Abstract

We report on the development of optomechanical “trampoline” resonators composed of a tiny SiO2/Ta2O5 dielectric mirror on a silicon nitride micro-resonator. We observe optical finesses of up to 4 × 104 and mechanical quality factors as high as 9 × 105 in relatively massive (∼100 ng) and low frequency (10–200 kHz) devices. This results in a photon-phonon coupling efficiency considerably higher than previous Fabry-Perot-type optomechanical systems. These devices are well suited to ultra-sensitive force detection, ground-state optical cooling experiments, and demonstrations of quantum dynamics for such systems.

©2011 Optical Society of America

1. Introduction

Optomechanical systems offer a potential avenue for observing quantum effects in mesoscopic systems. Although integrated micro-optomechanical systems like microtoroids [1] and opto-mechanical crystals [2, 3] have demonstrated a large degree of optomechanical coupling, their relatively small mass and high frequencies make them unattractive for probing mass-induced decoherence [46]. Here we describe the fabrication and operation of low frequency optomechanical “trampoline” resonators composed of a tiny SiO2/Ta2O5 dielectric mirror on a silicon nitride micro-resonator. This combines the ideal mechanical properties of tensed Si3N4 resonators with the best available optical mirrors. The demonstrated systems have extraordinarily high mechanical quality factors and a photon-phonon coupling ratio comparable to the best integrated devices. If operated at cryogenic temperatures, these devices are well suited to ultra-sensitive force detection, ground-state optical cooling experiments [710], demonstrations of quantum effects [11, 12], and potentially even the realization of macroscopic quantum superpositions [6, 13, 14] with continued improvement in optical quality.

There have been several past realizations of optomechanical systems made from a tiny mirror on a mechanical resonator, for example, pieces of dielectric mirror glued to commercial AFM cantilevers [15] or deposited on top of a high frequency (MHz) Si3N4 resonator [16]. The combination of low optical and mechanical losses make Si3N4 an ideal mechanical material for this application; for tensed Si3N4 in particular the mechanical loss is typically observed to improve by an order of magnitude or more at the cryogenic temperatures required for quantum optomechanical experiments [17, 18]. The previously demonstrated mirror on Si3N4 systems had low mechanical quality factor, due to their high frequency and resulting clamping loss. Using an alternate fabrication method, we show that it is possible to increase the quality factor and make resonators at much lower mechanical frequencies. Furthermore, due to our unique undercutting method, our device allows free-space optical access to both sides of the mirror. This would make it ideal for “membrane in the middle” type optomechanical systems which would benefit greatly from the enhanced reflectivity of a dielectric mirror as compared to the single layer dielectric resonator that has been used previously [17], particularly if operating in the quadratic coupling regime [19, 20].

2. Fabrication of the system

The micro-optomechanical element is fabricated using standard cleanroom procedures (Fig. 1). We begin with a commercially deposited [21] dielectric mirror on a thin silicon (100 μm thick) wafer. This mirror is etched into disks of diameter 30–80 μm. We then deposit Si3N4 on both sides of the wafer, with a thickness in the range t = 300–500 nm. The front side Si3N4 is patterned into a cross resonator geometry (Fig. 2) with a diagonal length of a = 250–2000 μm and arm width of w = 2–30 μm. The back side of the wafer is patterned with a square hole to match the front side of the wafer. The wafer is then etched through with a silicon anisotropic etch (10% TMAH at 85° C), which releases the mechanical resonators with minimal undercutting of the Si3N4 where the structure connects to the bulk. Finally, the exposed layers of the dielectric mirror, composed of SiO2, are stripped with a short BHF etch; after this step the previously protected Ta2O5 layers form the new surfaces of the mirror.

 figure: Fig. 1

Fig. 1 The main steps in the fabrication process, carried out on a silicon wafer (gray). a) The process begins with the deposition of the SiO2 (blue) / Ta2O5 (pink) dielectric mirror, which is then etched into discs of the desired size (only 7 of the 33 dielectric layers are shown). b) Si3N4 (green) is deposited on both sides of the wafer. c) The front side Si3N4 is etched into the resonator geometry and the backside has square holes etched for the Si etch. d) The carrier wafer is etched through with a TMAH anisotropic etch, releasing the resonators. e) A short BHF etch strips the protective SiO2 layer off the front of the mirror, and the sample is then removed from solution with a critical point dry.

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 figure: Fig. 2

Fig. 2 Three micro-optomechanical resonators, as viewed from the top of the carrier wafer. Left: optical image, diameter d = 80 μm, Si3N4 of thickness t = 500 nm, with resonator arms of diagonal length a = 250 μm and width w = 20 μm. Center: optical image, d = 80 μm, t = 300 nm, a = 2000 μm, w = 2 μm. Right: scanning electron microscope image, d = 40 μm, t = 500 nm, a = 500 μm, w = 10 μm. Note that the anisotropic etch profile of TMAH is clearly visible in the silicon at the top of the image.

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We have also fabricated devices with Si3N4 resonators grown and etched before depositing the mirror layers. Although this method works, it has several disadvantages (including the fact that the roughness of the Si3N4 layer is then present on the mirror).

The other end of the optical cavity is a mirror with 50 mm radius of curvature and 15.9 mm outer diameter which was superpolished to better than 1 Å micro-roughness. The separation of the two mirrors is slightly (1–3 μm) shorter than the radius of curvature of the large mirror. This is required for a tight focus on the small mirror with a typical beam radius of 10 μm on a 60 μm diameter mirror. This gives a 1.6 mm beam radius on the large mirror and requires approximately 1 cm of clear aperture to minimize diffraction losses on both mirrors. In order to match the reflectivity of the optomechanical devices to the macroscopic end mirrors, the dielectric coating was deposited in the same run. The transmission of the coating was measured by the manufacturer to be 60 ± 10 PPM on the large mirror substrate at the design wavelength (λ = 1064 nm). The two ends of the optical cavity are placed in a specially constructed mount with five motorized degrees of freedom. The whole cavity assembly is then inserted into a vacuum chamber fitted with windows for optical access.

3. Optical characterization

To characterize the optical quality of the trampoline resonators, we measure the ring-down time of the cavity formed with the large mirror (Fig. 3).

 figure: Fig. 3

Fig. 3 The signal from the photodiode monitoring the cavity transmission during a typical optical ringdown measurement, showing the exponential decay of the signal after the pump laser is switched off via the AOM (averaged over 16 runs to reduce noise). Fitting the data starting 0.5 μs after the AOM switch results in an exponential decay time of τcav = 2.11 ± 0.02 μs.

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To measure the optical ringdown time, we first scan the length of the optical cavity by slightly more than half a wavelength of the Nd:YAG pump laser. When the cavity transmission rises above a certain threshold (set to about half of the fundamental mode peak height), a pulse generator is triggered which cuts off the laser intensity with an acousto-optical modulator (AOM). The switching time is less than 100 ns and the monitor avalanche photodiode amplifier has a bandwidth of 50 MHz, so the exponential decay of the cavity light is easily resolved provided F ≳ 103 (Fig. 3). Because this method provides a quick and robust measure of the cavity finesse, it is also used to fine tune the cavity alignment. The longest observed decay time was τcav = 2.11 ± 0.02 μs, corresponding to a finesse of F = 39,800 ± 400. Finesses for several of our devices compared to several other optomechanical devices [2, 9, 15, 16, 17, 22, 23, 24, 25] from the literature are found in Table 2. Although the maximum value was found for a cavity with an 80 μm tiny mirror, we routinely achieve finesses of greater than 3.5 × 104 for mirrors of 60 and 80 μm diameter which have had the Si3N4 removed from the mirror region. By comparison, using two of the 15.9 mm mirrors in a confocal configuration resulted in an optical finesse of F = 29,100 ± 200. The slightly higher finesse for the cavity with one tiny mirror is due to the fact that a dielectric mirror suspended in vacuum has higher reflectivity than one deposited on a glass substrate. (Samples with the resonator layer deposited first also show a slightly lower finesse, which then depends on the precise thickness of the Si3N4 dielectric layer.)

