Detecting Acoustic Blackbody Radiation with an Optomechanical Antenna

Nanomechanical systems are generally embedded in a macroscopic environment where the sources of thermal noise are difficult to pinpoint. We engineer a silicon nitride membrane optomechanical resonator such that its thermal noise is acoustically driven by a spatially well-defined remote macroscopic bath. This bath acts as an acoustic blackbody emitting and absorbing acoustic radiation through the silicon substrate. Our optomechanical system acts as a sensitive detector for the blackbody temperature and for photoacoustic imaging. We demonstrate that the nanomechanical mode temperature is governed by the blackbody temperature and not by the local material temperature of the resonator. Our work presents a route to mitigate self-heating effects in optomechanical thermometry and other quantum optomechanics experiments, as well as acoustic communication in quantum information.

Figure 1

Acoustic blackbody thermometry. (a) A silicon substrate acts as an acoustically transparent medium coupling a SiN membrane mechanical resonator to a remote acoustic blackbody. Thermal acoustic radiation emitted into the substrate by the blackbody drives Brownian motion of the resonator. The resonator motion is read out with a simple optical-lever detection scheme. (b) Dark-field image [12] of the (10,1) resonator mode. (c) Displacement noise spectrum of a thermally occupied (10,1) mode.

Figure 2

Finite element simulations of the acoustic radiation pattern of the modes of a 1 mm square by 200 nm thick SiN membrane resonator on a $200\mu \mathrm{m}$ thick silicon substrate. (a) Radiation pattern of (10,1) mode into a substrate of infinite transverse extent. (b) Far-field radiation pattern of several modes normalized to their energy damping rate. Modes of the form ($i,1$) show high directionality for $i\gg 1$, whereas, e.g., the (10,3) mode displays multiple small lobes of radiation. (c) Radiation pattern of mode (10,1) into a finite extent, square silicon substrate (10 mm side length). (d) Simulated model of the device engineered for the experiment. Four oblong acoustic blackbodies (modeled with mechanical loss tangent of 0.1), offer high absorption in a single pass, eliminating interference due to edge reflections and hence maintaining the directionality of the acoustic wave. Simulation geometry is chosen to match the experimental device parameters. Color schemes represent relative displacement of the membrane, silicon substrate, and acoustic blackbodies. Color bars are the same for (a), (c), and (d).

Figure 3

Photoacoustically driven frequency response of two membrane modes to periodic excitation of bath $X$ (blue) and bath $Y$ (brown), showing the directional sensitivity of our detection scheme. The mode frequencies shift between the two traces due to thermally induced stress (see main text).

Figure 4

Thermometry results. (a),(b) Brownian motion temperature profiles, derived from the area under the spectrogram, of (10,1) mode (orange) and (1,10) mode (green), when bath $X$ (a) or bath $Y$ (b) is heated with a 1 s laser pulse. Dotted lines represent the expected temperature rise using ${\tau }_{\mathrm{BB}}$ derived from the mechanical frequency shifts. In each case, the mode strongly coupled to the heated bath shows a rise in temperature, while the uncoupled mode stays at a constant temperature to within the measurement uncertainty. (c),(d) Temperature rise as a function of heating laser power. Error bars represent the $1\sigma$ statistical uncertainty from a few thousand experimental trials. Colored lines are linear fits to the data. (e),(f) Spectrograms of the resonator motion showing the thermally driven noise peaks of mechanical modes, taken when either bath $X$ (e) or bath $Y$ (f) are heated. Mode frequencies shift at two timescales following ${\tau }_{\mathrm{BB}}\approx 100\mathrm{ms}$, and the entire apparatus (several tens of seconds). Logarithmic color scale.