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Demonstration of Ultra Low Dissipation Optomechanical Resonators on a Chip

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Demonstration of Ultra Low Dissipation Optomechanical Resonators on a Chip Demonstration of Ultra Low Dissipation Optomechanical Resonators on a Chip G. Anetsberger, R. Rivi`ere,A. Schliesser, O. Arcizet & T. J. Kippenberg∗ Max-Planck-Institut f¨urQuantenoptik, Hans-Kopfermann-Str.1, 85748 Garching Cavity-enhanced radiation-pressure coupling of optical and mechanical degrees of freedom gives rise to a range of optomechanical phenomena, in particular providing a route to the quantum regime of mesoscopic mechanical oscillators. A prime challenge in cavity optomechanics has however been to realize systems which simultaneously maximize optical finesse and mechanical quality. Here we demonstrate for the first time independent control over both mechanical and optical degree of freedom within one and the same on-chip resonator. The first direct observation of mechanical normal mode coupling in a micromechanical system allows for a quantitative understanding of mechanical dissipation. Subsequent optimization of the resonator geometry enables intrinsic material loss limited mechanical Q-factors, rivalling the best values reported in the high MHz frequency range, while simultaneously preserving the resonators' ultra-high optical finesse. Besides manifesting a complete understanding of mechanical dissipation in microresonator based optomechanical systems, our results provide an ideal setting for cavity optomechanics. Over the past years it has become experimentally pos- of both is important for applications such as low loss, sible to study the coupling of optical and mechanical narrow-band \photonic clocks"[2, 27] and indispensable modes via cavity enhanced radiation pressure, which for fundamental studies aiming at approaching and de- gives rise to a diverse set of long anticipated optome- tecting quantized motion in mesoscopic optomechanical chanical phenomena[1] such as radiation pressure driven systems[11, 12, 28]. oscillations[2] and, as demonstrated in 2006, dynamic Here we show for the first time independent control over backaction cooling[3, 4, 5, 6, 7]. Moreover, this coupling both optical and mechanical degree of freedom in one can be exploited to perform highly sensitive measure- and the same microscale optomechanical resonator. The ments of displacement[8, 9] which may enable the obser- demonstration of mechanical normal mode coupling[29] vation of radiation pressure quantum backaction[10] or within a micromechanical device and the concomitant ge- related phenomena. Major goals in the emerging field ometry dependence of clamping losses allows a quantita- of cavity-optomechanics[11, 12], such as ground-state tive understanding of mechanical dissipation. We demon- cooling[13, 14] necessitate high optical finesse and high strate monolithic spoke-supported silica resonators com- mechanical quality factors at mechanical oscillation fre- prising a toroidal boundary which allows ultra-high op- quencies exceeding the optical cavity's linewidth. While tical finesse (> 106)[24] rivalling the best values ob- recently impressive progress has been made in creating tained in Fabry-Perot cavities[25]. Independent con- experimental settings in which radiation pressure effects trol of their mechanical properties leads to strongly re- can be studied[3, 4, 5, 15, 16, 17], a prime challenge still duced clamping losses allowing for unprecedented me- concerns attaining simultaneously high optical finesse chanical quality factors (e.g. 80,000 at 38 MHz) { ri- and high mechanical Q-factors. Nearly all approaches so valling the best published values of strained silicon nitride far have combined traditional cm-sized optical elements nanoresonators[19, 20] as well as radial contour-mode (mirrors) with micro- or nanoscale mechanical oscillators disk resonators[21] at similarly high frequencies which which simultaneously act as mirrors[3, 4, 15, 16] (or as allow entering the resolved sideband regime[30, 31] using dispersive element[17]). Other approaches have used the state-of-the-art optical cavities. It is shown that the mea- intrinsic mechanical modes of the optical elements[18]. sured Q-factors are only limited by temperature depen- Yet, in general, the required high reflectivity of the micro- dent intrinsic dissipation[32, 33], which can be reduced arXiv:0802.4384v2 [quant-ph] 18 Jul 2008 element limits its dimension to wavelength size and thus by low temperature operation. Moreover, the observed sets an upper limit to the mechanical frequencies that geometry dependent loss mediated by normal mode cou- can be achieved. Also, it is exceedingly difficult to at- pling may be of relevance across a wide range of micro- tain high mechanical quality factors while maintaining and nanomechanical oscillators, for which a detailed un- high optical reflectivity as independent control of opti- derstanding of dissipation is lacking. cal and mechanical degrees of freedom is generally not possible. Thus, although remarkably high mechanical Q- factors at low frequencies have been obtained[17], this RESULTS and previous approaches[3, 4, 5, 15, 16, 18] have so far not succeeded in combining