Tables Icon

Table 1. Dependence of frequency and quality factor on temperature as 157.7 kHz device is cooled to 300 mK with a dilution refrigerator.

Tables Icon

Table 2. A comparison of trampoline resonators with other previously demonstrated opto-mechanical systems.

Samples with mirrors of 30 and 40 μm diameter are observed to have a lower cavity finesse, approximately 5 × 103 and 2 × 104, respectively. Although such a reduction might be expected from diffraction effects, theoretical studies indicate that in the absence of mirror imperfections the diffraction limited finesse of all devices should be considerably higher (≳ 106) than the limitation imposed by the reflectivity of the dielectric mirrors [26]. The most likely source of imperfection is the wavefront error of our large mirror, which is on the order of several nm. This is consistent with the observed finesse, and suggests more sophisticated mirror polishing and surface figure correction techniques [27, 28] will be required for significant increase of the optical finesse, even with larger mirrors.

4. Mechanical characterization

To measure the intrinsic mechanical quality factor of the trampoline resonators, we monitor the motion of the tiny mirror with a laser locked to the fringe of a low finesse (F ∼ 100) optical cavity. Depending on the frequency of the device in question, we determine the quality factor (Qm) either by measuring the spectral linewidth or the mechanical decay time (see Fig. 4).

 figure: Fig. 4

Fig. 4 a) The normalized amplitude of the fundamental mechanical resonance of a low frequency (9.174 kHz) resonator after it is excited by moving by one of the alignment motors by a single step. Data from the first minute after the excitation (not shown) is heavily distorted due to the mechanical amplitude becoming larger than the equivalent width of the optical peak (λ/2F ∼ 5 nm). Fitting the data after t = 80 s results in a power decay time of τ = 15.4 ± 0.3 s, or a mechanical quality factor of Qm = (9.4 ± 0.2) × 105. b) The thermal resonance spectrum of a high frequency (ωm = 2π × 157.7 kHz) trampoline resonator. A fit to a Lorentzian gives a peak width (FWHM) of δωm = 2π × 3.64±0.15 Hz, corresponding to Qm = (4.3 ± 0.2) × 104.

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To measure the intrinsic mechanical quality factor of the resonators, we must first reduce the optical cavity finesse so that optical heating/cooling effects can be neglected. In practice this is most easily done by increasing the cavity length by a small amount (ΔL ∼ 100 μm) so that the beam no longer is able to tightly focus on the small mirror, increasing losses and decreasing finesse. We then lock the laser to the fringe of an optical resonance. To do this, we first modulate the laser frequency at a rate of 30 kHz with an amplitude of ∼7.5 MHz. This generates 30 kHz harmonics in the transmitted intensity, as monitored on the photodiode at the output of the cavity. A lock-in amplifier measures the second harmonic of the modulation frequency, which is used as the input to an integrator circuit connected piezoelectric transducer which changes the cavity length. This locks the laser to the point of maximum slope on the optical fringe, resulting in an accurate measurement of the resonator’s motion which is assumed to be much faster than the speed of the feedback loop (∼ 1 Hz).

To measure the mechanical ring-down of low frequency resonators, we excite the system by moving one of the cavity alignment motors by a single 20 nm step. Due to the high frequency slip-stick motion of the motors, this causes a relatively large excitation (≳ 10 nm) of the mechanical resonator whose decay time can easily be measured. Because the mechanical displacement can become comparable to or larger than the equivalent linewidth of the optical resonance, we use the fundamental harmonic (30 kHz) signal from the frequency modulation as a reference to linearize the fundamental mechanical amplitude signal. Although the ringdown provides a robust measure of mechanical quality, the excitation is large enough that it disturbs the locking of the pump laser to the cavity mode. Thus it can only be used for devices whose decay time is longer than the approximate locking time of the cavity feedback loop (∼ 1 s); for higher frequency devices we instead measure the spectral linewidth of the thermally excited mechanical resonance.

We observe high mechanical quality factors for all devices, even at room temperature (see Table 2). For the lowest frequency device we measured a quality factor of Qm = (9.4 ± 0.2) × 105 at ωm = 2π × 9.714 kHz. In general, Qm is highest for the lowest frequency devices, following an approximate Qmωm1 trend, as is commonly seen in micromechanical systems [29, 30]. A slight deviation from this trend is seen for the highest frequency devices, in which case the stress relaxation induced by the mirror causes a moderate reduction in the tension of the resonator.

In general, the quality factor of tensed Si3N4 resonators is observed to increase at cryogenic temperatures [18, 31, 32]. Using a preliminary cryogenic version of our optical cavity, we measured the Qm at temperatures down to 300 mK. Using one of the higher frequency devices with frequency 157.7 kHz, we observed the quality factor to first increase as the device was cooled to 77 K. The Qm increased to a maximum of 120, 000 at 300 mK. The frequency and Qm at various temperatures are displayed in Table 1. Although this increase is less than that of [31], this is likely due to the lower stress of our thin film.

5. Prospects and conclusion

To analyze the suitability of trampoline resonators for quantum experiments, we need to characterize the degree of coupling between the optical and mechanical modes. The quantum hamiltonian of a standard optomechanical system is characterized by a linear optomechanical coupling rate, g, which couples the photon number of the optical mode to the position of the mechanical mode. For a Fabry-Perot cavity with one moving end mirror this coupling is given by [13, 33]:

g=ωcLx0,
where ωc is the optical mode frequency, L is the cavity length and x 0 = [/(2meffωm)]1/2 is the ground state wavepacket size of the mechanical mode (where meff is the effective mass of the fundamental mode). As a figure of merit, we will consider the product of the coupling rate, g, and the optical ring-down time, τcav:
g=gτcav=2Fx0λ.
This gives a dimensionless measure of how close a device is to being strongly coupled. (Note that coherent pumping can also make a weakly coupled device become strongly coupled: in this case an effective coupling is given by geffng and 〈n〉 is the mean number of photons in the optical cavity [12, 16].) In the limit g′ ≪ 1 and ωmτcav1, g′ gives the probability that a photon in the optical mode would excite the mechanical resonator out of the ground state. A comparison of the optical and mechanical quality of trampoline resonators to other optomechanical systems is shown in Table 2. The mass of our resonator is calculated from the mirror geometry.

We find the our devices have an optomechanical coupling efficiency nearly equal to the best integrated optical devices (microtoroids), despite having an order of magnitude larger mass. We are also within an order of magnitude of the best reported RF devices [9]. If the finesse could be increased to the theoretical diffraction limited value it should be possible to create devices with considerably higher optomechanical coupling than any current device. The finesse increases exponentially with the number of layers so can be increased dramatically with only minor mass increase. The main limitation is then wavefront error which must be improved before substantially lower loss coatings can effectively be used.

