We present a new micromechanical resonator designed for cavity optomechanics.
We have used a micropillar geometry to obtain a high-frequency mechanical
resonance with a low effective mass and a very high quality factor. We have
coated a 60-$\mu$m diameter low-loss dielectric mirror on top of the pillar and
are planning to use this micromirror as part of a high-finesse Fabry-Perot
cavity, to laser cool the resonator down to its quantum ground state and to
monitor its quantum position fluctuations by quantum-limited optical
interferometry

Bahriz, M.

Briant, T.

Chartier, C.

Cohadon, P. -F.

Ducloux, O.

Flaminio, R.

Heidmann, A.

Kuhn, A. G.

Michel, C.

Pinard, L.

Traon, O. Le

English

arXiv

A. G. Kuhn

M. Bahriz

O. Ducloux

C. Chartier

O. Le Traon

T. Briant

P.-F. Cohadon

A. Heidmann

C. Michel

L. Pinard

R. Flaminio

Crossref

Applied Physics Letters

A micropillar for cavity optomechanics

International audienceWe present a new micromechanical resonator designed for cavity optomechanics. We have used a micropillar geometry to obtain a high-frequency mechanical resonance with a low effective mass and a very high quality factor. We have coated a 60-µm diameter low-loss dielectric mirror on top of the pillar and are planning to use this micromirror as part of a high-finesse Fabry-Perot cavity, to laser cool the resonator down to its quantum ground state and to monitor its quantum position fluctuations by quantum-limited optical interferometry

Le Traon, O.

Cohadon, P.-F.

