J. D. Teufel, T. Donner, M. A. Castellanos-Beltran, J. W. Harlow, and K. W. Lehnert, “Nanomechanical motion measured with an imprecision below that at the standard quantum limit,” Nat. Nanotechnol. 4, 820–823 (2009).
[Crossref] [PubMed]

A. K. Naik, M. S. Hanay, W. K. Hiebert, X. L. Feng, and M. L. Roukes, “A self-sustaining ultrahigh-frequency nanoelectromechanical oscillator,” Nat. Nanotechnol. 4, 445–450 (2009).
[Crossref] [PubMed]

2008 (4)

X. L. Feng, C. J. White, A. Hajimiri, and M. L. Roukes, “A self-sustaining ultrahigh-frequency nanoelectromechanical oscillator,” Nat. Nanotechnol. 3, 342–346 (2008).
[Crossref] [PubMed]

G. Anetsberger, R. Rivière, A. Schliesser, O. Arcizet, and T. J. Kippenberg, “Ultralow-dissipation optomechanical resonators on a chip,” Nat. Photonics 2, 627–633 (2008).
[Crossref]

A. Schliesser, G. Anetsberger, R. Rivière, O. Arcizet, and T. J. Kippenberg, “High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators,” New J. Phys. 10, 095015 (2008).
[Crossref]

K. Jensen, K. Kim, and A. Zettl, “An atomic-resolution nanomechanical mass sensor,” Nat. Nanotechnol. 3, 533–537 (2008).
[Crossref] [PubMed]

2007 (2)

L. Haiberger, M. Weingran, and S. Schiller, “Highly sensitive silicon crystal torque sensor operating at the thermal noise limit,” Rev. Sci. Instrum. 78, 025101 (2007).
[Crossref] [PubMed]

J. Verd, A. Uranga, G. Abadal, J. Teva, F. Torres, F. Pérez-Murano, J. Fraxedas, J. Esteve, and N. Barniol, “Monolithic mass sensor fabricated using a conventional technology with attogram resolution in air conditions,” Appl. Phys. Lett. 91, 013501 (2007).
[Crossref]

2006 (3)

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B 82, 265–273 (2006).
[Crossref]

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A 74, 23813–23827 (2006).
[Crossref]

H. Rokhsari, M. Hossein-Zadeh, A. Hajimiri, and K. J. Vahala, “Brownian noise in radiation-pressure-driven micromechanical oscillators,” Appl. Phys. Lett. 89, 261109 (2006).
[Crossref]

2005 (2)

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[Crossref] [PubMed]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95, 033901 (2005).
[Crossref] [PubMed]

2004 (2)

D. Rugar, R. Budakian, H. J. Mamin, and B. W. Chui, “Single spin detection by magnetic resonance force microscopy,” Nature 430, 329–332 (2004).
[Crossref] [PubMed]

K. L. Ekinci, Y. T. Yang, and M. L. Roukes, “Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems,” J. Appl. Phys. 95, 2682–2689 (2004).
[Crossref]

2003 (1)

W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, “Towards quantum superpositions of a mirror,” Phys. Rev. Lett. 91, 130401 (2003).
[Crossref] [PubMed]

2002 (1)

W. Zhang, R. Baskaran, and K. L. Turner, “Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor,” Sens. Actuators A, Phys. 102, 139–150 (2002).
[Crossref]

1999 (1)

M. Pinard, Y. Hadjar, and A. Heidmann, “Effective mass in quantum effects of radiation pressure,” Eur. Phys. J. D 7, 107–116 (1999).

1998 (1)

A. Cleland and M. Roukes, “A nanometre-scale mechanical electrometer,” Nature 392, 160–162 (1998).
[Crossref]

1995 (1)

1991 (1)

D. Rugar and P. Grutter, “Mechanical parametric amplification and thermomechanical noise squeezing, Phys. Rev. Lett. 67, 699–702 (1991).
[Crossref] [PubMed]

1960 (1)

W. A. Edson, “Noise in oscillators,” Proc. IRE 48, 1454–1466 (1960).
[Crossref]

1958 (1)

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
[Crossref]

1955 (1)

J. P. Gordon, H. J. Zeiger, and C. H. Townes, “The Maser–new type of microwave amplifier, frequency standard, and spectrometer,” Phys. Rev. 99, 1264–1274 (1955).
[Crossref]

Abadal, G.