This high degree of optomechanical coupling of trampoline resonators makes them ideal for demonstrations of quantum effects in massive systems. A first step towards demonstrating quantum effects is ground state optical cooling, which also requires low initial temperature and a “sideband-resolved” mechanical resonance [7, 8]. In particular, the bath temperature of the resonator must be low enough that [7, 8]:

Qm1exp(h¯ωmkBT)1
In the kBTh̄ωm regime, this simplifies to:
TQmh¯ωmkB.
For our devices, this corresponds to T ≪ 0.5 K. Although we have already demonstrated base temperatures in this regime, there are significant experimental challenges with aligning a high quality optical cavity at these temperatures. The sideband-resolved requirement is that the optical decay rate be smaller than the mechanical resonance frequency, τcav1<ωm which is met for our devices with ωm ≳ 2π × 80 kHz, provided the sample finesse can be achieved in cryogenic conditions. If ground state optical cooling can be achieved, this opens the door to a number of other demonstrations of quantum effects [6, 14, 17, 19, 35].

Trampoline resonators are also suitable for use as ultra-high resolution force sensors. Assuming the quality factor increase is also seen for the lowest frequency devices, it should be possible to obtain a thermal force noise in the aN/Hz regime at demonstrated temperatures. This is comparable to or better than the single crystal Si resonators currently used in magnetic resonance force microscopy (MRFM) experiments [36, 37]. Furthermore, the rear side optical access can be used to provide extremely precise position sensitivity while leaving the front side free for surface modifications required for use as sensors.

In conclusion, we have demonstrated the development of low frequency micro-optomechanical systems with an extraordinarily high optical and mechanical quality by combining the best properties of previous systems in a single device. Due to their ideal properties, including the highest published photon-phonon coupling efficiencies for optical Fabry-Perot type systems, and unique double sided optical access, these devices are well suited for both practical applications and demonstrations of quantum effects with mesoscopic objects.

Acknowledgments

The authors gratefully acknowledge support by the National Science Foundation (grant PHY-0504825 and NIRT grant 0304678), Marie-Curie EXT-CT-2006-042580, the U.S. Department of Education GAANN grant, European Commission Project MINOS, and the NWO VICI award. A portion of this work was done in the UCSB Nanofabrication Facility, part of the NSF-funded NNIN network.

References and links

1. A. Schliesser, O. Arcizet, R. Rivière, G. Anetsberger, and T. J. Kippenberg, “Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit,” Nat. Phys. 5, 509–514 (2009). [CrossRef]  

2. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009). [CrossRef]   [PubMed]  

3. J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17, 3802–3817 (2009). [CrossRef]   [PubMed]  

4. L. Diósi, “Models for universal reduction of macroscopic quantum fluctuations,” Phys. Rev. A 40, 1165–1174 (1989). [CrossRef]   [PubMed]  

5. R. Penrose, “On Gravity’s role in Quantum State Reduction,” Gen. Relativ. Gravit. 28, 581–600 (1996). [CrossRef]  

6. D. Kleckner, I. Pikovski, E. Jeffrey, L. Ament, E. Eliel, J. van den Brink, and D. Bouwmeester, “Creating and verifying a quantum superposition in a micro-optomechanical system,” New J. Phys. 10, 095020 (2008). [CrossRef]  

7. I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of Ground State Cooling of a Mechanical Oscillator Using Dynamical Backaction,” Phys. Rev. Lett. 99, 093901 (2007). [CrossRef]   [PubMed]  

8. F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, “Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion,” Phys. Rev. Lett. 99, 093902 (2007). [CrossRef]   [PubMed]  

9. J. D. Teufel, T. Donner, D. Li, J. H. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband Cooling Micromechanical Motion to the Quantum Ground State,” ArXiv e-prints (2011).

10. J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” ArXiv e-prints (2011).

11. D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical Entanglement between a Movable Mirror and a Cavity Field,” Phys. Rev. Lett. 98, 030405 (2007). [CrossRef]   [PubMed]  

12. U. Akram, N. Kiesel, M. Aspelmeyer, and G. J. Milburn, “Single-photon opto-mechanics in the strong coupling regime,” New J. Phys. 12, 083030 (2010). [CrossRef]  

13. S. Bose, K. Jacobs, and P. L. Knight, “Scheme to probe the decoherence of a macroscopic object,” Phys. Rev. A 59, 3204–3210 (1999). [CrossRef]  

14. W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, “Towards Quantum Superpositions of a Mirror,” Phys. Rev. Lett. 91, 130401 (2003). [CrossRef]   [PubMed]  

15. D. Kleckner, W. Marshall, M. J. A. de Dood, K. N. Dinyari, B.-J. Pors, W. T. M. Irvine, and D. Bouwmeester, “High Finesse Opto-Mechanical Cavity with a Movable Thirty-Micron-Size Mirror,” Phys. Rev. Lett. 96, 173901 (2006). [CrossRef]   [PubMed]  

16. S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724 (2009). [CrossRef]   [PubMed]  

17. J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008). [CrossRef]   [PubMed]  

18. S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5, 485–488 (2009). [CrossRef]  

19. A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008). [CrossRef]  

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21. Mirrors were deposited by Coastline Optics, LLC, located in Camarillo, CA, USA.

22. A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved Sideband Cooling of a Micromechanical Oscillator,” Nat. Phys. 4, 415–419 (2008). [CrossRef]  

23. G. Cole, I. Wilson-Rae, M. Vanner, S. Gröblacher, J. Pohl, M. Zorn, M. Weyers, A. Peters, and M. Aspelmeyer, “Megahertz monocrystalline optomechanical resonators with minimal dissipation,” in “Proc. IEEE Micr. Elect. ,” (2010), pp. 847–850.

24. D. Brodoceanu, G. D. Cole, N. Kiesel, M. Aspelmeyer, and D. Bauerle, “Femtosecond laser fabrication of high reflectivity micromirrors,” Appl. Phys. Lett. 97, 041104 (2010). [CrossRef]  

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27. M. Yamamoto, “Sub-nm figure error correction of an extreme ultraviolet multilayer mirror by its surface milling,” Nucl. Instrum. Methods Phys. Res., A 467–468, 1282–1285 (2001). [CrossRef]  

28. K. Kamijo, R. Uozumi, K. Moriziri, S. A. Pahlovy, and I. Miyamoto, “Two stage ion beam figuring and smoothening method for shape error correction of ULE substrates of extreme ultraviolet lithography projection optics: Evaluation of high-spatial frequency roughness,” J. Vac. Sci. Technol. B 27, 2900 (2009) [CrossRef]  

29. S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006). [CrossRef]  

30. S. S. Verbridge, D. F. Shapiro, H. G. Craighead, and J. M. Parpia, “Macroscopic tuning of nanomechanics: substrate bending for reversible control of frequency and quality factor of nanostring resonators,” Nano Lett. 7, 1728–1735 (2007). [CrossRef]   [PubMed]  

31. B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. B. Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008). [CrossRef]  

32. M. Roseman and P. Grutter, “Cryogenic magnetic force microscope,” Rev. Sci. Instrum. 71, 3782–3787 (2000). [CrossRef]  

33. C. K. Law, “Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation,” Phys. Rev. A 51, 2537–2541 (1995). [CrossRef]   [PubMed]  

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

35. A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Quantum measurement of phonon shot noise,” Phys. Rev. Lett. 104, 213603 (2010). [CrossRef]   [PubMed]  

36. H. J. Mamin and D. Rugar, “Sub-attonewton force detection at millikelvin temperatures,” Appl. Phys. Lett. 79, 3358–3360 (2001). [CrossRef]  

37. C. L. Degen, M. Poggio, H. J. Mamin, C. T. Rettner, and D. Rugar, “Nanoscale magnetic resonance imaging,” Proc. Natl. Acad. Sci. USA 106, 1313–1317 (2009). [CrossRef]   [PubMed]  

