Abstract

We demonstrate simultaneous center-of-mass cooling of two coupled oscillators, consisting of a microsphere-cantilever and a tapered optical fiber. Excitation of a whispering gallery mode (WGM) of the microsphere, via the evanescent field of the taper, provides a transduction signal that continuously monitors the relative motion between these two microgram objects with a sensitivity of 3 pm. The cavity enhanced optical dipole force is used to provide feedback damping on the motion of the micron-diameter taper, whereas a piezo stack is used to damp the motion of the much larger (up to 180 μm in diameter), heavier (up to 1.5 × 10−7 kg) and stiffer microsphere-cantilever. In each feedback scheme multiple mechanical modes of each oscillator can be cooled, and mode temperatures below 10 K are reached for the dominant mode, consistent with limits determined by the measurement noise of our system. This represents stabilization on the picometer level and is the first demonstration of using WGM resonances to cool the mechanical modes of both the WGM resonator and its coupling waveguide.

© 2016 Optical Society of America

1. Introduction

Optomechanical devices on the nano- and microscale are important tools, both for exploring fundamental quantum physics, and for technological applications. These systems, in which mechanical motion is controlled by light, can be used as exquisitely sensitive force [1–3], position [4] or mass [5, 6] sensors.

An important class of optomechanical systems exploit high optical quality factor whispering gallery mode (WGM) resonances (Qopt > 108) in objects such as dielectric spheres or toroids. High-Qopt WGM resonators [7–9] have been used for microwave-to-optical conversion [10,11], optical storage [12], frequency comb creation [13], and single-molecule sensing in both air and liquids [14]. Strong optomechanical coupling can be achieved using the interaction between the optical WGM and internal mechanical modes [15], which has been used to cool the radial breathing modes of a toroid to the ground state in a sideband-resolved regime [16]. Unlike schemes which use optical forces such as radiation pressure to cool a cavity mirror or an object inside a cavity [17, 18], WGM resonances offer the ability to cool and manipulate the center-of-mass (c.o.m.) motion of external objects placed in the evanescent field of the WGM cavity [2, 19].

Many WGM experiments involve excitation using a tapered optical fiber. This form of coupling is prone to modulation due to the mechanical modes of the waveguide and coupling distance drifts. This extraneous noise is problematic for high-bandwidth sensor development [20] and is present in many types of optomechanical systems [21]. Stabilization of the coupling junction has so far been limited to seismic bandwidths [22].

The use of WGMs to cool and manipulate the external c.o.m. motion of the cavity that supports them has not been explored. An example of such a scheme has been proposed which utilizes narrow WGM resonances to cool the WGM cavity in a similar way to the Doppler cooling of atoms [23]. Cooling the c.o.m. of macroscopic objects is attractive for developing ultrasensitive closed-loop force sensors and exploration of quantum physics at large mass scales [24,25]. Recently, the mechanism for transducing the c.o.m. motion of a silica microsphere-cavity on the end of a silica pendulum (analogous to our system) has been observed and studied using light coupled into a WGM from a tapered optical fiber [26]. This high resolution transduction at the taper-microsphere junction is dependent on coupling distance and detuning, and is seen as an important first step for implementation of active feedback cooling of either the microsphere resonator or the tapered fiber. Simultaneous damping of both these objects is an attractive feature for inertial sensing, as the taper stabilization minimizes drift, and damping of the microsphere-cantilever can extend the sensing range and decrease integration times [27].

In this article we use this transduction provided by a WGM of a microsphere-cantilever to feedback-cool the c.o.m. of the microsphere-cantilever and the tapered fiber to the noise floor. Light is coupled into the WGM via the tapered optical fiber, and its motion is feedback-cooled using the optical dipole force (effective mode mass ≈ 1.4 μg). Simultaneously, a piezoelectric stack (PZT) attached to the heavier and stiffer microsphere-cantilever allows us to damp its motion as well (effective mode mass ≈ 20 μg). We demonstrate cooling of many mechanical modes of both mechanical oscillators.

2. Transduction of thermal motion

To demonstrate c.o.m. cooling using WGMs we fabricate two oscillators from tapered optical fiber. The first oscillator is a dielectric microsphere on a cantilever, fabricated by melting the end of a fiber with a focused CO2 laser, which can produce microspheres 40 μm – 200 μm in diameter, see for example Fig. 1(a). A microsphere with a diameter of 177 μm is selected, which remains attached to the fiber stem 120 μm in diameter and 5.6 mm long. The second oscillator consists of the tapered fiber which couples light into WGMs of the microsphere. The taper is produced in the standard way by pulling an optical fiber while it is heated, to create a 1 μm waist. In order to excite a WGM resonance of the microsphere, laser light is coupled into the tapered fiber which is brought within close proximity (less than 1 μm) to the surface of the microsphere (Figs. 1(a) and 1(b)). The laser frequency is scanned to locate a resonance (Fig. 1(c)). Typically, an upper limit of 80% of the light propagating through the fiber is coupled into a WGM. The remaining 20% loss is due to non-resonant scattering from the fiber.

 figure: Fig. 1

Fig. 1 (a) A microscope image of a typical microsphere-cantilever. (b) Artist’s impression of the microsphere-cantilever, which is brought close to, but never touches, the tapered optical fiber underneath it. The evanescent fields of the WGM and tapered fiber are illustrated. (c) Monitoring the transmission t through the taper as the laser frequency is scanned reveals a WGM resonance (black), fitted with a Lorentzian function (blue) with a FWHM of 6.8 MHz.

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The optical layout is shown in Fig. 2. The tapered optical fiber is placed directly below the microsphere-cantilever and the system is within a vacuum chamber. We use a weak beam (≈ 70 μW) propagating through the tapered fiber to measure the separation, d, between the taper and the microsphere, which we call the transduction beam. The transduction results from changes in the coupling efficiency due to fluctuations of the coupling gap between the taper and microsphere, which is seen as a change in the transmission through the fiber. A strong beam (≈ 300 μW) counterpropagates through the same fiber, and is used to control the position of the taper via the cavity enhanced optical dipole force (CEODF) [28] between it and the microsphere. The strong beam is locked to the center of the WGM using Pound-Drever-Hall (PDH) locking or via thermal self locking [29] when a large modulation of the light intensity to control the CEODF is required which destabilizes the PDH. The frequency of the transduction beam can be tuned with respect to the strong beam using acousto-optic modulators (AOM 1&2). The transmitted light is detected on a photodetector (PD 2) and the power spectral density (PSD) of the fluctuation of the transmitted light is used to extract the mechanical motion of both the microsphere-cantilever and the tapered fiber. Reducing the pressure from atmospheric to 1 mbar enhances the mechanical quality factor Qm of the taper by over a factor of 30, whereas Qm for the much more massive microsphere-cantilever only increases by a factor of 1.2 over this range. Using this setup, we find that the fundamental c.o.m. mode of the microsphere-cantilever is at approximately 2.8 kHz, while a number of taper modes are observed between 0.3 kHz – 15 kHz, with prominent higher order peaks found between 3.8 kHz – 8 kHz due to their large mass participation factors. The modes are experimentally distinguished by resonantly driving either the taper or the microsphere-cantilever, with further evidence provided by modeling the system using the finite element modeling package COMSOL. The full PSD is presented in Fig. 3.

 figure: Fig. 2

Fig. 2 A schematic of the transduction and feedback system. A 1064 nm Nd:YVO4 laser with an intracavity electro-optic modulator (EOM) is tuned to excite the WGM. A PDH locking scheme is implemented, with sidebands created using an RF signal applied to the EOM. The light is split into a strong beam (blue), and a weak, red-detuned, transduction beam (red) that counterpropagate along the tapered optical fiber with fixed detuning. Feedback cooling is achieved by amplifying (increasing the gain, g) and differentiating the transduction signal from photodiode PD 2, which is sent to a piezo stack (PZT) supporting the microsphere-cantilever, and / or used to modulate the locking beam intensity using AOM 2.

