Evidence for structural damping in a high-stress silicon nitride nanobeam and its implications for quantum optomechanics

Abstract

We resolve the thermal motion of a high-stress silicon nitride nanobeam at frequencies far below its fundamental flexural resonance (3.4 MHz) using cavity-enhanced optical interferometry. Over two decades, the displacement spectrum is well-modeled by that of a damped harmonic oscillator driven by a 1/f thermal force, suggesting that the loss angle of the beam material is frequency-independent. The inferred loss angle at 3.4 MHz, φ = 4.5·10 −6 , agrees well with the quality factor (Q) of the fundamental beam mode (φ = Q −1 ). In conjunction with Q measurements made on higher order flexural modes, and accounting for the mode dependence of stress-induced loss dilution, we find that the intrinsic (undiluted) loss angle of the beam changes by less than a factor of 2 between 50 kHz and 50 MHz. We discuss the impact of such "structural damping" on experiments in quantum optomechanics, in which the thermal force acting on a mechanical oscillator coupled to an optical cavity is overwhelmed by radiation pressure shot noise. As an illustration, we show that structural damping reduces the bandwidth of ponderomotive squeezing.

Quantum Correlations of Light from a Room-Temperature Mechanical Oscillator

“…3, the relative contribution of the quantum correlation increases, leading to a progressively larger antisymmetry near the amplitude quadrature. We note that classical sources of noise may also affect the antisymmetric feature: laser amplitude noise can establish classical amplitudephase correlations leading to excess antisymmetry [38], or anharmonicity of the mechanical oscillator can lead to structured thermal noise which at large Fourier frequency detuning modifies the antisymmetry [40]. These and various other sources of systematics are found to be negligible in our experiment (see SM [33]).…”

Quantum theory of feedback cooling of an anelastic macro-mechanical oscillator

“…Levitated nano-mechanical systems, recently prepared in their motional ground state [15,16], appear to be immune to internal dissipation, despite large internal temperatures [19], apparently due to negligible coupling between internal modes and center-of-mass motion. Nano-mechanical objects are elastically bound so as to realize radiofrequency mechanical oscillators; the effects of internal dissipation are largely masked at such high frequencies [20]. The upshot is that all existing theoretical consideration of laser cooling of mechanical oscillators implicitly assumes a velocity damped oscillator [21][22][23][24].…”

“…Internal damping therefore dominates their decoherence. A most ubiquitous form of internal damping in elastic oscillators is so called anelasticity [20,28,29], for which the damping is not velocity-proportional, but is described by a frequency dependent "structural damping" rate, Γ 0 [Ω] = (Ω 0 /Q)(Ω 0 /Ω), where Ω 0 is the resonance frequency, and Q is the (frequency-independent) quality factor.…”

Commercializing optomechanical sensors: from the classical to quantum regime

“…This is now an active research area, where MEMS processes are used to create chip-scale silicon photonic structures on silicon-on-insulator wafers, resulting in sub-milimeter scale Fabry-Perot cavities, 16 evanescent strip waveguides replacing tapered optical fibers, 17 tethered photonic crystal membranes, 18 and suspended strings with ultrahigh mechanical quality factors. 19 The significant size reduction offered by optomechanical MEMS sensors, combined with their ability to reach displacement sensitivities on the order of 10 −18 mHz −1/2 , 7, 20 makes them a particularly disruptive technology. Many optomechanical systems, including the one reported in this proceedings, were originally developed to probe macroscopic quantum behavior by cooling the centre-of-mass motion of the test-mass towards an average phonon occupancy < 1.…”