References

  • View by:

  1. A. Schliesser, O. Arcizet, R. Rivière, G. Anetsberger, and T. J. Kippenberg, “Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit,” Nat. Phys. 5, 509–514 (2009).
    [Crossref]
  2. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
    [Crossref] [PubMed]
  3. J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17, 3802–3817 (2009).
    [Crossref] [PubMed]
  4. L. Diósi, “Models for universal reduction of macroscopic quantum fluctuations,” Phys. Rev. A 40, 1165–1174 (1989).
    [Crossref] [PubMed]
  5. R. Penrose, “On Gravity’s role in Quantum State Reduction,” Gen. Relativ. Gravit. 28, 581–600 (1996).
    [Crossref]
  6. D. Kleckner, I. Pikovski, E. Jeffrey, L. Ament, E. Eliel, J. van den Brink, and D. Bouwmeester, “Creating and verifying a quantum superposition in a micro-optomechanical system,” New J. Phys. 10, 095020 (2008).
    [Crossref]
  7. I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of Ground State Cooling of a Mechanical Oscillator Using Dynamical Backaction,” Phys. Rev. Lett. 99, 093901 (2007).
    [Crossref] [PubMed]
  8. F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, “Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion,” Phys. Rev. Lett. 99, 093902 (2007).
    [Crossref] [PubMed]
  9. J. D. Teufel, T. Donner, D. Li, J. H. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband Cooling Micromechanical Motion to the Quantum Ground State,” ArXiv e-prints (2011).
  10. J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” ArXiv e-prints (2011).
  11. D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical Entanglement between a Movable Mirror and a Cavity Field,” Phys. Rev. Lett. 98, 030405 (2007).
    [Crossref] [PubMed]
  12. U. Akram, N. Kiesel, M. Aspelmeyer, and G. J. Milburn, “Single-photon opto-mechanics in the strong coupling regime,” New J. Phys. 12, 083030 (2010).
    [Crossref]
  13. S. Bose, K. Jacobs, and P. L. Knight, “Scheme to probe the decoherence of a macroscopic object,” Phys. Rev. A 59, 3204–3210 (1999).
    [Crossref]
  14. W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, “Towards Quantum Superpositions of a Mirror,” Phys. Rev. Lett. 91, 130401 (2003).
    [Crossref] [PubMed]
  15. D. Kleckner, W. Marshall, M. J. A. de Dood, K. N. Dinyari, B.-J. Pors, W. T. M. Irvine, and D. Bouwmeester, “High Finesse Opto-Mechanical Cavity with a Movable Thirty-Micron-Size Mirror,” Phys. Rev. Lett. 96, 173901 (2006).
    [Crossref] [PubMed]
  16. S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724 (2009).
    [Crossref] [PubMed]
  17. J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
    [Crossref] [PubMed]
  18. S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5, 485–488 (2009).
    [Crossref]
  19. A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
    [Crossref]
  20. A. Nunnenkamp, K. Børkje, J. G. E. Harris, and S. M. Girvin, “Cooling and squeezing via quadratic optomechanical coupling,” Phys. Rev. A 82, 021806 (2010).
    [Crossref]
  21. Mirrors were deposited by Coastline Optics, LLC, located in Camarillo, CA, USA.
  22. A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved Sideband Cooling of a Micromechanical Oscillator,” Nat. Phys. 4, 415–419 (2008).
    [Crossref]
  23. G. Cole, I. Wilson-Rae, M. Vanner, S. Gröblacher, J. Pohl, M. Zorn, M. Weyers, A. Peters, and M. Aspelmeyer, “Megahertz monocrystalline optomechanical resonators with minimal dissipation,” in “Proc. IEEE Micr. Elect.,” (2010), pp. 847–850.
  24. D. Brodoceanu, G. D. Cole, N. Kiesel, M. Aspelmeyer, and D. Bauerle, “Femtosecond laser fabrication of high reflectivity micromirrors,” Appl. Phys. Lett. 97, 041104 (2010).
    [Crossref]
  25. 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]
  26. D. Kleckner, W. T. M. Irvine, S. S. R. Oemrawsingh, and D. Bouwmeester, “Diffraction-limited high-finesse optical cavities,” Phys. Rev. A 81 (2010).
    [Crossref]
  27. M. Yamamoto, “Sub-nm figure error correction of an extreme ultraviolet multilayer mirror by its surface milling,” Nucl. Instrum. Methods Phys. Res., A 467–468, 1282–1285 (2001).
    [Crossref]
  28. K. Kamijo, R. Uozumi, K. Moriziri, S. A. Pahlovy, and I. Miyamoto, “Two stage ion beam figuring and smoothening method for shape error correction of ULE substrates of extreme ultraviolet lithography projection optics: Evaluation of high-spatial frequency roughness,” J. Vac. Sci. Technol. B 27, 2900 (2009)
    [Crossref]
  29. S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
    [Crossref]
  30. S. S. Verbridge, D. F. Shapiro, H. G. Craighead, and J. M. Parpia, “Macroscopic tuning of nanomechanics: substrate bending for reversible control of frequency and quality factor of nanostring resonators,” Nano Lett. 7, 1728–1735 (2007).
    [Crossref] [PubMed]
  31. B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. B. Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008).
    [Crossref]
  32. M. Roseman and P. Grutter, “Cryogenic magnetic force microscope,” Rev. Sci. Instrum. 71, 3782–3787 (2000).
    [Crossref]
  33. C. K. Law, “Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation,” Phys. Rev. A 51, 2537–2541 (1995).
    [Crossref] [PubMed]
  34. Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfeld, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nat. Photonics 4, 236–242 (2010).
    [Crossref]
  35. A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Quantum measurement of phonon shot noise,” Phys. Rev. Lett. 104, 213603 (2010).
    [Crossref] [PubMed]
  36. H. J. Mamin and D. Rugar, “Sub-attonewton force detection at millikelvin temperatures,” Appl. Phys. Lett. 79, 3358–3360 (2001).
    [Crossref]
  37. C. L. Degen, M. Poggio, H. J. Mamin, C. T. Rettner, and D. Rugar, “Nanoscale magnetic resonance imaging,” Proc. Natl. Acad. Sci. USA 106, 1313–1317 (2009).
    [Crossref] [PubMed]

2010 (7)

U. Akram, N. Kiesel, M. Aspelmeyer, and G. J. Milburn, “Single-photon opto-mechanics in the strong coupling regime,” New J. Phys. 12, 083030 (2010).
[Crossref]

A. Nunnenkamp, K. Børkje, J. G. E. Harris, and S. M. Girvin, “Cooling and squeezing via quadratic optomechanical coupling,” Phys. Rev. A 82, 021806 (2010).
[Crossref]

G. Cole, I. Wilson-Rae, M. Vanner, S. Gröblacher, J. Pohl, M. Zorn, M. Weyers, A. Peters, and M. Aspelmeyer, “Megahertz monocrystalline optomechanical resonators with minimal dissipation,” in “Proc. IEEE Micr. Elect.,” (2010), pp. 847–850.

