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Device and optomechanical coupling. (a) (Left) Sample electron micrograph showing the electromechanical capacitor formed by silicon nitride (SiNx) membrane and Al top gate. An Al spiral inductor (not shown) completes the microwave LC resonator. (Right) Sideview of structure. (b) Measurement schematic. (c) Mechanical damping rate vs. number of pump photons. The solid line is a fit to optical damping.
Evidence of TLS. (a) and (b) Microwave resonance shift vs. temperature. (a) Above 0.2 K, the data fit to BCS theory 40 (green line). (b) At lower temperatures, a fit to TLS model (Eq. (2) ) matches to the observed shift (red line). (c) Microwave damping rate vs. number of pump photons. The red line is a fit to the TLS model (Eq. (3) ) with a constant offset ( s−1) from non-TLS contributions. (d) Mechanical resonance shift vs. temperature with a TLS model fit to Eq. (4) . (Inset) Mechanical damping rate shows a linear behavior over temperature.
TLS-induced microwave shift and optical spring. (a) Microwave resonance frequency shifts over np . The solid line is a fit to the TLS model in strong driving regime, Eq. (1) . (b) Mechanical resonance frequency also shifts, agreeing well with a prediction of optical spring calculated from solid line in (a).
(a)–(c) Two-tone BAE measurements and parametric instability. Red crosses are from detuned two-tone measurements, 6,7 and green circles are from BAE measurements. (a) The average occupation number of the mechanical resonator in the BAE measurement shows abrupt increase above , whereas such instability is absent in the detuned two-tone measurements. (b) In BAE, the mechanical damping rates also drop significantly accompanying the increase in nm . In the detuned two-tone measurements, there is no sign of such linewidth narrowing. (c) The quadrature imprecision in BAE reaches before parametric instability. (d) The average occupation number of LC resonator (nLC ) vs. number of pump photons. The pumped LC resonator becomes populated with noise power, which is quantified by the average occupation number nLC . It shows reasonable agreement to dependence.
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