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 figure: Fig. 3

Fig. 3 The full PSD from the transduction signal shows multiple mechanical modes belonging to the microsphere-cantilever or the tapered fibre which are identified by resonantly driving either oscillator. The predicted mode-shapes are shown as inset diagrams.

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Optimal feedback cooling requires maximizing the transduction signal τ above noise. This signal varies with the taper-microsphere separation, d, and the detuning from the WGM resonance. We determine the optimal coupling distance by changing d to maximize the amplitude of the detected mechanical motion above the noise floor, as shown in Fig. 4(a). The peak of this motion is defined as τ, and the optimization of τ with d is shown in Fig. 4(b). The optimum separation was found to be 150 nm, which corresponds to the distance at which the maximum power is coupled into the WGM. These results are in very good agreement with recent work [26], where the authors show a maximum in transduction at the critical coupling distance. Previous studies revealed that red-detuning the transduction beam from resonance provided the strongest transduction [26], which we verified for this system by measuring the peak amplitude relative to the background level as the laser is tuned in frequency across the WGM [30]. This detuning sign-dependence indicates that both dispersive and dissipative changes in the coupling are important. Our transduction sensitivity can detect displacements as small as 3 pm which was confirmed by calibration with the supporting PZT stack.

 figure: Fig. 4

Fig. 4 (a) The FFT of the transduction signal, showing the motion of the microsphere-cantilever with d = 0.42 μm, 0.18 μm, and 0.03 μm, illustrating the change in transduction, defined as the peak height above the background level. The FFT is normalized with respect to the maximum measured peak height. (b) The effect of the coupling distance, d, on the power coupled into the WGM, Pc, normalized to the input power propagating through the taper (blue), fitted with the on-resonance transmission relationship from [28]. Also shown is the transduction, τ, of the fundamental mechanical mode of a microsphere-cantilever (black) when the transduction beam is red-detuned by 20 MHz using a WGM with 40 MHz FWHM, fitted using reference [26].

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3. Active feedback cooling

We can cool both mechanical oscillators, individually or simultaneously. We perform active feedback cooling of the tapered fiber motion using the CEODF, first to demonstrate that optically cooling a micron sized object is achievable, and second, to show stabilization of the coupling junction through reducing the mechanical motion of the taper itself. This type of stabilization differs from that reported in reference [22] which prevents low frequency drifts (< 20 Hz) in coupling distance. Modulation of the CEODF can cool the taper modes, but cannot efficiently actuate the heavier microsphere-cantilever. This is because the effective motional mass is over an order of magnitude lower for the taper modes (≈ 1.4 μg) compared to the microsphere-cantilever (≈ 20 μg). The transduction signal at the taper frequency is amplified and differentiated to provide a velocity dependent damping term that is used to modulate the power of the strong beam. The arising CEODF is attractive and given by [28]:

Fo(d)=8ψχtVtγe(0)Qopt2PcΘ02nt2Vs×eψd(eψd+(γe(0)Qopt/Θ0))3,
where Vs and Vt are the effective mode volumes of the microsphere and taper respectively, n = 1.54 is the refractive index of silica, χt = 0.8 is the effective susceptibility of the taper, γe(0) is the extrinsic (taper waveguide to WGM resonator) coupling rate at d = 0, ψ is the decay constant, Θ0 is the WGM resonance frequency in rad s−1 and Pc is the power coupled into the WGM. We extrapolate γe(0) = 1.8 × 1010 rad s−1 and ψ = 1.4 × 107 m for a WGM resonance with an optical Q-factor of 6.1 × 105, following the procedure in [28]. The force between the taper and microsphere is predicted to be 28 pN when using 100 μW of light coupled into a WGM supported by a 100 μm diameter microsphere, at the optimum coupling separation.

In the presence of feedback the PSD of the mechanical motion becomes:

Sfb(ω)=2Γ0kBT0Meff1(ω02ω2)2+(1+g)2Γ02ω2,
where ω is the observed mechanical frequency, ω0 is the natural mechanical frequency, Γ0 is the mechanical damping factor, Meff is the effective mass of the resonator mode, T0 is the undamped temperature, and g is the feedback gain. The value of g is proportional to the feedback signal which is differentiated in time to provide velocity damping. This feedback signal modulates the laser power which changes the power coupled to the WGM, Pc, in Eq. 1. When active feedback is applied, the mechanical motion is equivalent to that of an oscillator with a higher damping factor Γfb = (1 + g0, and a lower temperature, Tfb, where Tfb = (1 + g)−1T0.

In Fig. 5 is displayed a plot of the recorded PSD of two taper modes at 5.50 kHz (t1) and 6.88 kHz (t2), for different values of the feedback gain gt1, gt2. The feedback is onto the strong beam intensity, which modulates the CEODF. The modes are simultaneously cooled to 8 K and 85 K, respectively, at a pressure of 0.5 mbar. Taper mode t1 has a different feedback phase relationship to t2, leading to different complex feedback gains gt1, gt2 for each mode, so both cannot be simultaneously cooled efficiently with the same signal.

 figure: Fig. 5

Fig. 5 Simultaneous cavity enhanced optical dipole force cooling of two mechanical modes of the tapered optical fiber, obtained at a pressure of 0.5 mbar. Representational mode shapes are shown. Each mode temperature is defined as Tt1, Tt2, at varying gain, gt1, gt2. Curves are fitted using Eq. 2 to infer the mode temperatures, and the values of Tt1, t2 are found with less than 10% uncertainty. The mechanical quality factor of each mode is Qm1 = 380 and Qm2 = 510.

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The second mechanical oscillator is the microsphere-cantilever. The large effective mass of this simple structure is a promising candidate for ultrasensitive acceleration detection, whose resolution can be quantified by its thermal noise equivalent acceleration ath=4kBTω0MeffQm. It is interesting to note that for these massive microsphere-cantilevers Qm is only weakly effected by lowering the pressure, allowing ambient operation. The value of ath is unaffected by feedback cooling, as the ratio TQm remains fixed. However, following the work of [31], the use of periodic quiescence feedback cooling could offer an advantage for improving signal-to-noise ratios for the measurement of classical impulse forces.

To feedback cool the fundamental c.o.m. motion of the microsphere-cantilever we again use the transduction signal but apply the amplified and differentiated signal to a PZT supporting the clamped end of the microsphere-cantilever. The motion of the fundamental frequency at 2.80 kHz (c1), as well as the second eigenfrequency at 17.73 kHz (c2) can be detected, and in Fig. 6 we show the PSD for these modes as we apply feedback cooling. Cooled mode temperatures of Tc1 = 9 K and Tc2 = 108 K are reached for the fundamental mechanical frequency and the second eigenfrequency at the maximum gain, at atmospheric pressure.

 figure: Fig. 6

Fig. 6 PZT feedback cooling of the fundamental mode of the microsphere-cantilever with Qm1 = 370, reaching Tc1 at varying feedback gains gc1. The second mechanical eigenfrequency at 17.73 kHz, with Qm2 = 640, is simultaneously cooled to Tc2 = 108 K. Mechanical mode shapes are shown as inset diagrams. Data was taken at atmospheric pressure, with curves fitted using Eq. 2 to infer the mode temperatures Tc1,c2, with uncertainties of less than 10%.