D. Brodoceanu, G. D. Cole, N. Kiesel, M. Aspelmeyer, and D. Bauerle, “Femtosecond laser fabrication of high reflectivity micromirrors,” Appl. Phys. Lett. 97, 041104 (2010).
[Crossref]

D. Kleckner, W. T. M. Irvine, S. S. R. Oemrawsingh, and D. Bouwmeester, “Diffraction-limited high-finesse optical cavities,” Phys. Rev. A 81 (2010).
[Crossref]

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

A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Quantum measurement of phonon shot noise,” Phys. Rev. Lett. 104, 213603 (2010).
[Crossref] [PubMed]

2009 (8)

C. L. Degen, M. Poggio, H. J. Mamin, C. T. Rettner, and D. Rugar, “Nanoscale magnetic resonance imaging,” Proc. Natl. Acad. Sci. USA 106, 1313–1317 (2009).
[Crossref] [PubMed]

K. Kamijo, R. Uozumi, K. Moriziri, S. A. Pahlovy, and I. Miyamoto, “Two stage ion beam figuring and smoothening method for shape error correction of ULE substrates of extreme ultraviolet lithography projection optics: Evaluation of high-spatial frequency roughness,” J. Vac. Sci. Technol. B 27, 2900 (2009)
[Crossref]

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]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724 (2009).
[Crossref] [PubMed]

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5, 485–488 (2009).
[Crossref]

A. Schliesser, O. Arcizet, R. Rivière, G. Anetsberger, and T. J. Kippenberg, “Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit,” Nat. Phys. 5, 509–514 (2009).
[Crossref]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref] [PubMed]

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17, 3802–3817 (2009).
[Crossref] [PubMed]

2008 (5)

D. Kleckner, I. Pikovski, E. Jeffrey, L. Ament, E. Eliel, J. van den Brink, and D. Bouwmeester, “Creating and verifying a quantum superposition in a micro-optomechanical system,” New J. Phys. 10, 095020 (2008).
[Crossref]

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
[Crossref]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
[Crossref] [PubMed]

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved Sideband Cooling of a Micromechanical Oscillator,” Nat. Phys. 4, 415–419 (2008).
[Crossref]

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. B. Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008).
[Crossref]

2007 (4)

S. S. Verbridge, D. F. Shapiro, H. G. Craighead, and J. M. Parpia, “Macroscopic tuning of nanomechanics: substrate bending for reversible control of frequency and quality factor of nanostring resonators,” Nano Lett. 7, 1728–1735 (2007).
[Crossref] [PubMed]

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of Ground State Cooling of a Mechanical Oscillator Using Dynamical Backaction,” Phys. Rev. Lett. 99, 093901 (2007).
[Crossref] [PubMed]

F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, “Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion,” Phys. Rev. Lett. 99, 093902 (2007).
[Crossref] [PubMed]

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical Entanglement between a Movable Mirror and a Cavity Field,” Phys. Rev. Lett. 98, 030405 (2007).
[Crossref] [PubMed]

2006 (2)

D. Kleckner, W. Marshall, M. J. A. de Dood, K. N. Dinyari, B.-J. Pors, W. T. M. Irvine, and D. Bouwmeester, “High Finesse Opto-Mechanical Cavity with a Movable Thirty-Micron-Size Mirror,” Phys. Rev. Lett. 96, 173901 (2006).
[Crossref] [PubMed]

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[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]

2001 (2)

M. Yamamoto, “Sub-nm figure error correction of an extreme ultraviolet multilayer mirror by its surface milling,” Nucl. Instrum. Methods Phys. Res., A 467–468, 1282–1285 (2001).
[Crossref]

H. J. Mamin and D. Rugar, “Sub-attonewton force detection at millikelvin temperatures,” Appl. Phys. Lett. 79, 3358–3360 (2001).
[Crossref]

2000 (1)

M. Roseman and P. Grutter, “Cryogenic magnetic force microscope,” Rev. Sci. Instrum. 71, 3782–3787 (2000).
[Crossref]

1999 (1)

S. Bose, K. Jacobs, and P. L. Knight, “Scheme to probe the decoherence of a macroscopic object,” Phys. Rev. A 59, 3204–3210 (1999).
[Crossref]

1996 (1)

R. Penrose, “On Gravity’s role in Quantum State Reduction,” Gen. Relativ. Gravit. 28, 581–600 (1996).
[Crossref]

1995 (1)

C. K. Law, “Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation,” Phys. Rev. A 51, 2537–2541 (1995).
[Crossref] [PubMed]

1989 (1)

L. Diósi, “Models for universal reduction of macroscopic quantum fluctuations,” Phys. Rev. A 40, 1165–1174 (1989).
[Crossref] [PubMed]

Akram, U.

U. Akram, N. Kiesel, M. Aspelmeyer, and G. J. Milburn, “Single-photon opto-mechanics in the strong coupling regime,” New J. Phys. 12, 083030 (2010).
[Crossref]

Alegre, T. P. M.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” ArXiv e-prints (2011).

Allman, M. S.

J. D. Teufel, T. Donner, D. Li, J. H. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband Cooling Micromechanical Motion to the Quantum Ground State,” ArXiv e-prints (2011).

Ament, L.

D. Kleckner, I. Pikovski, E. Jeffrey, L. Ament, E. Eliel, J. van den Brink, and D. Bouwmeester, “Creating and verifying a quantum superposition in a micro-optomechanical system,” New J. Phys. 10, 095020 (2008).
[Crossref]

Anetsberger, G.

A. Schliesser, O. Arcizet, R. Rivière, G. Anetsberger, and T. J. Kippenberg, “Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit,” Nat. Phys. 5, 509–514 (2009).
[Crossref]

A. Schliesser, R. Rivière, 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, O. Arcizet, R. Rivière, G. Anetsberger, and T. J. Kippenberg, “Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit,” Nat. Phys. 5, 509–514 (2009).
[Crossref]

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved Sideband Cooling of a Micromechanical Oscillator,” Nat. Phys. 4, 415–419 (2008).
[Crossref]

Aspelmeyer, M.

G. Cole, I. Wilson-Rae, M. Vanner, S. Gröblacher, J. Pohl, M. Zorn, M. Weyers, A. Peters, and M. Aspelmeyer, “Megahertz monocrystalline optomechanical resonators with minimal dissipation,” in “Proc. IEEE Micr. Elect.,” (2010), pp. 847–850.

D. Brodoceanu, G. D. Cole, N. Kiesel, M. Aspelmeyer, and D. Bauerle, “Femtosecond laser fabrication of high reflectivity micromirrors,” Appl. Phys. Lett. 97, 041104 (2010).
[Crossref]

U. Akram, N. Kiesel, M. Aspelmeyer, and G. J. Milburn, “Single-photon opto-mechanics in the strong coupling regime,” New J. Phys. 12, 083030 (2010).
[Crossref]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724 (2009).
[Crossref] [PubMed]

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5, 485–488 (2009).
[Crossref]

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical Entanglement between a Movable Mirror and a Cavity Field,” Phys. Rev. Lett. 98, 030405 (2007).
[Crossref] [PubMed]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” ArXiv e-prints (2011).

Bauerle, D.

D. Brodoceanu, G. D. Cole, N. Kiesel, M. Aspelmeyer, and D. Bauerle, “Femtosecond laser fabrication of high reflectivity micromirrors,” Appl. Phys. Lett. 97, 041104 (2010).
[Crossref]

Bellan, L. M.

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[Crossref]

Böhm, H. R.

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical Entanglement between a Movable Mirror and a Cavity Field,” Phys. Rev. Lett. 98, 030405 (2007).
[Crossref] [PubMed]

Børkje, K.

A. Nunnenkamp, K. Børkje, J. G. E. Harris, and S. M. Girvin, “Cooling and squeezing via quadratic optomechanical coupling,” Phys. Rev. A 82, 021806 (2010).
[Crossref]

Bose, S.