J. Verd, A. Uranga, G. Abadal, J. Teva, F. Torres, F. Pérez-Murano, J. Fraxedas, J. Esteve, and N. Barniol, “Monolithic mass sensor fabricated using a conventional technology with attogram resolution in air conditions,” Appl. Phys. Lett. 91, 013501 (2007).
[Crossref]

Abidi, A. A.

A. Mirzaei and A. A. Abidi, “The spectrum of a noisy free-running oscillator explained by random frequency pulling,” IEEE Trans. Circuits Syst., I: Regul. Pap. 57, 642–653 (2010).
[Crossref]

Anetsberger, G.

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

G. Anetsberger, R. Rivière, A. Schliesser, O. Arcizet, and T. J. Kippenberg, “Ultralow-dissipation optomechanical resonators on a chip,” Nat. Photonics 2, 627–633 (2008).
[Crossref]

A. Schliesser, G. Anetsberger, R. Rivière, O. Arcizet, and T. J. Kippenberg, “High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators,” New J. Phys. 10, 095015 (2008).
[Crossref]

Arcizet, O.

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

G. Anetsberger, R. Rivière, A. Schliesser, O. Arcizet, and T. J. Kippenberg, “Ultralow-dissipation optomechanical resonators on a chip,” Nat. Photonics 2, 627–633 (2008).
[Crossref]

A. Schliesser, G. Anetsberger, R. Rivière, O. Arcizet, and T. J. Kippenberg, “High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators,” New J. Phys. 10, 095015 (2008).
[Crossref]

Arndt, M.

M. Arndt, M. Aspelmeyer, and A. Zeilinger, “How to extend quantum experiments,” Fortschr. Phys. 57, 1153–1162 (2009).
[Crossref]

Aspelmeyer, M.

M. Arndt, M. Aspelmeyer, and A. Zeilinger, “How to extend quantum experiments,” Fortschr. Phys. 57, 1153–1162 (2009).
[Crossref]

Barniol, N.

J. Verd, A. Uranga, G. Abadal, J. Teva, F. Torres, F. Pérez-Murano, J. Fraxedas, J. Esteve, and N. Barniol, “Monolithic mass sensor fabricated using a conventional technology with attogram resolution in air conditions,” Appl. Phys. Lett. 91, 013501 (2007).
[Crossref]

Baskaran, R.

W. Zhang, R. Baskaran, and K. L. Turner, “Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor,” Sens. Actuators A, Phys. 102, 139–150 (2002).
[Crossref]

Bhave, S. A.

Bouwmeester, D.

W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, “Towards quantum superpositions of a mirror,” Phys. Rev. Lett. 91, 130401 (2003).
[Crossref] [PubMed]

Bowen, W. P.

K. H. Lee, T. G. McRae, G. I. Harris, J. Knittel, and W. P. Bowen, “Cooling and control of a cavity optoelectromechanical system,” Phys. Rev. Lett. 104, 123604–123607 (2010).
[Crossref] [PubMed]

T. G. McRae, K. H. Lee, G. I. Harris, J. Knittel, and W. P. Bowen, “Cavity optoelectromechanical system combining strong electrical actuation with ultrasensitive transduction,” Phys. Rev. A 82, 23825–23831 (2010).
[Crossref]

Budakian, R.

D. Rugar, R. Budakian, H. J. Mamin, and B. W. Chui, “Single spin detection by magnetic resonance force microscopy,” Nature 430, 329–332 (2004).
[Crossref] [PubMed]

Burg, T. P.

J. Lee, W. Shen, K. Payer, T. P. Burg, and S. R. Manalis, “Toward attogram mass measurements in solution with suspended nanochannel resonators,” Nano Lett. 10, 2537–2542 (2010).
[Crossref] [PubMed]

Callegari, C.

Y. T. Yang, C. Callegari, X. L. Feng, and M. L. Roukes, “Surface adsorbate fluctuations and noise in nanoelectromechanical systems,” Nano Lett. 11, 1753–1759 (2011).
[Crossref] [PubMed]

Camacho, R.

Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nat. Photonics 4, 236–242 (2010).
[Crossref]

Carmon, T.