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For both the optical cooling of the taper modes, and the PZT cooling of the microsphere-cantilever, we reach close to the cooling limit, as set by noise from electronics, photodetectors and laser noise. We note that the predicted lowest mode temperature is set by Tmin=kω0T0SdetkBQm, where k is the spring constant and Sdet is the detection noise (≈ 2 × 10−26 m2rad−1s). We place a lower bound of Tt1 ≈ 8 K for the cooling of the taper mode at ω0/2π = 5.50 kHz (k = 1.7 Nm−1, Qm = 380), and Tc1 ≈ 11 K for the microsphere-cantilever mode at ω0/2π = 2.80 kHz (k = 6.3 Nm−1, Qm = 370). The second mechanical eigenfrequency of the cantilever is cooled close to its respective limit of Tc2 ≈ 80 K, representing effective broadband cooling for this particular oscillator.

By using a different microsphere-cantilever, with similar dimensions, but a lower mechanical Qm of 280 and a higher electronic noise floor, we show the effect of squashing [31,32] through high feedback gain in Fig. 7(b). Under these conditions, increasing the gain beyond the cooling limit pushes the measured thermal noise spectra below the measurement noise. The feedback loop counteracts intensity fluctuations in the light field, which heats the actual cantilever motion as noise is imprinted on the oscillator. Calculation of the mode temperature therefore requires a modified PSD function [31, 32]:

Smod(ω)=Sfb(ω)+Sdet(ω02ω2)2+Γ02ω2(ω02ω2)2+(1+g)2Γ02ω2,
where Sfb is defined in Eq. 2. The effective mode temperature for high gain was inferred using Tmod=T01+g+g21+gkω0Sdet4kBQm, showing heating of the microsphere-cantilever motion at large values of g.

 figure: Fig. 7

Fig. 7 PZT cooling of a microsphere-cantilever with a lower Qm = 280 than in Fig. 6 and higher noise floor, showing squashing with large feedback gain, gc. The mechanical mode is shown as an inset. Data was taken at atmospheric pressure, with curves fitted using Eq. 2 and Eq. 3 to infer the mode temperatures, with less than 10% uncertainty unless stated.

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Ultimately, for microsphere-cantilevers of this size and mechanical Qm, improving the cooling limit can only be achieved by lowering the noise floor of our system, and optimizing the displacement resolution of the transduction by using narrower WGMs.

Finally, we show simultaneous operation of both feedback cooling schemes. The performance for simultaneous cooling of the taper mode at 5.5 kHz (Fig. 5) and the microsphere-cantilever mode at 2.8 kHz (Fig. 6) is not as efficient as the cooling of each mode separately. This occurs because the bandwidth of our feedback amplifiers is not narrow enough to isolate only one mechanical mode. This leads to crosstalk in the feedback signals sent to the PZT and for laser power modulation. Significant improvements in performance are possible by employing narrower filters that would completely isolate each mode. Instead, a different microsphere-cantilever and taper system is selected where the mechanical modes are less than 250 Hz apart in frequency, and we remove any filters from the feedback scheme. We choose this system to demonstrate that the same transduction signal can be used to cool two separate mechanical oscillators when the elimination of cross-talk by using filters is not possible. The PSD of this system is presented in Fig. 8(a). Fitting with Eq. 2 can not be reliably applied at high gain, as the mechanical damping factor and the effective mode temperature no longer obey (g+1)=ΓfbΓ0=T0Tfb. This is due to the interplay between the feedback schemes which rely on the transduction signal that measures relative displacement changes between these two seperate oscillators. Instead, we infer the cooled mode temperatures by integrating the area, and show cooling of both oscillators to less than 70 K. Such a coupled system requires further investigation, but using experimental data shown in Fig. 8(b) it is observed that each individual feedback scheme has an effect on the apparent mechanical damping factor and center frequency of the other oscillator.

 figure: Fig. 8

Fig. 8 (a) Simultaneous cooling of a taper mode at Tt and the microsphere-cantilever mode at Tc using both the PZT and the CEODF, performed at atmospheric pressure. Mode temperatures are approximated by integrating the area under the respective peaks. (b) Cooling with only the CEODF or the PZT scheme, each optimized for the taper mode and cantilever mode respectively, can influence the transduced PSD of the other oscillator.

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4. Conclusion

In conclusion, we have shown c.o.m. feedback cooling of two micron-scale, microgram, coupled mechanical oscillators using a WGM resonance. Mechanical modes belonging to the microsphere-cantilever and the tapered optical fiber used to excite this WGM can be individually cooled to below 10 K, representing position stabilization on the picometer scale. The mechanical modes of the fiber can be troublesome for any hybrid WGM system using tapered fiber coupling [20], and to our knowledge, direct cooling of these modes has not previously been demonstrated. Both oscillators can be cooled simultaneously, stabilizing the coupling distance, which enhances the potential to use the cooled system for ultraprecise closed-loop force sensing. Currently, our cooling scheme is limited by detection noise and the low mechanical Qm of the oscillators. However, the ability to cool the c.o.m. motion of objects within this intermediate size and mass scale has not been fully investigated, and is attractive for creating macroscopic quantum objects. By stiffening the tapered fiber, or coupling light using a prism, the cavity enhanced optical dipole force could be used to cool the c.o.m. motion of a microsphere 10’s μm in size, which could then be unclamped, i.e. levitated. Other cooling schemes for levitated particles, such as cavity or feedback cooling, would not work for such large objects. We note that when the laser input is locked to the WGM the transduction is purely dissipative and could be used for dissipative cooling of the microsphere taper system. Such dissipative cooling can in principle lead to ground state cooling even in the unresolved sideband regime [33, 34].