S. Bose, K. Jacobs, and P. L. Knight, “Scheme to probe the decoherence of a macroscopic object,” Phys. Rev. A 59, 3204–3210 (1999).
[Crossref]

Bouwmeester, D.

D. Kleckner, W. T. M. Irvine, S. S. R. Oemrawsingh, and D. Bouwmeester, “Diffraction-limited high-finesse optical cavities,” Phys. Rev. A 81 (2010).
[Crossref]

D. Kleckner, I. Pikovski, E. Jeffrey, L. Ament, E. Eliel, J. van den Brink, and D. Bouwmeester, “Creating and verifying a quantum superposition in a micro-optomechanical system,” New J. Phys. 10, 095020 (2008).
[Crossref]

D. Kleckner, W. Marshall, M. J. A. de Dood, K. N. Dinyari, B.-J. Pors, W. T. M. Irvine, and D. Bouwmeester, “High Finesse Opto-Mechanical Cavity with a Movable Thirty-Micron-Size Mirror,” Phys. Rev. Lett. 96, 173901 (2006).
[Crossref] [PubMed]

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

Brodoceanu, D.

D. Brodoceanu, G. D. Cole, N. Kiesel, M. Aspelmeyer, and D. Bauerle, “Femtosecond laser fabrication of high reflectivity micromirrors,” Appl. Phys. Lett. 97, 041104 (2010).
[Crossref]

Camacho, R.

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

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17, 3802–3817 (2009).
[Crossref] [PubMed]

Camacho, R. M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref] [PubMed]

Chan, J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref] [PubMed]

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17, 3802–3817 (2009).
[Crossref] [PubMed]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” ArXiv e-prints (2011).

Chang, D.

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

Chen, J. P.

F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, “Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion,” Phys. Rev. Lett. 99, 093902 (2007).
[Crossref] [PubMed]

Cicak, K.

J. D. Teufel, T. Donner, D. Li, J. H. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband Cooling Micromechanical Motion to the Quantum Ground State,” ArXiv e-prints (2011).

Clerk, A. A.

A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Quantum measurement of phonon shot noise,” Phys. Rev. Lett. 104, 213603 (2010).
[Crossref] [PubMed]

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
[Crossref]

F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, “Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion,” Phys. Rev. Lett. 99, 093902 (2007).
[Crossref] [PubMed]

Cole, G.

G. Cole, I. Wilson-Rae, M. Vanner, S. Gröblacher, J. Pohl, M. Zorn, M. Weyers, A. Peters, and M. Aspelmeyer, “Megahertz monocrystalline optomechanical resonators with minimal dissipation,” in “Proc. IEEE Micr. Elect.,” (2010), pp. 847–850.

Cole, G. D.

D. Brodoceanu, G. D. Cole, N. Kiesel, M. Aspelmeyer, and D. Bauerle, “Femtosecond laser fabrication of high reflectivity micromirrors,” Appl. Phys. Lett. 97, 041104 (2010).
[Crossref]

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5, 485–488 (2009).
[Crossref]

Craighead, H. G.

S. S. Verbridge, D. F. Shapiro, H. G. Craighead, and J. M. Parpia, “Macroscopic tuning of nanomechanics: substrate bending for reversible control of frequency and quality factor of nanostring resonators,” Nano Lett. 7, 1728–1735 (2007).
[Crossref] [PubMed]

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[Crossref]

de Dood, M. J. A.

D. Kleckner, W. Marshall, M. J. A. de Dood, K. N. Dinyari, B.-J. Pors, W. T. M. Irvine, and D. Bouwmeester, “High Finesse Opto-Mechanical Cavity with a Movable Thirty-Micron-Size Mirror,” Phys. Rev. Lett. 96, 173901 (2006).
[Crossref] [PubMed]

Degen, C. L.

C. L. Degen, M. Poggio, H. J. Mamin, C. T. Rettner, and D. Rugar, “Nanoscale magnetic resonance imaging,” Proc. Natl. Acad. Sci. USA 106, 1313–1317 (2009).
[Crossref] [PubMed]

Dinyari, K. N.

D. Kleckner, W. Marshall, M. J. A. de Dood, K. N. Dinyari, B.-J. Pors, W. T. M. Irvine, and D. Bouwmeester, “High Finesse Opto-Mechanical Cavity with a Movable Thirty-Micron-Size Mirror,” Phys. Rev. Lett. 96, 173901 (2006).
[Crossref] [PubMed]

Diósi, L.

L. Diósi, “Models for universal reduction of macroscopic quantum fluctuations,” Phys. Rev. A 40, 1165–1174 (1989).
[Crossref] [PubMed]

Donner, T.

J. D. Teufel, T. Donner, D. Li, J. H. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband Cooling Micromechanical Motion to the Quantum Ground State,” ArXiv e-prints (2011).

Eichenfeld, M.

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

Eichenfield, M.

Eliel, E.

D. Kleckner, I. Pikovski, E. Jeffrey, L. Ament, E. Eliel, J. van den Brink, and D. Bouwmeester, “Creating and verifying a quantum superposition in a micro-optomechanical system,” New J. Phys. 10, 095020 (2008).
[Crossref]

Ferreira, A.

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical Entanglement between a Movable Mirror and a Cavity Field,” Phys. Rev. Lett. 98, 030405 (2007).
[Crossref] [PubMed]

Gigan, S.

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B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. B. Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008).
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J. D. Teufel, T. Donner, D. Li, J. H. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband Cooling Micromechanical Motion to the Quantum Ground State,” ArXiv e-prints (2011).

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D. Kleckner, W. Marshall, M. J. A. de Dood, K. N. Dinyari, B.-J. Pors, W. T. M. Irvine, and D. Bouwmeester, “High Finesse Opto-Mechanical Cavity with a Movable Thirty-Micron-Size Mirror,” Phys. Rev. Lett. 96, 173901 (2006).
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U. Akram, N. Kiesel, M. Aspelmeyer, and G. J. Milburn, “Single-photon opto-mechanics in the strong coupling regime,” New J. Phys. 12, 083030 (2010).
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K. Kamijo, R. Uozumi, K. Moriziri, S. A. Pahlovy, and I. Miyamoto, “Two stage ion beam figuring and smoothening method for shape error correction of ULE substrates of extreme ultraviolet lithography projection optics: Evaluation of high-spatial frequency roughness,” J. Vac. Sci. Technol. B 27, 2900 (2009)
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I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of Ground State Cooling of a Mechanical Oscillator Using Dynamical Backaction,” Phys. Rev. Lett. 99, 093901 (2007).
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A. Nunnenkamp, K. Børkje, J. G. E. Harris, and S. M. Girvin, “Cooling and squeezing via quadratic optomechanical coupling,” Phys. Rev. A 82, 021806 (2010).
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D. Kleckner, W. T. M. Irvine, S. S. R. Oemrawsingh, and D. Bouwmeester, “Diffraction-limited high-finesse optical cavities,” Phys. Rev. A 81 (2010).
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K. Kamijo, R. Uozumi, K. Moriziri, S. A. Pahlovy, and I. Miyamoto, “Two stage ion beam figuring and smoothening method for shape error correction of ULE substrates of extreme ultraviolet lithography projection optics: Evaluation of high-spatial frequency roughness,” J. Vac. Sci. Technol. B 27, 2900 (2009)
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Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfeld, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nat. Photonics 4, 236–242 (2010).
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S. S. Verbridge, D. F. Shapiro, H. G. Craighead, and J. M. Parpia, “Macroscopic tuning of nanomechanics: substrate bending for reversible control of frequency and quality factor of nanostring resonators,” Nano Lett. 7, 1728–1735 (2007).
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G. Cole, I. Wilson-Rae, M. Vanner, S. Gröblacher, J. Pohl, M. Zorn, M. Weyers, A. Peters, and M. Aspelmeyer, “Megahertz monocrystalline optomechanical resonators with minimal dissipation,” in “Proc. IEEE Micr. Elect.,” (2010), pp. 847–850.