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95, 033901 (2005).
[Crossref] [PubMed]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[Crossref] [PubMed]

Castellanos-Beltran, M. A.

J. D. Teufel, T. Donner, M. A. Castellanos-Beltran, J. W. Harlow, and K. W. Lehnert, “Nanomechanical motion measured with an imprecision below that at the standard quantum limit,” Nat. Nanotechnol. 4, 820–823 (2009).
[Crossref] [PubMed]

Chang, D.

Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nat. Photonics 4, 236–242 (2010).
[Crossref]

Chui, B. W.

D. Rugar, R. Budakian, H. J. Mamin, and B. W. Chui, “Single spin detection by magnetic resonance force microscopy,” Nature 430, 329–332 (2004).
[Crossref] [PubMed]

Cleland, A.

A. Cleland and M. Roukes, “A nanometre-scale mechanical electrometer,” Nature 392, 160–162 (1998).
[Crossref]

Donner, T.

J. D. Teufel, T. Donner, M. A. Castellanos-Beltran, J. W. Harlow, and K. W. Lehnert, “Nanomechanical motion measured with an imprecision below that at the standard quantum limit,” Nat. Nanotechnol. 4, 820–823 (2009).
[Crossref] [PubMed]

Edson, W. A.

W. A. Edson, “Noise in oscillators,” Proc. IRE 48, 1454–1466 (1960).
[Crossref]

Eichenfield, M.

Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nat. Photonics 4, 236–242 (2010).
[Crossref]

Ekinci, K. L.

K. L. Ekinci, Y. T. Yang, and M. L. Roukes, “Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems,” J. Appl. Phys. 95, 2682–2689 (2004).
[Crossref]

Esteve, J.

J. Verd, A. Uranga, G. Abadal, J. Teva, F. Torres, F. Pérez-Murano, J. Fraxedas, J. Esteve, and N. Barniol, “Monolithic mass sensor fabricated using a conventional technology with attogram resolution in air conditions,” Appl. Phys. Lett. 91, 013501 (2007).
[Crossref]

Feng, X. L.

Y. T. Yang, C. Callegari, X. L. Feng, and M. L. Roukes, “Surface adsorbate fluctuations and noise in nanoelectromechanical systems,” Nano Lett. 11, 1753–1759 (2011).
[Crossref] [PubMed]

A. K. Naik, M. S. Hanay, W. K. Hiebert, X. L. Feng, and M. L. Roukes, “A self-sustaining ultrahigh-frequency nanoelectromechanical oscillator,” Nat. Nanotechnol. 4, 445–450 (2009).
[Crossref] [PubMed]

X. L. Feng, C. J. White, A. Hajimiri, and M. L. Roukes, “A self-sustaining ultrahigh-frequency nanoelectromechanical oscillator,” Nat. Nanotechnol. 3, 342–346 (2008).
[Crossref] [PubMed]

Fraxedas, J.

J. Verd, A. Uranga, G. Abadal, J. Teva, F. Torres, F. Pérez-Murano, J. Fraxedas, J. Esteve, and N. Barniol, “Monolithic mass sensor fabricated using a conventional technology with attogram resolution in air conditions,” Appl. Phys. Lett. 91, 013501 (2007).
[Crossref]

Gavartin, E.

E. Gavartin, P. Verlot, and T. J. Kippenberg, “A hybrid on-chip opto-nanomechanical transducer for ultra-sensitive force measurements,” arXiv:1112.0797v1 (2011).

Gordon, J. P.

J. P. Gordon, H. J. Zeiger, and C. H. Townes, “The Maser–new type of microwave amplifier, frequency standard, and spectrometer,” Phys. Rev. 99, 1264–1274 (1955).
[Crossref]

Grutter, P.

D. Rugar and P. Grutter, “Mechanical parametric amplification and thermomechanical noise squeezing, Phys. Rev. Lett. 67, 699–702 (1991).
[Crossref] [PubMed]

Hadjar, Y.

M. Pinard, Y. Hadjar, and A. Heidmann, “Effective mass in quantum effects of radiation pressure,” Eur. Phys. J. D 7, 107–116 (1999).

Haiberger, L.