References and links

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References

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  1. A. A. Geraci, S. B. Papp, and J. Kitching, “Short-range force detection using optically cooled levitated microspheres,” Phys. Rev. Lett. 105, 101101 (2010).
    [Crossref]
  2. D. J. Wilson, V. Sudhir, N. Piro, R. Schilling, A. Ghadimi, and T. J. Kippenberg, “Measurement-based control of a mechanical oscillator at its thermal decoherence rate,” Nature 524, 325–329 (2015).
    [Crossref]
  3. G. Ranjit, D. P. Atherton, J. H. Stutz, M. Cunningham, and A. A. Geraci, “Attonewton force detection using microspheres in a dual-beam optical trap in high vacuum,” Phys. Rev. A 91, 051805 (2015)
    [Crossref]
  4. O. Arcizet, P. -F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. -M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, “High sensitivity optical monitoring of a micromechanical resonator with a quantum limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006)
    [Crossref]
  5. J. -J. Li and K. -D. Zhu, “Nonlinear optical mass sensor with an optomechanical microresonator,” Appl. Phys. Lett. 101, 141905 (2012)
    [Crossref]
  6. F. Liu, S. Alaie, Z. C. Leseman, and M. Hossein-Zadeh, “Sub-pg mass sensing and measurement with an optomechanical oscillator,” Opt. Express 21(17), 19555–19567 (2013)
    [Crossref]
  7. L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering gallery mode resonances observed in fused silica microspheres,” Europhys. Lett. 23(5), 327–334 (1993).
    [Crossref]
  8. D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, “High-Q measurements of fused silica microspheres in the near infrared,” Opt. Lett. 23(4), 247–249 (1998).
    [Crossref]
  9. M. Pöllinger, D. O’Shea, F. Warken, and A. Rauschenbeutel, “Ultrahigh-Q tunable whispering-gallery-mode microresonator,” Phys. Rev. Lett. 103, 053901 (2009).
    [Crossref] [PubMed]
  10. V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Whispering-gallery-modes electro-optic modulator and photonic microwave receiver,” J. Opt. Soc. Am. B 20(2), 333–342 (2003).
    [Crossref]
  11. D. V. Strekalov, H. G. L. Schwefel, A. A. Savchenkov, A. B. Matsko, L. J. Wang, and N. Yu, “Microwave whispering-gallery mode resonator for efficient optical upconversion,” Phys. Rev. A. 80, 033810 (2009).
    [Crossref]
  12. V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
    [Crossref]
  13. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008)..
    [Crossref]
  14. F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
    [Crossref]
  15. A. Schliesser and M. Aspelmeyer, “Cavity optomechanics with whispering-gallery-mode microresonators,” in Cavity Optomechanics, M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, eds. (SpringerBerlin Heidelberg, 2014).
  16. A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4, 415–419 (2008).
    [Crossref]
  17. D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444, 75–78 (2006).
    [Crossref]
  18. T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
    [Crossref]
  19. Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
    [Crossref] [PubMed]
  20. A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nature Photonics,  6, 768–772 (2012).
    [Crossref]
  21. O. Basarir, S. Bramhavar, and K. L. Ekinci, “Near-field optical transducer for nanomechanical resonators,’ Appl. Phys. Lett. 97, 253114 (2010).
    [Crossref]
  22. J. H. Chow, M. A. Taylor, T. T-Y. Lam, J. Knittel, J. D. Sawtell-Rickson, D. A. Shaddock, M. B. Gray, D. E. McClelland, and W. P. Bowen, “Critical coupling control of a microresonator by laser amplitude modulation,” Opt. Express 20(11), 12622–12630 (2012).
    [Crossref] [PubMed]
  23. P. Barker, “Doppler cooling a microsphere,” Phys. Rev. Lett. 105, 073002 (2010).
    [Crossref] [PubMed]
  24. Y. Chen, “Macroscopic quantum mechanics: theory and experimental concepts of optomechanics,” J. Phys. B. Atomic Mol. Opt. Phys. 46, 104001 (2013).
    [Crossref]
  25. M. Arndt and K. Hornberger, “Testing the limits of quantum mechanical superpositions,” Nat. Phys. 10, 271–277 (2014).
    [Crossref]
  26. R. Madugani, Y. Yang, J. M. Ward, V.H. Le, and S. Nic Chormaic, “Optomechanical transduction and characterization of a silica microsphere pendulum via evanescent light,” Appl. Phys. Lett. 106, 241101 (2015).
    [Crossref]
  27. E. Gavartin, P. Verlot, and T. J. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7, 509–514 (2012).
    [Crossref] [PubMed]
  28. M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416–422 (2007).
    [Crossref]
  29. T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behaviour and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004).
    [Crossref] [PubMed]
  30. Y. L. Li, J. Millen, and P. F. Barker, “Cooling the centre-of-mass motion of a silica microsphere,” Proc. SPIE 9164, 916404 (2014).
    [Crossref]
  31. M. Hosseini, G. Guccione, H. J. Slatyer, B. C. Buchler, and P. Koy Lam, “Multimode laser cooling and ultra-high sensitivity force sensing with nanowires,” Nat. Commun. 5, 4663 (2014).
    [Crossref] [PubMed]
  32. M. Poggio, C. L. Degen, H. J. Mamin, and D. Rugar, “Feedback cooling of a cantilever’s fundamental mode below 5 mK,” Phys. Rev. Lett. 99, 017201 (2007).
    [Crossref]
  33. F. Elste, S. M. Girvin, and A. A. Clerk, “Quantum noise interference and backaction cooling in cavity nanomechanics,” Phys. Rev. Lett. 102, 207209 (2009).
    [Crossref] [PubMed]
  34. M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103, 223901 (2009).
    [Crossref]

2015 (3)

D. J. Wilson, V. Sudhir, N. Piro, R. Schilling, A. Ghadimi, and T. J. Kippenberg, “Measurement-based control of a mechanical oscillator at its thermal decoherence rate,” Nature 524, 325–329 (2015).
[Crossref]

G. Ranjit, D. P. Atherton, J. H. Stutz, M. Cunningham, and A. A. Geraci, “Attonewton force detection using microspheres in a dual-beam optical trap in high vacuum,” Phys. Rev. A 91, 051805 (2015)
[Crossref]

R. Madugani, Y. Yang, J. M. Ward, V.H. Le, and S. Nic Chormaic, “Optomechanical transduction and characterization of a silica microsphere pendulum via evanescent light,” Appl. Phys. Lett. 106, 241101 (2015).
[Crossref]

2014 (3)

M. Arndt and K. Hornberger, “Testing the limits of quantum mechanical superpositions,” Nat. Phys. 10, 271–277 (2014).
[Crossref]

Y. L. Li, J. Millen, and P. F. Barker, “Cooling the centre-of-mass motion of a silica microsphere,” Proc. SPIE 9164, 916404 (2014).
[Crossref]

M. Hosseini, G. Guccione, H. J. Slatyer, B. C. Buchler, and P. Koy Lam, “Multimode laser cooling and ultra-high sensitivity force sensing with nanowires,” Nat. Commun. 5, 4663 (2014).
[Crossref] [PubMed]

2013 (2)

Y. Chen, “Macroscopic quantum mechanics: theory and experimental concepts of optomechanics,” J. Phys. B. Atomic Mol. Opt. Phys. 46, 104001 (2013).
[Crossref]

F. Liu, S. Alaie, Z. C. Leseman, and M. Hossein-Zadeh, “Sub-pg mass sensing and measurement with an optomechanical oscillator,” Opt. Express 21(17), 19555–19567 (2013)
[Crossref]

2012 (4)

J. -J. Li and K. -D. Zhu, “Nonlinear optical mass sensor with an optomechanical microresonator,” Appl. Phys. Lett. 101, 141905 (2012)
[Crossref]

E. Gavartin, P. Verlot, and T. J. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7, 509–514 (2012).
[Crossref] [PubMed]

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nature Photonics,  6, 768–772 (2012).
[Crossref]

J. H. Chow, M. A. Taylor, T. T-Y. Lam, J. Knittel, J. D. Sawtell-Rickson, D. A. Shaddock, M. B. Gray, D. E. McClelland, and W. P. Bowen, “Critical coupling control of a microresonator by laser amplitude modulation,” Opt. Express 20(11), 12622–12630 (2012).
[Crossref] [PubMed]

2011 (1)

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
[Crossref]

2010 (3)

A. A. Geraci, S. B. Papp, and J. Kitching, “Short-range force detection using optically cooled levitated microspheres,” Phys. Rev. Lett. 105, 101101 (2010).
[Crossref]

P. Barker, “Doppler cooling a microsphere,” Phys. Rev. Lett. 105, 073002 (2010).
[Crossref] [PubMed]

O. Basarir, S. Bramhavar, and K. L. Ekinci, “Near-field optical transducer for nanomechanical resonators,’ Appl. Phys. Lett. 97, 253114 (2010).
[Crossref]

2009 (5)

F. Elste, S. M. Girvin, and A. A. Clerk, “Quantum noise interference and backaction cooling in cavity nanomechanics,” Phys. Rev. Lett. 102, 207209 (2009).
[Crossref] [PubMed]

M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103, 223901 (2009).
[Crossref]

M. Pöllinger, D. O’Shea, F. Warken, and A. Rauschenbeutel, “Ultrahigh-Q tunable whispering-gallery-mode microresonator,” Phys. Rev. Lett. 103, 053901 (2009).
[Crossref] [PubMed]

D. V. Strekalov, H. G. L. Schwefel, A. A. Savchenkov, A. B. Matsko, L. J. Wang, and N. Yu, “Microwave whispering-gallery mode resonator for efficient optical upconversion,” Phys. Rev. A. 80, 033810 (2009).
[Crossref]

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
[Crossref] [PubMed]

2008 (3)

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008)..
[Crossref]

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref]

A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4, 415–419 (2008).
[Crossref]

2007 (3)

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
[Crossref]

M. Poggio, C. L. Degen, H. J. Mamin, and D. Rugar, “Feedback cooling of a cantilever’s fundamental mode below 5 mK,” Phys. Rev. Lett. 99, 017201 (2007).
[Crossref]

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416–422 (2007).
[Crossref]

2006 (2)

D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444, 75–78 (2006).
[Crossref]

O. Arcizet, P. -F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. -M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, “High sensitivity optical monitoring of a micromechanical resonator with a quantum limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006)
[Crossref]

2004 (1)

2003 (1)

1998 (1)

1993 (1)

L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering gallery mode resonances observed in fused silica microspheres,” Europhys. Lett. 23(5), 327–334 (1993).
[Crossref]

Alaie, S.

