Multidimensional optomechanical cantilevers for high-frequency force sensing

Doolin, C.; Kim, P H; Hauer, Bradley; MacDonald, Andrew; Davis, J. P.

doi:10.1088/1367-2630/16/3/035001

Cited by 52 publications

(45 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In dispersivelycoupled systems, the motion of the mechanical resonator shifts the resonance frequency of the optical cavity, which can in turn be observed as periodic changes in the amplitude or phase of light traversing the cavity. Optomechanics thus provides an extremely sensitive readout for micro-and nano-mechanical resonators, enabling their use as exquisite sensors of a variety of phenomena on small scales, including displacement [2], force [3][4][5], torque [6,7] and acceleration [8]. This readout sensitivity has also motivated fundamental searches for quantum properties of nanomechanical resonators [9] at, or near, their vibrational ground state where mechanical motion originates from quantum zero-point fluctuations.…”

Section: Introductionmentioning

confidence: 99%

Optomechanics and thermometry of cryogenic silica microresonators

et al. 2016

View full text Add to dashboard Cite

We present measurements of silica optomechanical resonators, known as bottle resonators, passively cooled in a cryogenic environment. These devices possess a suite of properties that make them advantageous for preparation and measurement in the mechanical ground state, including high mechanical frequency, high optical and mechanical quality factors, and optomechanical sideband resolution. Performing thermometry of the mechanical motion, we find that the optical and mechanical modes demonstrate quantitatively similar laser-induced heating, limiting the lowest average phonon occupation observed to just ∼1500. Thermalization to the 9 mK thermal bath would facilitate quantum measurements on these promising nanogram-scale mechanical resonators.

show abstract

Section: Introductionmentioning

confidence: 99%

Optomechanics and thermometry of cryogenic silica microresonators

et al. 2016

View full text Add to dashboard Cite

show abstract

“…We also demonstrate the role of second order optomechanical coupling in our signals, providing a framework for enhancing this effect. Maximizing second order optomechanical coupling while eliminating first order coupling should provide a route to QND measurements at low temperatures.The optomechanical cavity being measured is a nanocantilever with effective mass m = 240 fg, as described elsewhere [29], fabricated on-chip, in the evanescent field of an optical microdisk. The Hamiltonian for independent optical and mechanical cavities can be writtenĤ =Ĥ opt +Ĥ m , whereĤ opt =hω 0 â †â + 1/2 and H m =hΩ 0 b †b + 1/2 are the Hamiltonians of the optical and mechanical resonators.…”

mentioning

confidence: 99%

“…The optomechanical cavity being measured is a nanocantilever with effective mass m = 240 fg, as described elsewhere [29], fabricated on-chip, in the evanescent field of an optical microdisk. The Hamiltonian for independent optical and mechanical cavities can be writtenĤ =Ĥ opt +Ĥ m , whereĤ opt =hω 0 â †â + 1/2 and H m =hΩ 0 b †b + 1/2 are the Hamiltonians of the optical and mechanical resonators.…”

mentioning

confidence: 99%

“…Thereforê is the interaction Hamiltonian to second order. For a device with symmetric out-of-plane motion in a symmetric evanescent optical field one anticipates second order optomechanical coupling, with first order coupling arising from asymmetries in the motion or optical field [29]. We measure the optical transmission through a tapered optical fiber coupled to the optical resonator, Fig.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear optomechanics in the stationary regime

et al. 2014

View full text Add to dashboard Cite

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...

show abstract

“…A resonator with high Q supplies high sensitivity, low noise, and low energy consumption. Besides high Q, the resonators also requires to operate at high frequency, for example, to enhance the time resolution of measurement in atomic force microscopy and real-time measurements [6]. In order to increase the resonant frequency, the size of the resonator needs to be decreased.…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic Damping Depending on Vibration Modes of Nano Beam Resonator

Hoang¹

2016

Comm. in Phys.

View full text Add to dashboard Cite

Abstract. The obtainable quality factor for a nano beam resonator is limited due to internal damping such as thermoelastic damping. Therefore, understanding how internal damping varies with the respective resonant modes is very important to design a high performance nanoresonator. In this research, we investigate thermoelastic damping depending on vibration modes of nano beam resonators using finite element method. The study results show that the quality factor of a nanoresonator is lower than at high order modes. The silicon nano beam resonator with the quality factor larger than one million can be achieved by optimizing the dimensions of the resonant beam.

show abstract

Multidimensional optomechanical cantilevers for high-frequency force sensing

Cited by 52 publications

References 52 publications

Optomechanics and thermometry of cryogenic silica microresonators

Optomechanics and thermometry of cryogenic silica microresonators

Nonlinear optomechanics in the stationary regime

Thermoelastic Damping Depending on Vibration Modes of Nano Beam Resonator

Contact Info

Product

Resources

About