HAL-IN2P3

A micropillar for cavity optomechanicsA. G. Kuhn, M. Bahriz, O. Ducloux, C. Chartier, O. Le Traon, T. Briant, P.-F. Cohadon, A. Heidmann, Christine Michel, L. Pinard, et al.To cite this version:A. G. Kuhn, M. Bahriz, O. Ducloux, C. Chartier, O. Le Traon, et al.. A micropillar for cavityoptomechanics. Applied Physics Letters, American Institute of Physics, 2011, 99, pp.121103.<10.1063/1.3641871>. <hal-00609698>HAL Id: hal-00609698https://hal.archives-ouvertes.fr/hal-00609698Submitted on 19 Jul 2011HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.A micropillar for cavity optomechanicsA. G. Kuhn,2, a) M. Bahriz,1 O. Ducloux,1 C. Chartier,1 O. Le Traon,1, b) T. Briant,2 P.-F. Cohadon,2 A.Heidmann,2 C. Michel,3 L. Pinard,3 and R. Flaminio31)ONERA, Physics Department; 29 avenue de la Division Leclerc, 92322 Châtillon,France2)Laboratoire Kastler Brossel, ENS, UPMC, CNRS; case 74, 4 place Jussieu, 75005 Paris,France3)Laboratoire des Matériaux Avancés, CNRS, IN2P3; Bâtiment Virgo, 7 avenue Pierre de Coubertin,69622 Villeurbanne, FranceWe present a new micromechanical resonator designed for cavity optomechanics. We have used a micropillargeometry to obtain a high-frequency mechanical resonance with a low effective mass and a very high qualityfactor. We have coated a 60-µm diameter low-loss dielectric mirror on top of the pillar and are planning to usethis micromirror as part of a high-finesse Fabry-Perot cavity, to laser cool the resonator down to its quantumground state and to monitor its quantum position fluctuations by quantum-limited optical interferometry.Reaching the quantum ground state of a macroscopicmechanical object is a major experimental challenge inphysics, at the origin of the rapid emergence of the cav-ity optomechanics research field. Many groups havebeen targeting this objective for a decade1–4, using awide range of resonators oscillating at frequencies froma few Hz to the GHz-band1,3, and different techniquesof displacement sensing2,3,5,6. The development of avery sensitive position sensor combined with a mechan-ical resonator in its ground state would have importantconsequences7, not only for fundamental aspects in quan-tum physics such as entanglement8 and decoherence ofmechanical resonators, but also for potential applicationssuch as the detection of very weak forces.Two conditions have to be fulfilled in order to reachand demonstrate the mechanical ground state. The ther-mal energy has to be small with respect to the zero-pointquantum energy: kBTc  hνm. For a resonator oscillat-ing at a frequency νm = 4MHz, the resulting tempera-ture Tc is in the sub-mK range and conventional cryo-genic cooling has therefore to be combined with novelcooling mechanisms such as cavity cooling in a Fabry-Perot cavity4,9–11.The second requirement is obviously to be able to de-tect the very small residual displacement fluctuations as-sociated with the quantum ground state. The measure-ment sensitivity must be better than the expected dis-placement noise at resonance, which scales asSx[νm] '(25µgM)(Qc2× 103)(4MHzνm)210−38m2/Hz,whereM is the effective mass of the resonator and Qc itsmechanical quality factor. As all optical cooling mecha-nisms increase the damping, Qc is here the final qualityfactor related to the intrinsic quality factor Q of the res-onator by QcTc = QT , where Tc/T is the cooling ratio.a)Electronic mail: aurelien.kuhn@spectro.jussieu.frb)Electronic mail: Olivier.Le_Traon@onera.fr(a)(b)MicropillarMembraneLaser beamDynamical frameFigure 1. 3D artist view of the micropillar (a) and finite-element simulation of the displacement field of the firstcompression-expansion mode of the pillar (b).One thus may use a resonator with an ultra-highQ, largerthan 106, at a cryogenic temperature of 100mK, in or-der to ensure a sufficient Qc ' 1000 at the final effectivetemperature.In this letter, we present the mechanical design and ex-perimental characterization of such a resonator. It con-sists in a micropillar mechanically decoupled from thewafer by a dynamical frame and clamped at its center bya thin membrane. A high-reflectivity mirror is coated ontop of the pillar, thus providing a way for interferometricsensing of its motion and for future applications in cav-ity optomechanics. Advantages of such a pillar geometryare twofold. First, a compression-expansion mechanicalmode of the pillar has a longitudinal node at its center,decreasing mechanical loss through the membrane. Sec-ond, the top area of the pillar has a quasi-null strain,reducing the influence of the relatively poor mechanicalquality of the optical layers13 on the overall mechanicalQ.We present in the following the full design of theresonator using finite-element modelling (FEM) simula-tions, its microfabrication and experimental mechanicalcharacterization (resonance frequency and Q factor) us-ing a Michelson-interferometer test bench.As shown in Fig. 1, the basic structure is a L = 1mmlong and 240-µm wide pillar made of crystalline quartz,clamped at its center to the external frame by a 20-µm11 mm(a)1 mm(b)100 mm(c)100 mm(d)Figure 2. Optical view (a) and scanning electron microscope picture (b) of the full structure with the micropillar at the center,its clamping membrane and dynamical frame; closer view of the micropillar before the optical coating (c), and top view of thecoating (d).thin membrane. According to FEM simulations, with abulk Young modulus E = 102.7GPa and a density ρ =2648 kg/m3, resonance frequency and effective mass areexpected around 3.2MHz and 25µg for the fundamentalvibration mode.We have chosen to use a single quartz crystal as bulkmaterial to benefit from its high intrinsic quality fac-tor, with a value Qint ' 5 × 106 expected at roomtemperature14,15, which can be increased by one to twoorders of magnitude at cryogenic temperature16. Viscousair damping might be another limiting factor, but is ex-perimentally negligible for pressures below 10−1mBar.As the effect of the mirror coated on top of the pillar isexpected to be negligible as well, the main limitation tothe quality factor is due to Poisson effects induced insidethe membrane by the radial deformations of the pillar atthe vibration node. A crystallographic orientation of thepillar along the Z axis has been chosen, as well as a pillarequilateral cross-section with respect to the quartz trig-onal symmetry: a nominally symmetric structure withregard to its median plane is thus possible, which is asine qua non condition to obtain a good balancing of thelength extension mode. In order to reduce mechanicallosses, we have carefully designed an external dynamicalframe12 clamped to the wafer by another membrane (seeFigs. 