Anetsberger, G.

A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4, 415–419 (2008).
[Crossref]

Arcizet, O.

A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4, 415–419 (2008).
[Crossref]

O. Arcizet, P. -F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. -M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, “High sensitivity optical monitoring of a micromechanical resonator with a quantum limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006)
[Crossref]

Arndt, M.

M. Arndt and K. Hornberger, “Testing the limits of quantum mechanical superpositions,” Nat. Phys. 10, 271–277 (2014).
[Crossref]

Arnold, S.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref]

Aspelmeyer, M.

A. Schliesser and M. Aspelmeyer, “Cavity optomechanics with whispering-gallery-mode microresonators,” in Cavity Optomechanics, M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, eds. (SpringerBerlin Heidelberg, 2014).

Atherton, D. P.

G. Ranjit, D. P. Atherton, J. H. Stutz, M. Cunningham, and A. A. Geraci, “Attonewton force detection using microspheres in a dual-beam optical trap in high vacuum,” Phys. Rev. A 91, 051805 (2015)
[Crossref]

Barbour, R.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
[Crossref]

Barker, P.

P. Barker, “Doppler cooling a microsphere,” Phys. Rev. Lett. 105, 073002 (2010).
[Crossref] [PubMed]

Barker, P. F.

Y. L. Li, J. Millen, and P. F. Barker, “Cooling the centre-of-mass motion of a silica microsphere,” Proc. SPIE 9164, 916404 (2014).
[Crossref]

Basarir, O.

O. Basarir, S. Bramhavar, and K. L. Ekinci, “Near-field optical transducer for nanomechanical resonators,’ Appl. Phys. Lett. 97, 253114 (2010).
[Crossref]

Blasius, T. D.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nature Photonics,  6, 768–772 (2012).
[Crossref]

Bodiya, T.

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
[Crossref]

Bouwmeester, D.

D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444, 75–78 (2006).
[Crossref]

Bowen, W. P.

Bramhavar, S.

O. Basarir, S. Bramhavar, and K. L. Ekinci, “Near-field optical transducer for nanomechanical resonators,’ Appl. Phys. Lett. 97, 253114 (2010).
[Crossref]

Briant, T.

O. Arcizet, P. -F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. -M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, “High sensitivity optical monitoring of a micromechanical resonator with a quantum limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006)
[Crossref]

Brune, M.

L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering gallery mode resonances observed in fused silica microspheres,” Europhys. Lett. 23(5), 327–334 (1993).
[Crossref]

Buchler, B. C.

M. Hosseini, G. Guccione, H. J. Slatyer, B. C. Buchler, and P. Koy Lam, “Multimode laser cooling and ultra-high sensitivity force sensing with nanowires,” Nat. Commun. 5, 4663 (2014).
[Crossref] [PubMed]

Carmon, T.

Chen, Y.

Y. Chen, “Macroscopic quantum mechanics: theory and experimental concepts of optomechanics,” J. Phys. B. Atomic Mol. Opt. Phys. 46, 104001 (2013).
[Crossref]

Chow, J. H.

Clerk, A. A.

F. Elste, S. M. Girvin, and A. A. Clerk, “Quantum noise interference and backaction cooling in cavity nanomechanics,” Phys. Rev. Lett. 102, 207209 (2009).
[Crossref] [PubMed]

Cohadon, P. -F.

O. Arcizet, P. -F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. -M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, “High sensitivity optical monitoring of a micromechanical resonator with a quantum limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006)
[Crossref]

Collot, L.

L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering gallery mode resonances observed in fused silica microspheres,” Europhys. Lett. 23(5), 327–334 (1993).
[Crossref]

Corbitt, T.

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
[Crossref]

Cunningham, M.

G. Ranjit, D. P. Atherton, J. H. Stutz, M. Cunningham, and A. A. Geraci, “Attonewton force detection using microspheres in a dual-beam optical trap in high vacuum,” Phys. Rev. A 91, 051805 (2015)
[Crossref]

Degen, C. L.

M. Poggio, C. L. Degen, H. J. Mamin, and D. Rugar, “Feedback cooling of a cantilever’s fundamental mode below 5 mK,” Phys. Rev. Lett. 99, 017201 (2007).
[Crossref]

Eichenfield, M.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416–422 (2007).
[Crossref]

Ekinci, K. L.

O. Basarir, S. Bramhavar, and K. L. Ekinci, “Near-field optical transducer for nanomechanical resonators,’ Appl. Phys. Lett. 97, 253114 (2010).
[Crossref]

Elste, F.

F. Elste, S. M. Girvin, and A. A. Clerk, “Quantum noise interference and backaction cooling in cavity nanomechanics,” Phys. Rev. Lett. 102, 207209 (2009).
[Crossref] [PubMed]

Fiore, V.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
[Crossref]

Francais, O.

O. Arcizet, P. -F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. -M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, “High sensitivity optical monitoring of a micromechanical resonator with a quantum limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006)
[Crossref]

Gavartin, E.

E. Gavartin, P. Verlot, and T. J. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7, 509–514 (2012).
[Crossref] [PubMed]

Geraci, A. A.

G. Ranjit, D. P. Atherton, J. H. Stutz, M. Cunningham, and A. A. Geraci, “Attonewton force detection using microspheres in a dual-beam optical trap in high vacuum,” Phys. Rev. A 91, 051805 (2015)
[Crossref]

A. A. Geraci, S. B. Papp, and J. Kitching, “Short-range force detection using optically cooled levitated microspheres,” Phys. Rev. Lett. 105, 101101 (2010).
[Crossref]

Ghadimi, A.

D. J. Wilson, V. Sudhir, N. Piro, R. Schilling, A. Ghadimi, and T. J. Kippenberg, “Measurement-based control of a mechanical oscillator at its thermal decoherence rate,” Nature 524, 325–329 (2015).
[Crossref]

Girvin, S. M.

F. Elste, S. M. Girvin, and A. A. Clerk, “Quantum noise interference and backaction cooling in cavity nanomechanics,” Phys. Rev. Lett. 102, 207209 (2009).
[Crossref] [PubMed]

Gray, M. B.

Guccione, G.

M. Hosseini, G. Guccione, H. J. Slatyer, B. C. Buchler, and P. Koy Lam, “Multimode laser cooling and ultra-high sensitivity force sensing with nanowires,” Nat. Commun. 5, 4663 (2014).
[Crossref] [PubMed]

Haroche, S.

L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering gallery mode resonances observed in fused silica microspheres,” Europhys. Lett. 23(5), 327–334 (1993).
[Crossref]

Heidmann, A.

O. Arcizet, P. -F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. -M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, “High sensitivity optical monitoring of a micromechanical resonator with a quantum limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006)
[Crossref]

Hornberger, K.

M. Arndt and K. Hornberger, “Testing the limits of quantum mechanical superpositions,” Nat. Phys. 10, 271–277 (2014).
[Crossref]

Hosseini, M.