L. Haiberger, M. Weingran, and S. Schiller, “Highly sensitive silicon crystal torque sensor operating at the thermal noise limit,” Rev. Sci. Instrum. 78, 025101 (2007).
[Crossref] [PubMed]

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Appl. Phys. Lett. (2)

H. Rokhsari, M. Hossein-Zadeh, A. Hajimiri, and K. J. Vahala, “Brownian noise in radiation-pressure-driven micromechanical oscillators,” Appl. Phys. Lett. 89, 261109 (2006).
[Crossref]

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Y. T. Yang, C. Callegari, X. L. Feng, and M. L. Roukes, “Surface adsorbate fluctuations and noise in nanoelectromechanical systems,” Nano Lett. 11, 1753–1759 (2011).
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J. Lee, W. Shen, K. Payer, T. P. Burg, and S. R. Manalis, “Toward attogram mass measurements in solution with suspended nanochannel resonators,” Nano Lett. 10, 2537–2542 (2010).
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Figures (4)

Fig. 1
Fig. 1 A schematic of the experiment. FPC, fiber polarization control. The Feedback Control includes filtering and control over both feedback phase and amplitude. The network analyzer was used to characterize the driven response of the system, and all other results were taken with the signal analyzer. The subplots show the motion of the mechanical mode investigated here, (a) with driving from the network analyzer, and (b) the thermal motion measured on the spectrum analyzer. Shown in light blue is a fit to the data shown in green, which determines the intrinsic decay rate Γ0 and frequency ωm. The vertical axis of each subplot is in dB against an arbitrary reference.

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Fig. 2
Fig. 2 Oscillator mechanical energy as a function of small-signal feedback gain. Green trace: measured data. Below saturation the theoretical model (blue dashed line) is given by Eq. (6). To estimate the above-threshold mechanical energy, Eq. (1) is numerically solved for sinusoidal motion with a limit applied to the magnitude of the feedback force Ffb(t). Two fitting parameters are used; one normalizes the gain such that saturation occurs at G0 = 1, and another defines the mechanical energy at which saturation occurs. Inset: A finite-element model of the mechanical mode being amplified.

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Fig. 3
Fig. 3 Blue and green traces respectively show the mechanical power spectrum with and without amplification. These were measured by sending the signal from the optical detector directly into a spectrum analyzer. Note that this mode is composed of two degenerate modes which are distinguished only by the azimuthal position of the nodes and antinodes. Only the mode with greatest overlap with the driving field is amplified, although both are present in the measurements. Inset: A near resonance spectrum with amplification and a 1 Hz resolution bandwidth (right).

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Fig. 4
Fig. 4 (a) An example of a phase noise trace. The fitted noise floor is for a linewidth Γ = 13.3 ± 3.7 mHz. A low Q mechanical resonance at 108 Hz is clearly visible, and electronic noise from the signal analyzer also appears for frequency offsets above 1 kHz. The dotted line indicates the phase noise typically achievable with optomechanical driving only [23]. (b) The measured linewidth as a function of oscillator energy. Fitting to the data (green) shows shows a dependence of Γ ∝ E osc − 0.91 ± 0.12, while theory predicts Γ ∝ E osc − 1.

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Equations (9)

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m [ x ¨ ( t ) + Γ 0 x ˙ ( t ) + ω m 2 x ( t ) ] = F f b ( t ) + F opt + F T ( t ) ,
m [ x ¨ ( t ) + Γ r x ˙ ( t ) + ω r 2 x ( t ) ] = F f b ( t ) + F T ( t ) ,
x ( ω ) = F T ( ω ) m ( ω r 2 − ω 2 + i Γ r ω ) − i m ω m Γ r G .
x ( Δ ) = 1 m ω m F T ( ω ) − 2 Δ + i Γ r ( 1 − G ) .
Γ = Γ 0 ( 1 − P opt P thresh ) ( 1 − G ) .
E osc = 1 2 π m ω m 2 ∫ − ∞ ∞ | x ( ω ) | 2 d ω = 1 2 k T ( 1 − P opt P thresh ) ( 1 − G ) ,
Γ = Γ 0 2 E T E osc .
10 ℒ ( Δ Ω ) / 10 = Γ Δ Ω − 2 ,
δ m min = 2 m mode ( E T E osc ) 1 / 2 ( Γ 2 π Q ω m ) 1 / 2 ,

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