Pikovski, I.

D. Kleckner, I. Pikovski, E. Jeffrey, L. Ament, E. Eliel, J. van den Brink, and D. Bouwmeester, “Creating and verifying a quantum superposition in a micro-optomechanical system,” New J. Phys. 10, 095020 (2008).
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Poggio, M.

C. L. Degen, M. Poggio, H. J. Mamin, C. T. Rettner, and D. Rugar, “Nanoscale magnetic resonance imaging,” Proc. Natl. Acad. Sci. USA 106, 1313–1317 (2009).
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G. Cole, I. Wilson-Rae, M. Vanner, S. Gröblacher, J. Pohl, M. Zorn, M. Weyers, A. Peters, and M. Aspelmeyer, “Megahertz monocrystalline optomechanical resonators with minimal dissipation,” in “Proc. IEEE Micr. Elect.,” (2010), pp. 847–850.

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D. Kleckner, W. Marshall, M. J. A. de Dood, K. N. Dinyari, B.-J. Pors, W. T. M. Irvine, and D. Bouwmeester, “High Finesse Opto-Mechanical Cavity with a Movable Thirty-Micron-Size Mirror,” Phys. Rev. Lett. 96, 173901 (2006).
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S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
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C. L. Degen, M. Poggio, H. J. Mamin, C. T. Rettner, and D. Rugar, “Nanoscale magnetic resonance imaging,” Proc. Natl. Acad. Sci. USA 106, 1313–1317 (2009).
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A. Schliesser, O. Arcizet, R. Rivière, G. Anetsberger, and T. J. Kippenberg, “Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit,” Nat. Phys. 5, 509–514 (2009).
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A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved Sideband Cooling of a Micromechanical Oscillator,” Nat. Phys. 4, 415–419 (2008).
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M. Roseman and P. Grutter, “Cryogenic magnetic force microscope,” Rev. Sci. Instrum. 71, 3782–3787 (2000).
[Crossref]

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

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C. L. Degen, M. Poggio, H. J. Mamin, C. T. Rettner, and D. Rugar, “Nanoscale magnetic resonance imaging,” Proc. Natl. Acad. Sci. USA 106, 1313–1317 (2009).
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J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” ArXiv e-prints (2011).

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A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
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Schliesser, A.

A. Schliesser, O. Arcizet, R. Rivière, G. Anetsberger, and T. J. Kippenberg, “Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit,” Nat. Phys. 5, 509–514 (2009).
[Crossref]

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved Sideband Cooling of a Micromechanical Oscillator,” Nat. Phys. 4, 415–419 (2008).
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S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5, 485–488 (2009).
[Crossref]

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B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. B. Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008).
[Crossref]

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S. S. Verbridge, D. F. Shapiro, H. G. Craighead, and J. M. Parpia, “Macroscopic tuning of nanomechanics: substrate bending for reversible control of frequency and quality factor of nanostring resonators,” Nano Lett. 7, 1728–1735 (2007).
[Crossref] [PubMed]

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J. D. Teufel, T. Donner, D. Li, J. H. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband Cooling Micromechanical Motion to the Quantum Ground State,” ArXiv e-prints (2011).

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W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, “Towards Quantum Superpositions of a Mirror,” Phys. Rev. Lett. 91, 130401 (2003).
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J. D. Teufel, T. Donner, D. Li, J. H. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband Cooling Micromechanical Motion to the Quantum Ground State,” ArXiv e-prints (2011).

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]

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J. D. Teufel, T. Donner, D. Li, J. H. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband Cooling Micromechanical Motion to the Quantum Ground State,” ArXiv e-prints (2011).

Thompson, J. D.

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
[Crossref]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
[Crossref] [PubMed]

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. B. Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008).
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D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical Entanglement between a Movable Mirror and a Cavity Field,” Phys. Rev. Lett. 98, 030405 (2007).
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Uozumi, R.

K. Kamijo, R. Uozumi, K. Moriziri, S. A. Pahlovy, and I. Miyamoto, “Two stage ion beam figuring and smoothening method for shape error correction of ULE substrates of extreme ultraviolet lithography projection optics: Evaluation of high-spatial frequency roughness,” J. Vac. Sci. Technol. B 27, 2900 (2009)
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Vahala, K. J.

Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfeld, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nat. Photonics 4, 236–242 (2010).
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M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
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van den Brink, J.

D. Kleckner, I. Pikovski, E. Jeffrey, L. Ament, E. Eliel, J. van den Brink, and D. Bouwmeester, “Creating and verifying a quantum superposition in a micro-optomechanical system,” New J. Phys. 10, 095020 (2008).
[Crossref]

Vanner, M.

G. Cole, I. Wilson-Rae, M. Vanner, S. Gröblacher, J. Pohl, M. Zorn, M. Weyers, A. Peters, and M. Aspelmeyer, “Megahertz monocrystalline optomechanical resonators with minimal dissipation,” in “Proc. IEEE Micr. Elect.,” (2010), pp. 847–850.

Vanner, M. R.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5, 485–488 (2009).
[Crossref]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724 (2009).
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Vedral, V.

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical Entanglement between a Movable Mirror and a Cavity Field,” Phys. Rev. Lett. 98, 030405 (2007).
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Verbridge, S. S.

S. S. Verbridge, D. F. Shapiro, H. G. Craighead, and J. M. Parpia, “Macroscopic tuning of nanomechanics: substrate bending for reversible control of frequency and quality factor of nanostring resonators,” Nano Lett. 7, 1728–1735 (2007).
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S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[Crossref]

Vitali, D.

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical Entanglement between a Movable Mirror and a Cavity Field,” Phys. Rev. Lett. 98, 030405 (2007).
[Crossref] [PubMed]

Weyers, M.

G. Cole, I. Wilson-Rae, M. Vanner, S. Gröblacher, J. Pohl, M. Zorn, M. Weyers, A. Peters, and M. Aspelmeyer, “Megahertz monocrystalline optomechanical resonators with minimal dissipation,” in “Proc. IEEE Micr. Elect.,” (2010), pp. 847–850.

Whittaker, J. D.

J. D. Teufel, T. Donner, D. Li, J. H. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband Cooling Micromechanical Motion to the Quantum Ground State,” ArXiv e-prints (2011).

Wilson-Rae, I.

G. Cole, I. Wilson-Rae, M. Vanner, S. Gröblacher, J. Pohl, M. Zorn, M. Weyers, A. Peters, and M. Aspelmeyer, “Megahertz monocrystalline optomechanical resonators with minimal dissipation,” in “Proc. IEEE Micr. Elect.,” (2010), pp. 847–850.

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of Ground State Cooling of a Mechanical Oscillator Using Dynamical Backaction,” Phys. Rev. Lett. 99, 093901 (2007).
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Yamamoto, M.

M. Yamamoto, “Sub-nm figure error correction of an extreme ultraviolet multilayer mirror by its surface milling,” Nucl. Instrum. Methods Phys. Res., A 467–468, 1282–1285 (2001).
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Yang, C.

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
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B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. B. Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008).
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Zeilinger, A.