M. Hosseini, G. Guccione, H. J. Slatyer, B. C. Buchler, and P. Koy Lam, “Multimode laser cooling and ultra-high sensitivity force sensing with nanowires,” Nat. Commun. 5, 4663 (2014).
[Crossref] [PubMed]

Hossein-Zadeh, M.

Ilchenko, V. S.

Jiang, X.

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
[Crossref] [PubMed]

Kimble, H. J.

Kippenberg, T. J.

D. J. Wilson, V. Sudhir, N. Piro, R. Schilling, A. Ghadimi, and T. J. Kippenberg, “Measurement-based control of a mechanical oscillator at its thermal decoherence rate,” Nature 524, 325–329 (2015).
[Crossref]

E. Gavartin, P. Verlot, and T. J. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7, 509–514 (2012).
[Crossref] [PubMed]

A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4, 415–419 (2008).
[Crossref]

Kitching, J.

A. A. Geraci, S. B. Papp, and J. Kitching, “Short-range force detection using optically cooled levitated microspheres,” Phys. Rev. Lett. 105, 101101 (2010).
[Crossref]

Kleckner, D.

D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444, 75–78 (2006).
[Crossref]

Knittel, J.

Koy Lam, P.

M. Hosseini, G. Guccione, H. J. Slatyer, B. C. Buchler, and P. Koy Lam, “Multimode laser cooling and ultra-high sensitivity force sensing with nanowires,” Nat. Commun. 5, 4663 (2014).
[Crossref] [PubMed]

Krause, A. G.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nature Photonics,  6, 768–772 (2012).
[Crossref]

Kuzyk, M. C.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
[Crossref]

Lam, T. T-Y.

Le, V.H.

R. Madugani, Y. Yang, J. M. Ward, V.H. Le, and S. Nic Chormaic, “Optomechanical transduction and characterization of a silica microsphere pendulum via evanescent light,” Appl. Phys. Lett. 106, 241101 (2015).
[Crossref]

Lefevre-Seguin, V.

L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering gallery mode resonances observed in fused silica microspheres,” Europhys. Lett. 23(5), 327–334 (1993).
[Crossref]

Leseman, Z. C.

Li, J. -J.

J. -J. Li and K. -D. Zhu, “Nonlinear optical mass sensor with an optomechanical microresonator,” Appl. Phys. Lett. 101, 141905 (2012)
[Crossref]

Li, M.

M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103, 223901 (2009).
[Crossref]

Li, Y. L.

Y. L. Li, J. Millen, and P. F. Barker, “Cooling the centre-of-mass motion of a silica microsphere,” Proc. SPIE 9164, 916404 (2014).
[Crossref]

Lin, Q.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nature Photonics,  6, 768–772 (2012).
[Crossref]

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
[Crossref] [PubMed]

Liu, F.

Mabuchi, H.

Mackowski, J. -M.

O. Arcizet, P. -F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. -M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, “High sensitivity optical monitoring of a micromechanical resonator with a quantum limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006)
[Crossref]

Madugani, R.

R. Madugani, Y. Yang, J. M. Ward, V.H. Le, and S. Nic Chormaic, “Optomechanical transduction and characterization of a silica microsphere pendulum via evanescent light,” Appl. Phys. Lett. 106, 241101 (2015).
[Crossref]

Maleki, L.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008)..
[Crossref]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Whispering-gallery-modes electro-optic modulator and photonic microwave receiver,” J. Opt. Soc. Am. B 20(2), 333–342 (2003).
[Crossref]

Mamin, H. J.

M. Poggio, C. L. Degen, H. J. Mamin, and D. Rugar, “Feedback cooling of a cantilever’s fundamental mode below 5 mK,” Phys. Rev. Lett. 99, 017201 (2007).
[Crossref]

Matsko, A. B.

D. V. Strekalov, H. G. L. Schwefel, A. A. Savchenkov, A. B. Matsko, L. J. Wang, and N. Yu, “Microwave whispering-gallery mode resonator for efficient optical upconversion,” Phys. Rev. A. 80, 033810 (2009).
[Crossref]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008)..
[Crossref]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Whispering-gallery-modes electro-optic modulator and photonic microwave receiver,” J. Opt. Soc. Am. B 20(2), 333–342 (2003).
[Crossref]

Mavalvala, N.

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
[Crossref]

McClelland, D. E.

Michael, C. P.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416–422 (2007).
[Crossref]

Michel, C.

O. Arcizet, P. -F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. -M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, “High sensitivity optical monitoring of a micromechanical resonator with a quantum limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006)
[Crossref]

Millen, J.

Y. L. Li, J. Millen, and P. F. Barker, “Cooling the centre-of-mass motion of a silica microsphere,” Proc. SPIE 9164, 916404 (2014).
[Crossref]

Nic Chormaic, S.

R. Madugani, Y. Yang, J. M. Ward, V.H. Le, and S. Nic Chormaic, “Optomechanical transduction and characterization of a silica microsphere pendulum via evanescent light,” Appl. Phys. Lett. 106, 241101 (2015).
[Crossref]

O’Shea, D.

M. Pöllinger, D. O’Shea, F. Warken, and A. Rauschenbeutel, “Ultrahigh-Q tunable whispering-gallery-mode microresonator,” Phys. Rev. Lett. 103, 053901 (2009).
[Crossref] [PubMed]

Ottaway, D.

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
[Crossref]

Painter, O.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nature Photonics,  6, 768–772 (2012).
[Crossref]

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
[Crossref] [PubMed]

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416–422 (2007).
[Crossref]

Papp, S. B.

A. A. Geraci, S. B. Papp, and J. Kitching, “Short-range force detection using optically cooled levitated microspheres,” Phys. Rev. Lett. 105, 101101 (2010).
[Crossref]

Perahia, R.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416–422 (2007).
[Crossref]

Pernice, W. H. P.

M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103, 223901 (2009).
[Crossref]

Pinard, L.

O. Arcizet, P. -F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. -M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, “High sensitivity optical monitoring of a micromechanical resonator with a quantum limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006)
[Crossref]

Pinard, M.

O. Arcizet, P. -F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. -M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, “High sensitivity optical monitoring of a micromechanical resonator with a quantum limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006)
[Crossref]

Piro, N.

D. J. Wilson, V. Sudhir, N. Piro, R. Schilling, A. Ghadimi, and T. J. Kippenberg, “Measurement-based control of a mechanical oscillator at its thermal decoherence rate,” Nature 524, 325–329 (2015).
[Crossref]

Poggio, M.

M. Poggio, C. L. Degen, H. J. Mamin, and D. Rugar, “Feedback cooling of a cantilever’s fundamental mode below 5 mK,” Phys. Rev. Lett. 99, 017201 (2007).
[Crossref]

Pöllinger, M.

M. Pöllinger, D. O’Shea, F. Warken, and A. Rauschenbeutel, “Ultrahigh-Q tunable whispering-gallery-mode microresonator,” Phys. Rev. Lett. 103, 053901 (2009).
[Crossref] [PubMed]

Raimond, J. M.

L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering gallery mode resonances observed in fused silica microspheres,” Europhys. Lett. 23(5), 327–334 (1993).
[Crossref]

Ranjit, G.

G. Ranjit, D. P. Atherton, J. H. Stutz, M. Cunningham, and A. A. Geraci, “Attonewton force detection using microspheres in a dual-beam optical trap in high vacuum,” Phys. Rev. A 91, 051805 (2015)
[Crossref]

Rauschenbeutel, A.

M. Pöllinger, D. O’Shea, F. Warken, and A. Rauschenbeutel, “Ultrahigh-Q tunable whispering-gallery-mode microresonator,” Phys. Rev. Lett. 103, 053901 (2009).
[Crossref] [PubMed]

Riviere, R.

