Theoretical Analysis of Mechanical Displacement Measurement Using a Multiple Cavity Mode Transducer

Abstract

We present an optomechanical displacement transducer, that relies on three cavity modes parametrically coupled to a mechanical oscillator and whose frequency spacing matches the mechanical resonance frequency. The additional resonances allow to reach the standard quantum limit at substantially lower input power (compared to the case of only one resonance), as both, sensitivity and quantum backaction are enhanced. Furthermore, it is shown that in the case of multiple cavity modes, coupling between the modes is induced via reservoir interaction, e.g., enabling quantum backaction noise cancellation. Experimental implementation of the schemes is discussed in both the optical and microwave domain. Introduction.-High frequency nano-and micromechanical oscillators have received a high degree of attention recently. They have been used as sensitive detectors, e.g. for spin [1] or particle mass [2], but also carry an intrinsic interest in the study of small scale dissipation of mechanical systems [3], quantum limited motion detection [18], and backaction cooling of vibrational modes [4]. These studies have in common that a sensitive motion transduction is required, which can be implemented by parametric coupling to an optical, electrical, or microwave resonator. The ideal transducer should i) have a high sensitivity and possibly operate at the standard quantum limit(SQL), and ii) should operate at low power. The latter is experimentally advantageous, as high power may cause excess heating due to intrinsic losses. The former pertains to the minimum uncertainty in motion detection and arises from the trade off between measurement imprecision, inherent to the meter (i.e., detector shot noise), and (for linear continuous measurements) inevitable quantum backaction (QBA) [5,6]. These processes are characterized by the displacement spectral densityS xx (Ω) and the QBA force spectral densityS F F (Ω) [28]. For a parametric motion transducer, where a single cavity mode (with frequency ω 0 and energy decay rate κ) is parametrically coupled to a mechanical oscillator [7], the spectral densities are given bȳ

Spatial mapping of multimode Brownian motions in high-frequency silicon carbide microdisk resonators

“…The unique transparency of SiC and its near-zero absorption of wide range in visible also make the SiC-on-SiO 2 microdisks an ideal platform for multimodal sensing in liquids 43,44 . Further, visualizing the shapes of Brownian motions up to high-order modes help create unprecedented freedom for coupling spatial or topological signatures into fundamental noise processes, which could be of fundamental importance for both classical and quantum-limited measurements (for example, of displacements and forces) 45,46 . We have also demonstrated that the multimode mapping is highly responsive to, and offers a new multifold probe for precisely identifying, structural defects such as a sub-500-nm anchor offset.…”

Metrology withPT-Symmetric Cavities: Enhanced Sensitivity near thePT-Phase Transition

“…In fact, the displacement spectral density S xx,PT (ω) and the backaction force spectral density S FF,PT (ω) of the PT optomechanical transducer can be calculated as [39,42]:…”

“…In CAM, the coupling between the resonator and the DUT manifests itself as a back-action-induced resonance frequency shift, resonance mode splitting, or a sideband in the output transmission spectrum [8]. Cavity-assisted metrology has been successfully applied for reading out the state of a qubit [9], measuring tiny mechanical motions [10,[12][13][14][15][16][17]42], and detecting nanoparticles with single-particle resolution [18,19].The readout signal (i.e., the transmission spectrum) of CAM is determined by the sum between the background spectrum of the cavity and the back-action spectrum of the DUT. The background spectrum is determined by the Q of the cavity whereas the back-action spectrum is determined by the strength of the cavity- * Electronic address: jing-zhang@mail.tsinghua.edu.cn † Electronic address: ozdemir@ese.wustl.edu DUT coupling (also dependent on Q) and the quantity to be measured.…”

Reservoir engineering and dynamical phase transitions in optomechanical arrays

“…Over the past years, this coupling has been successfully employed to cool mechanical systems close to the quantum ground state [19][20][21][22][23], using techniques analogous to laser cooling of atoms. In parallel, rapid progress in the fabrication and control of OMS, and in particular new designs for microscale and nanoscale devices [20,21,24,25], have led to a drastic improvement of OMS and pave the way for realizing various strongly coupled [26][27][28] and multimode [29][30][31][32][33][34][35] scenarios. Here, we describe the appearance of dissipation processes in extended OM arrays, where in contrast to OM laser cooling, now the mechanical systems provide a decoherence channel for light.…”