We have observed nonlinear transduction of the thermomechanical motion of a nanomechanical resonator when detected as laser transmission through a sideband unresolved optomechanical cavity. Nonlinear detection mechanisms are of considerable interest as special cases allow for quantum nondemolition measurements of the mechanical resonator's energy. We investigate the origin of the nonlinearity in the optomechanical detection apparatus and derive a theoretical framework for the nonlinear signal transduction, and the optical spring effect, from both nonlinearities in the optical transfer function and second order optomechanical coupling. By measuring the dependence of the linear and nonlinear signal transduction -as well as the mechanical frequency shift -on laser detuning from optical resonance, we provide estimates of the contributions from the linear and quadratic optomechanical couplings.Cavity optomechanics has resulted in new levels of extremely precise displacement transduction [1, 2] of ultrahigh frequency resonators [3]. This has created much interest in pursuing quantum measurements [4] of nanomechancial devices [5][6][7], as well as dynamical back action cooling [8][9][10][11].One of the most fundamental, and as of yet unattained, quantum measurements that could be performed is that of the quantized energy eigenstates of a nanomechanical resonator (as has been demonstrated with an electron in a cyclotron orbit [12]). To achieve this, one cannot measure the displacement of the resonator [13], but instead must measure the energy directly -preferably without destroying the quantum state, a so-called quantum non-demolition (QND) measurement. Whereas the accuracy in continuously measuring two conjugate quantities is limited by the Heisenberg uncertainty principle to the standard quantum limit (SQL) [13], QND measurements allow for continuous measurements of an observable to be taken to arbitrary precision [14][15][16][17]. Here our interest lies in a QND measurement of the energy, and thereby the number of phonons [18]. In an optomechanical system, this is expected to be possible by having strong second order optomechanical coupling [19][20][21][22]. This has been demonstrated in membrane-in-the-middle Fabry-Pérot cavities [23,24], however it has been pointed out there remains first order coupling between the two optical modes, possibly obscuring QND measurements [25].Signal from second order optomechanical coupling, hence measurement of x 2 , will display mechanical peaks at twice the fundamental frequency. However, we would also expect that nonlinear transduction of the displacement, x, of a mechanical resonator from a nonlinear optical transfer function would also appear at harmonics of the mechanical resonance frequency, as has been observed [26][27][28].In this Letter we report observation of peaks in the mechanical power spectra at exactly twice the fundamental mechanical frequency, as shown in Fig. 1. We derive a model for the origin of the harmonic signal, as well as the optical spring effect, from bo...

Non-linear mixing in coupled photonic crystal nanobeam cavities due to cross-coupling opto-mechanical mechanisms Appl.

Reducing the moment of inertia improves the sensitivity of a mechanically based torque sensor, the parallel of reducing the mass of a force sensor, yet the correspondingly small displacements can be difficult to measure. To resolve this, we incorporate cavity optomechanics, which involves co-localizing an optical and mechanical resonance. With the resulting enhanced readout, cavity-optomechanical torque sensors are now limited only by thermal noise. Further progress requires thermalizing such sensors to low temperatures, where sensitivity limitations are instead imposed by quantum noise. Here, by cooling a cavity-optomechanical torque sensor to 25 mK, we demonstrate a torque sensitivity of 2.9 yNm/. At just over a factor of ten above its quantum-limited sensitivity, such cryogenic optomechanical torque sensors will enable both static and dynamic measurements of integrated samples at the level of a few hundred spins.

Micro and nanomechanical resonators with ultra-low dissipation have great potential as useful quantum resources. The superfluid micromechanical resonators presented here possess several advantageous characteristics: straightforward thermalization, dissipationless flow, and in situ tunability. We identify and quantitatively model the various dissipation mechanisms in two resonators, one fabricated from borosilicate glass and one from single crystal quartz. As the resonators are cryogenically cooled into the superfluid state, the damping from thermal effects and from the normal fluid component are strongly suppressed. At our lowest temperatures, damping is limited solely by internal dissipation in the substrate materials, and reach quality factors up to 913,000 at 13 mK. By lifting this limitation through substrate material choice and resonator design, modelling suggests that the resonators should reach quality factors as high as 10 8 at 100 mK, putting this architecture in an ideal position to harness mechanical quantum effects. * souris@ualberta.ca † Present address:

Cavity optomechanics has demonstrated remarkable capabilities, such as measurement and control of mechanical motion at the quantum level. Yet many compelling applications of optomechanics—such as microwave-to-telecom wavelength conversion, quantum memories, materials studies, and sensing applications—require hybrid devices, where the optomechanical system is coupled to a separate, typically condensed matter, system. Here, we demonstrate such a hybrid optomechanical system, in which a mesoscopic ferromagnetic needle is integrated with an optomechanical torsional resonator. Using this system we quantitatively extract the magnetization of the needle, not known a priori, demonstrating the potential of this system for studies of nanomagnetism. Furthermore, we show that we can magnetically dampen its torsional mode from room-temperature to 11.6 K—improving its mechanical response time without sacrificing torque sensitivity. Future extensions will enable studies of high-frequency spin dynamics and broadband wavelength conversion via torque mixing.