A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4, 415–419 (2008).
[Crossref]

Rosenberg, J.

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
[Crossref] [PubMed]

Rousseau, L.

O. Arcizet, P. -F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. -M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, “High sensitivity optical monitoring of a micromechanical resonator with a quantum limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006)
[Crossref]

Rugar, D.

M. Poggio, C. L. Degen, H. J. Mamin, and D. Rugar, “Feedback cooling of a cantilever’s fundamental mode below 5 mK,” Phys. Rev. Lett. 99, 017201 (2007).
[Crossref]

Savchenkov, A. A.

D. V. Strekalov, H. G. L. Schwefel, A. A. Savchenkov, A. B. Matsko, L. J. Wang, and N. Yu, “Microwave whispering-gallery mode resonator for efficient optical upconversion,” Phys. Rev. A. 80, 033810 (2009).
[Crossref]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008)..
[Crossref]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Whispering-gallery-modes electro-optic modulator and photonic microwave receiver,” J. Opt. Soc. Am. B 20(2), 333–342 (2003).
[Crossref]

Sawtell-Rickson, J. D.

Schilling, R.

D. J. Wilson, V. Sudhir, N. Piro, R. Schilling, A. Ghadimi, and T. J. Kippenberg, “Measurement-based control of a mechanical oscillator at its thermal decoherence rate,” Nature 524, 325–329 (2015).
[Crossref]

Schliesser, A.

A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4, 415–419 (2008).
[Crossref]

A. Schliesser and M. Aspelmeyer, “Cavity optomechanics with whispering-gallery-mode microresonators,” in Cavity Optomechanics, M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, eds. (SpringerBerlin Heidelberg, 2014).

Schwefel, H. G. L.

D. V. Strekalov, H. G. L. Schwefel, A. A. Savchenkov, A. B. Matsko, L. J. Wang, and N. Yu, “Microwave whispering-gallery mode resonator for efficient optical upconversion,” Phys. Rev. A. 80, 033810 (2009).
[Crossref]

Seidel, D.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008)..
[Crossref]

Shaddock, D. A.

Sigg, D.

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
[Crossref]

Slatyer, H. J.

M. Hosseini, G. Guccione, H. J. Slatyer, B. C. Buchler, and P. Koy Lam, “Multimode laser cooling and ultra-high sensitivity force sensing with nanowires,” Nat. Commun. 5, 4663 (2014).
[Crossref] [PubMed]

Smith, N.

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
[Crossref]

Solomatine, I.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008)..
[Crossref]

Streed, E. W.

Strekalov, D. V.

D. V. Strekalov, H. G. L. Schwefel, A. A. Savchenkov, A. B. Matsko, L. J. Wang, and N. Yu, “Microwave whispering-gallery mode resonator for efficient optical upconversion,” Phys. Rev. A. 80, 033810 (2009).
[Crossref]

Stutz, J. H.

G. Ranjit, D. P. Atherton, J. H. Stutz, M. Cunningham, and A. A. Geraci, “Attonewton force detection using microspheres in a dual-beam optical trap in high vacuum,” Phys. Rev. A 91, 051805 (2015)
[Crossref]

Sudhir, V.

D. J. Wilson, V. Sudhir, N. Piro, R. Schilling, A. Ghadimi, and T. J. Kippenberg, “Measurement-based control of a mechanical oscillator at its thermal decoherence rate,” Nature 524, 325–329 (2015).
[Crossref]

Tang, H. X.

M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103, 223901 (2009).
[Crossref]

Taylor, M. A.

Tian, L.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
[Crossref]

Vahala, K. J.

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
[Crossref] [PubMed]

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behaviour and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004).
[Crossref] [PubMed]

Verlot, P.

E. Gavartin, P. Verlot, and T. J. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7, 509–514 (2012).
[Crossref] [PubMed]

Vernooy, D. W.

Vollmer, F.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref]

Wang, H.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
[Crossref]

Wang, L. J.

D. V. Strekalov, H. G. L. Schwefel, A. A. Savchenkov, A. B. Matsko, L. J. Wang, and N. Yu, “Microwave whispering-gallery mode resonator for efficient optical upconversion,” Phys. Rev. A. 80, 033810 (2009).
[Crossref]

Ward, J. M.

R. Madugani, Y. Yang, J. M. Ward, V.H. Le, and S. Nic Chormaic, “Optomechanical transduction and characterization of a silica microsphere pendulum via evanescent light,” Appl. Phys. Lett. 106, 241101 (2015).
[Crossref]

Warken, F.

M. Pöllinger, D. O’Shea, F. Warken, and A. Rauschenbeutel, “Ultrahigh-Q tunable whispering-gallery-mode microresonator,” Phys. Rev. Lett. 103, 053901 (2009).
[Crossref] [PubMed]

Whitcomb, S.

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
[Crossref]

Wilson, D. J.

D. J. Wilson, V. Sudhir, N. Piro, R. Schilling, A. Ghadimi, and T. J. Kippenberg, “Measurement-based control of a mechanical oscillator at its thermal decoherence rate,” Nature 524, 325–329 (2015).
[Crossref]

Winger, M.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nature Photonics,  6, 768–772 (2012).
[Crossref]

Wipf, C.

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
[Crossref]

Yang, L.

Yang, Y.

R. Madugani, Y. Yang, J. M. Ward, V.H. Le, and S. Nic Chormaic, “Optomechanical transduction and characterization of a silica microsphere pendulum via evanescent light,” Appl. Phys. Lett. 106, 241101 (2015).
[Crossref]

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
[Crossref]

Yu, N.

D. V. Strekalov, H. G. L. Schwefel, A. A. Savchenkov, A. B. Matsko, L. J. Wang, and N. Yu, “Microwave whispering-gallery mode resonator for efficient optical upconversion,” Phys. Rev. A. 80, 033810 (2009).
[Crossref]

Zhu, K. -D.

J. -J. Li and K. -D. Zhu, “Nonlinear optical mass sensor with an optomechanical microresonator,” Appl. Phys. Lett. 101, 141905 (2012)
[Crossref]

Appl. Phys. Lett. (3)

J. -J. Li and K. -D. Zhu, “Nonlinear optical mass sensor with an optomechanical microresonator,” Appl. Phys. Lett. 101, 141905 (2012)
[Crossref]

O. Basarir, S. Bramhavar, and K. L. Ekinci, “Near-field optical transducer for nanomechanical resonators,’ Appl. Phys. Lett. 97, 253114 (2010).
[Crossref]

R. Madugani, Y. Yang, J. M. Ward, V.H. Le, and S. Nic Chormaic, “Optomechanical transduction and characterization of a silica microsphere pendulum via evanescent light,” Appl. Phys. Lett. 106, 241101 (2015).
[Crossref]

Europhys. Lett. (1)

L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering gallery mode resonances observed in fused silica microspheres,” Europhys. Lett. 23(5), 327–334 (1993).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. B. Atomic Mol. Opt. Phys. (1)

Y. Chen, “Macroscopic quantum mechanics: theory and experimental concepts of optomechanics,” J. Phys. B. Atomic Mol. Opt. Phys. 46, 104001 (2013).
[Crossref]

Nat. Commun. (1)

M. Hosseini, G. Guccione, H. J. Slatyer, B. C. Buchler, and P. Koy Lam, “Multimode laser cooling and ultra-high sensitivity force sensing with nanowires,” Nat. Commun. 5, 4663 (2014).
[Crossref] [PubMed]

Nat. Methods (1)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref]

Nat. Nanotechnol. (1)

E. Gavartin, P. Verlot, and T. J. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7, 509–514 (2012).
[Crossref] [PubMed]

Nat. Photonics (1)

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416–422 (2007).
[Crossref]