1b, 2a and 2b). The oscillation of the frame withan opposite phase then makes up for Poisson effects. Thewhole geometry has been optimized by FEM simulation(using SAMCEF code) to get an exact matching betweenthe pillar and frame momenta, thus strongly decreasingthe energy density at the location of the external mem-brane, and reducing clamping losses to a minimum. As-suming that all the energy remaining within the externalmembrane is lost, one gets an underestimated value of Qaround 106.The resonator microfabrication process takes advan-tage of standard techniques of quartz wet etching, usingfluorhydric acid. Starting from a superpolished (down to2Årms) ultrapure quartz substrate, the wafer is metal-lized with a 15-nm thick layer of chromium and a 200-nmlayer of gold. These layers are used as a long-time resistmask for the etching of the membrane, down to a thick-ness as low as 20µm. Wet etching ensures quasi perfectLaserOutInNetwork analyzerRFPZAMOLocaloscillator Vacuum chamberPZAPillarRF amp.Figure 3. Michelson interferometer setup used to characterizethe mechanical properties of the resonator.symmetry of the pillar with respect to the membrane,which appears as an essential condition to reduce clamp-ing losses and to reach a high Q.Another important condition to reduce mechanical lossis to coat the mirror only on top of the pillar. For thatpurpose we use a 3D 5-µm thick photoresist mask. A pho-tolithography followed by a developer bath allows one toremove the resist mask over a well-defined zone, which isa 60-µm diameter spot centered on the top of the pillar.The mirror coated by evaporation technique is a stack of15 SiO2/Ta2O5 quarter-wave doublets, with a 100 ppmexpected transmission. After coating, the photoresist isremoved by standard lift-off techniques, without damag-ing the optical properties (see Fig. 2d). Measurement ofthe micropillar reflectivity using a dedicated Fabry-Perotcavity is in progress.To characterize the mechanical properties of the res-onator, a Michelson interferometer with a Nd:YAG lasersource has been built (see Fig. 3). The micropillar ismounted on a high-frequency piezoelectric actuator (RFPZA) driven by a high-power RF amplifier. A micro-scope objective (MO) focuses the laser beam down to afew microns on the sample surface. The whole sensor armis in a vacuum chamber pumped down to 10−3mBar. Aphotodiode detects the laser intensity at the output ofthe interferometer, its low-frequency signal being used tocontrol the length of the local oscillator arm through a2Frequency (MHz)Spectral amplitude (dB)0-10-20-303.6642 3.6644 3.6646 3.6648Time (ms)0 5 10 15Amplitude (dB)0-5-10-15offonFigure 4. Spectrum of the micropillar mechanical responsearound its fundamental resonance frequency at 3.66MHz(left), and ring-down response for the same mechanical mode(right).feedback loop. The spectral mechanical response of themicropillar is obtained using a network analyzer to syn-chronously drive the resonator into motion and monitorthe radio-frequency photodiode signal.Fig. 4 (left) presents an example of such a mechanicalresponse spectrum: the mechanical resonance is observedaround 3.66MHz, in good agreement with the FEM sim-ulation results. The slight asymmetry of the resonanceis attributed to an electrical interference between the op-tomechanically induced RF signal detected on the pho-todiode and a spurious modulation radiated by the RFamplifier. The interferometric measurement being sensi-tive to longitudinal displacements of the surface, only afew and well-isolated compression-expansion mechanicalresonances are observed as expected from FEM simula-tions, with a dynamical response at least 40 dB over themechanical background.The optical spot can be swept over the whole surfaceof the resonator, allowing for a mapping of the vibrationprofile. It is mostly found uniform over the upper surfaceof the pillar, with a typical displacement amplitude ofthe order of 5 nm, to be compared to the piezoelectricactuator displacement, measured at a 20 pm level on thesubstrate.As the intrinsic interferometer jitter may widen theobserved mechanical resonance, its quality factor is mea-sured using a ring-down technique: once the resonatoris driven close to its resonance frequency, the actuationis switched off and we record the time evolution of thefree resonator motion using a spectrum analyzer in zero-span mode. The observed exponential decay then givesthe damping time, hence the quality factor. Results de-pend on the residual thickness of the membrane: typicalvalues are larger than 105, reaching values as large asQ = 1.8× 106 for the best samples without optical coat-ing. Work is in progress to reduce the membrane thick-ness and to improve the pillar symmetry, in particular byusing optical coatings on both sides.To conclude, we have developed a new quartz resonatorin a compression-expansion mode, suitable for cavity op-tomechanics. Preliminary mechanical and optical char-acterizations yield promising results for the optomechan-ical coupling that can be obtained with this device. Nextsteps will be the operation of the resonator in a dedi-cated high-finesse Fabry-Perot cavity, inside a dilutionfridge working at a base temperature of 30mK. Thanksto the very high mechanical quality factor of the oscilla-tor, we expect to reach a final effective temperature atthe 100µK level using laser cooling, thus demonstratingthe quantum ground state of such a macroscopic optome-chanical system.The authors acknowledge practical help from J.Teissier for the scanning electron microscope pictures,and financial support of the "Agence Nationale de laRecherche" (ANR) France, Programme blanc, N◦ ANR-07-BLAN-2060 ARQOMM and of FP7 Specific TargetedResearch Project Minos.REFERENCES1X.M.H. Huang, C.A. Zorman, M. Mehregany, and M.L.Roukes, Nature 421, 496 (2003).2M.D. LaHaye, O. Buu, B. Camarota, and K.C. Schwab,Science 304, 74 (2004).3A.D. O’Connell, M. Hofheinz, M. Ansmann, R.C. Bial-czak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H.Wang, M. Weides, J. Wenner, J.M. Martinis, and A.N.Cleland, Nature 464, 697 (2010).4J.D. Teufel, T. Donner, D. Li, J.H. Harlow, M.S. All-man, K. Cicak, A.J. Sirois, J.D. Whittaker, K.W.Lehnert, and R.W. 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