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical Entanglement between a Movable Mirror and a Cavity Field,” Phys. Rev. Lett. 98, 030405 (2007).
[Crossref] [PubMed]

Zorn, M.

G. Cole, I. Wilson-Rae, M. Vanner, S. Gröblacher, J. Pohl, M. Zorn, M. Weyers, A. Peters, and M. Aspelmeyer, “Megahertz monocrystalline optomechanical resonators with minimal dissipation,” in “Proc. IEEE Micr. Elect.,” (2010), pp. 847–850.

Zwerger, W.

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of Ground State Cooling of a Mechanical Oscillator Using Dynamical Backaction,” Phys. Rev. Lett. 99, 093901 (2007).
[Crossref] [PubMed]

Zwickl, B. M.

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
[Crossref]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
[Crossref] [PubMed]

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. B. Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008).
[Crossref]

Appl. Phys. Lett. (3)

D. Brodoceanu, G. D. Cole, N. Kiesel, M. Aspelmeyer, and D. Bauerle, “Femtosecond laser fabrication of high reflectivity micromirrors,” Appl. Phys. Lett. 97, 041104 (2010).
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B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. B. Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008).
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H. J. Mamin and D. Rugar, “Sub-attonewton force detection at millikelvin temperatures,” Appl. Phys. Lett. 79, 3358–3360 (2001).
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S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[Crossref]

J. Vac. Sci. Technol. B (1)

K. Kamijo, R. Uozumi, K. Moriziri, S. A. Pahlovy, and I. Miyamoto, “Two stage ion beam figuring and smoothening method for shape error correction of ULE substrates of extreme ultraviolet lithography projection optics: Evaluation of high-spatial frequency roughness,” J. Vac. Sci. Technol. B 27, 2900 (2009)
[Crossref]

Nano Lett. (1)

S. S. Verbridge, D. F. Shapiro, H. G. Craighead, and J. M. Parpia, “Macroscopic tuning of nanomechanics: substrate bending for reversible control of frequency and quality factor of nanostring resonators,” Nano Lett. 7, 1728–1735 (2007).
[Crossref] [PubMed]

Nat. Photonics (1)

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

Nat. Phys. (3)

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved Sideband Cooling of a Micromechanical Oscillator,” Nat. Phys. 4, 415–419 (2008).
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A. Schliesser, O. Arcizet, R. Rivière, G. Anetsberger, and T. J. Kippenberg, “Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit,” Nat. Phys. 5, 509–514 (2009).
[Crossref]

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5, 485–488 (2009).
[Crossref]

Nature (3)

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref] [PubMed]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724 (2009).
[Crossref] [PubMed]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
[Crossref] [PubMed]

New J. Phys. (3)

D. Kleckner, I. Pikovski, E. Jeffrey, L. Ament, E. Eliel, J. van den Brink, and D. Bouwmeester, “Creating and verifying a quantum superposition in a micro-optomechanical system,” New J. Phys. 10, 095020 (2008).
[Crossref]

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
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U. Akram, N. Kiesel, M. Aspelmeyer, and G. J. Milburn, “Single-photon opto-mechanics in the strong coupling regime,” New J. Phys. 12, 083030 (2010).
[Crossref]

Nucl. Instrum. Methods Phys. Res., A (1)

M. Yamamoto, “Sub-nm figure error correction of an extreme ultraviolet multilayer mirror by its surface milling,” Nucl. Instrum. Methods Phys. Res., A 467–468, 1282–1285 (2001).
[Crossref]

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Phys. Rev. Lett. (7)

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical Entanglement between a Movable Mirror and a Cavity Field,” Phys. Rev. Lett. 98, 030405 (2007).
[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).
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A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Quantum measurement of phonon shot noise,” Phys. Rev. Lett. 104, 213603 (2010).
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W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, “Towards Quantum Superpositions of a Mirror,” Phys. Rev. Lett. 91, 130401 (2003).
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[Crossref] [PubMed]

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of Ground State Cooling of a Mechanical Oscillator Using Dynamical Backaction,” Phys. Rev. Lett. 99, 093901 (2007).
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G. Cole, I. Wilson-Rae, M. Vanner, S. Gröblacher, J. Pohl, M. Zorn, M. Weyers, A. Peters, and M. Aspelmeyer, “Megahertz monocrystalline optomechanical resonators with minimal dissipation,” in “Proc. IEEE Micr. Elect.,” (2010), pp. 847–850.

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Other (3)

J. D. Teufel, T. Donner, D. Li, J. H. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband Cooling Micromechanical Motion to the Quantum Ground State,” ArXiv e-prints (2011).

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” ArXiv e-prints (2011).

Mirrors were deposited by Coastline Optics, LLC, located in Camarillo, CA, USA.

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Figures (4)

Fig. 1
Fig. 1 The main steps in the fabrication process, carried out on a silicon wafer (gray). a) The process begins with the deposition of the SiO2 (blue) / Ta2O5 (pink) dielectric mirror, which is then etched into discs of the desired size (only 7 of the 33 dielectric layers are shown). b) Si3N4 (green) is deposited on both sides of the wafer. c) The front side Si3N4 is etched into the resonator geometry and the backside has square holes etched for the Si etch. d) The carrier wafer is etched through with a TMAH anisotropic etch, releasing the resonators. e) A short BHF etch strips the protective SiO2 layer off the front of the mirror, and the sample is then removed from solution with a critical point dry.
Fig. 2
Fig. 2 Three micro-optomechanical resonators, as viewed from the top of the carrier wafer. Left: optical image, diameter d = 80 μm, Si3N4 of thickness t = 500 nm, with resonator arms of diagonal length a = 250 μm and width w = 20 μm. Center: optical image, d = 80 μm, t = 300 nm, a = 2000 μm, w = 2 μm. Right: scanning electron microscope image, d = 40 μm, t = 500 nm, a = 500 μm, w = 10 μm. Note that the anisotropic etch profile of TMAH is clearly visible in the silicon at the top of the image.
Fig. 3
Fig. 3 The signal from the photodiode monitoring the cavity transmission during a typical optical ringdown measurement, showing the exponential decay of the signal after the pump laser is switched off via the AOM (averaged over 16 runs to reduce noise). Fitting the data starting 0.5 μs after the AOM switch results in an exponential decay time of τcav = 2.11 ± 0.02 μs.
Fig. 4
Fig. 4 a) The normalized amplitude of the fundamental mechanical resonance of a low frequency (9.174 kHz) resonator after it is excited by moving by one of the alignment motors by a single step. Data from the first minute after the excitation (not shown) is heavily distorted due to the mechanical amplitude becoming larger than the equivalent width of the optical peak (λ/2F ∼ 5 nm). Fitting the data after t = 80 s results in a power decay time of τ = 15.4 ± 0.3 s, or a mechanical quality factor of Qm = (9.4 ± 0.2) × 105. b) The thermal resonance spectrum of a high frequency (ωm = 2π × 157.7 kHz) trampoline resonator. A fit to a Lorentzian gives a peak width (FWHM) of δωm = 2π × 3.64±0.15 Hz, corresponding to Qm = (4.3 ± 0.2) × 104.

Tables (2)

Tables Icon

Table 1 Dependence of frequency and quality factor on temperature as 157.7 kHz device is cooled to 300 mK with a dilution refrigerator.

Tables Icon

Table 2 A comparison of trampoline resonators with other previously demonstrated opto-mechanical systems.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

g = ω c L x 0 ,
g = g τ cav = 2 F x 0 λ .
Q m 1 exp ( h ¯ ω m k B T ) 1
T Q m h ¯ ω m k B .

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