Nat. Phys. (2)

M. Arndt and K. Hornberger, “Testing the limits of quantum mechanical superpositions,” Nat. Phys. 10, 271–277 (2014).
[Crossref]

A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4, 415–419 (2008).
[Crossref]

Nature (2)

D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444, 75–78 (2006).
[Crossref]

D. J. Wilson, V. Sudhir, N. Piro, R. Schilling, A. Ghadimi, and T. J. Kippenberg, “Measurement-based control of a mechanical oscillator at its thermal decoherence rate,” Nature 524, 325–329 (2015).
[Crossref]

Nature Photonics (1)

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nature Photonics,  6, 768–772 (2012).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. A (1)

G. Ranjit, D. P. Atherton, J. H. Stutz, M. Cunningham, and A. A. Geraci, “Attonewton force detection using microspheres in a dual-beam optical trap in high vacuum,” Phys. Rev. A 91, 051805 (2015)
[Crossref]

Phys. Rev. A. (1)

D. V. Strekalov, H. G. L. Schwefel, A. A. Savchenkov, A. B. Matsko, L. J. Wang, and N. Yu, “Microwave whispering-gallery mode resonator for efficient optical upconversion,” Phys. Rev. A. 80, 033810 (2009).
[Crossref]

Phys. Rev. Lett. (11)

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
[Crossref]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008)..
[Crossref]

O. Arcizet, P. -F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. -M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, “High sensitivity optical monitoring of a micromechanical resonator with a quantum limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006)
[Crossref]

M. Pöllinger, D. O’Shea, F. Warken, and A. Rauschenbeutel, “Ultrahigh-Q tunable whispering-gallery-mode microresonator,” Phys. Rev. Lett. 103, 053901 (2009).
[Crossref] [PubMed]

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
[Crossref]

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
[Crossref] [PubMed]

P. Barker, “Doppler cooling a microsphere,” Phys. Rev. Lett. 105, 073002 (2010).
[Crossref] [PubMed]

A. A. Geraci, S. B. Papp, and J. Kitching, “Short-range force detection using optically cooled levitated microspheres,” Phys. Rev. Lett. 105, 101101 (2010).
[Crossref]

M. Poggio, C. L. Degen, H. J. Mamin, and D. Rugar, “Feedback cooling of a cantilever’s fundamental mode below 5 mK,” Phys. Rev. Lett. 99, 017201 (2007).
[Crossref]

F. Elste, S. M. Girvin, and A. A. Clerk, “Quantum noise interference and backaction cooling in cavity nanomechanics,” Phys. Rev. Lett. 102, 207209 (2009).
[Crossref] [PubMed]

M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103, 223901 (2009).
[Crossref]

Proc. SPIE (1)

Y. L. Li, J. Millen, and P. F. Barker, “Cooling the centre-of-mass motion of a silica microsphere,” Proc. SPIE 9164, 916404 (2014).
[Crossref]

Other (1)

A. Schliesser and M. Aspelmeyer, “Cavity optomechanics with whispering-gallery-mode microresonators,” in Cavity Optomechanics, M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, eds. (SpringerBerlin Heidelberg, 2014).

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Figures (8)

Fig. 1
Fig. 1 (a) A microscope image of a typical microsphere-cantilever. (b) Artist’s impression of the microsphere-cantilever, which is brought close to, but never touches, the tapered optical fiber underneath it. The evanescent fields of the WGM and tapered fiber are illustrated. (c) Monitoring the transmission t through the taper as the laser frequency is scanned reveals a WGM resonance (black), fitted with a Lorentzian function (blue) with a FWHM of 6.8 MHz.
Fig. 2
Fig. 2 A schematic of the transduction and feedback system. A 1064 nm Nd:YVO4 laser with an intracavity electro-optic modulator (EOM) is tuned to excite the WGM. A PDH locking scheme is implemented, with sidebands created using an RF signal applied to the EOM. The light is split into a strong beam (blue), and a weak, red-detuned, transduction beam (red) that counterpropagate along the tapered optical fiber with fixed detuning. Feedback cooling is achieved by amplifying (increasing the gain, g) and differentiating the transduction signal from photodiode PD 2, which is sent to a piezo stack (PZT) supporting the microsphere-cantilever, and / or used to modulate the locking beam intensity using AOM 2.
Fig. 3
Fig. 3 The full PSD from the transduction signal shows multiple mechanical modes belonging to the microsphere-cantilever or the tapered fibre which are identified by resonantly driving either oscillator. The predicted mode-shapes are shown as inset diagrams.
Fig. 4
Fig. 4 (a) The FFT of the transduction signal, showing the motion of the microsphere-cantilever with d = 0.42 μm, 0.18 μm, and 0.03 μm, illustrating the change in transduction, defined as the peak height above the background level. The FFT is normalized with respect to the maximum measured peak height. (b) The effect of the coupling distance, d, on the power coupled into the WGM, Pc, normalized to the input power propagating through the taper (blue), fitted with the on-resonance transmission relationship from [28]. Also shown is the transduction, τ, of the fundamental mechanical mode of a microsphere-cantilever (black) when the transduction beam is red-detuned by 20 MHz using a WGM with 40 MHz FWHM, fitted using reference [26].
Fig. 5
Fig. 5 Simultaneous cavity enhanced optical dipole force cooling of two mechanical modes of the tapered optical fiber, obtained at a pressure of 0.5 mbar. Representational mode shapes are shown. Each mode temperature is defined as Tt1, Tt2, at varying gain, gt1, gt2. Curves are fitted using Eq. 2 to infer the mode temperatures, and the values of Tt1, t2 are found with less than 10% uncertainty. The mechanical quality factor of each mode is Qm1 = 380 and Qm2 = 510.
Fig. 6
Fig. 6 PZT feedback cooling of the fundamental mode of the microsphere-cantilever with Qm1 = 370, reaching Tc1 at varying feedback gains gc1. The second mechanical eigenfrequency at 17.73 kHz, with Qm2 = 640, is simultaneously cooled to Tc2 = 108 K. Mechanical mode shapes are shown as inset diagrams. Data was taken at atmospheric pressure, with curves fitted using Eq. 2 to infer the mode temperatures Tc1,c2, with uncertainties of less than 10%.
Fig. 7
Fig. 7 PZT cooling of a microsphere-cantilever with a lower Qm = 280 than in Fig. 6 and higher noise floor, showing squashing with large feedback gain, gc. The mechanical mode is shown as an inset. Data was taken at atmospheric pressure, with curves fitted using Eq. 2 and Eq. 3 to infer the mode temperatures, with less than 10% uncertainty unless stated.
Fig. 8
Fig. 8 (a) Simultaneous cooling of a taper mode at Tt and the microsphere-cantilever mode at Tc using both the PZT and the CEODF, performed at atmospheric pressure. Mode temperatures are approximated by integrating the area under the respective peaks. (b) Cooling with only the CEODF or the PZT scheme, each optimized for the taper mode and cantilever mode respectively, can influence the transduced PSD of the other oscillator.

Equations (3)

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F o ( d ) = 8 ψ χ t V t γ e ( 0 ) Q opt 2 P c Θ 0 2 n t 2 V s × e ψ d ( e ψ d + ( γ e ( 0 ) Q opt / Θ 0 ) ) 3 ,
S fb ( ω ) = 2 Γ 0 k B T 0 M eff 1 ( ω 0 2 ω 2 ) 2 + ( 1 + g ) 2 Γ 0 2 ω 2 ,
S mod ( ω ) = S fb ( ω ) + S det ( ω 0 2 ω 2 ) 2 + Γ 0 2 ω 2 ( ω 0 2 ω 2 ) 2 + ( 1 + g ) 2 Γ 0 2 ω 2 ,

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