mechanical Q-factors com- Starting point of our analysis are toroidal silica parable to those achieved in the field of NEMS and microcavites[34] that intrinsically combine ultra-high-Q MEMS[19, 20, 21, 22, 23] with the best values of op- optical whispering gallery modes with around 20 me- tical finesse[24, 25, 26]. But exactly the combination chanical modes in the 0-100 MHz range[9] which are 2 FIG. 1: Observation of mechanical mode coupling. a Mechanical Q-factors (upper panel) and frequencies (lower panel, where solid lines denote results of an FEM simulation) of the radial breathing mode (inset) for varying relative undercut u = L=R. The Q-factors were found to be remarkably reproducible for six different samples and strongly geometry dependent due to intermode coupling. b Q-factors (upper panel) and frequencies (lower panel) of radial breathing mode and a flexural mode of one toroid reveal an avoided crossing confirming that the dispersion lines of both modes do not cross. The mode patterns (radial and flexural modes) hybridize when approaching the coupling region while the corresponding mode patterns switch dispersion lines during the avoided crossing. A coupled harmonic oscillator model (solid lines: coupled Q-factors and frequencies; dashed lines: bare Q-factors and frequencies) allows an excellent fit to the data. observable in an interferometric readout using the struc- onator (cf. Fig. 1a) is varied. To this end consecutive ture's optical modes (see methods). Recent work has XeF2 etching cycles, undercutting the silica structure but shown that the intrinsic coupling of optical and mechani- leaving the silica itself unaffected, are applied. Thus, the cal modes of toroidal microcavities via radiation-pressure relative undercut u = L=R (R: radius of the cavity, L: can give rise to the effect of dynamical backaction[2], length of the free standing membrane, cf. inset of Fig. which allows realization of narrow bandwidth photonic 1a) can be controlled. The dependence of the measured oscillators[27] or photonic RF down-converters[35] as Q-factors of the radial breathing mode (RBM) on the rel- well as radiation pressure cooling of a mechanical ative undercut is depicted in Fig. 1a. Intuitively, it may oscillator[5]. The radial breathing mode (cf. Fig. 1a) in be expected that higher Q-factors are attained for larger particular exhibits strong optomechanical coupling, low undercut due to a reduced clamping area. Interestingly, effective mass (≈ 10−11 kg) and high frequency enabling however, the Q-factors of six different microresonators of the first demonstration of resolved sideband cooling of similar size show a strongly non-monotonous dependence a micromechanical oscillator[30]. To understand their on the relative undercut which contradicts the simple ex- mechanical Q-factors which have remained completely pectation of smaller losses for smaller clamping areas. unexplored so far, we first present a study of mechanical Moreover, the behaviour is remarkably reproducible for dissipation in microtoroids and subsequently show how the different samples. A plot of the measured frequen- the results from this study can be harnessed to devise cies along with an FEM simulation (see methods) of the structures with unprecedentedly low dissipation in the toroids' radially symmetric mechanical modes depicted in frequency range above 30 MHz. Fig. 1a shows excellent agreement of measured and sim- ulated frequencies. Furthermore, the FEM simulation in- dicates an avoided crossing between different mechanical modes as first predicted by Mindlin in 1951[29]. A mea- Observation of mechanical normal mode coupling surement with a different sample allows directly observ- ing this avoided crossing by employing highly sensitive quantum limited optical displacement sensing (see meth- In order to assess the contribution of clamping losses, ods) which allows to also monitor the flexural modes ex- the diameter of the silicon pillar holding the silica res- 3 (0) (1) angular frequencies Ωr=f = Ωr=f + Ωr=f u and Q-factors (0) (1) Qr=f = Qr=f + Qr=f u on the undercut u, these can be used to asymptotically fit the data (cf. Fig. 1b). Using the values obtained from this first fit, only g remains as free parameter in equation (1). A least square fit to both the measured frequencies and Q-factors yields a coupling rate of g = 14 MHz=2π, much larger than the damping rates Γr=f =2π. The corresponding coupled frequencies Ω±=2π and Q-factors Q± match the data remarkably well (cf. Fig. 1b) confirming that indeed both modes behave as two coupled harmonic oscillators giving rise to an avoided crossing between the RBM and the low-Q flexural mode. Moreover, the data presented here, to FIG. 2: Linear relation between D and measured Q- the authors' best knowledge, manifest the first direct factors. Mechanical Q-factors (dots with error bars, left observation of normal mode coupling of two different axis) and corresponding simulated D values (dashed lines, mechanical modes within a micromechanical resonator. right axis) for the radial breathing and a flexural mode of an on-chip toroid show a linear relation in the parameter range depicted where Q ≈ 3 · D. Inset: Mechanical Q-factors de- pending on the background gas pressure.
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