Detecting a phonon flux in superfluid ${}^4\mathrm{He}$ by a nanomechanical resonator

Nanoscale mechanical resonators are widely utilized to provide high sensitivity force detectors. Here we demonstrate that such high-quality-factor resonators immersed in superfluid ${}^4\mathrm{He}$ can be excited by a modulated flux of phonons. A nanosized heater immersed in superfluid ${}^4\mathrm{He}$ acts as a source of ballistic phonons in the liquid—“phonon wind”. When the modulation frequency of the phonon flux matches the resonance frequency of the mechanical resonator, the motion of the latter can be excited. This ballistic thermomechanical effect can potentially open up new types of experiments in quantum fluids.

Figure 1

False color scanning electron microscope image of a $150\text{−}\mu \mathrm{m}$-long composite aluminum on silicon nitride nanobeam. The nanobeam was characterized in vacuum and ${}^4\mathrm{He}$ by a magnetomotive scheme using a vector network analyzer (VNA) as shown. Phononic driving measurements in ${}^4\mathrm{He}$ were made using a spectrum analyzer. Inset shows a typical frequency response from the VNA of the nanobeam in vacuum at $10\mathrm{mK}$ in a magnetic field of $10\mathrm{mT}$, where the aluminum film is in the superconducting state.

Figure 2

Diagram of the experimental setup for driving the nanomechanical resonator by a phonon flux in superfluid ${}^4\mathrm{He}$. The $30\text{−}\mu \mathrm{m}$-long beam, operated off-resonance, is used as a heater. It is located $\sim 5\mathrm{mm}$ away from the $150\text{−}\mu \mathrm{m}$-long beam, which is used as a detector. Both beams are immersed in superfluid ${}^4\mathrm{He}$ at $10\mathrm{mK}$ in a magnetic field $1.3\mathrm{T}$. An AC current is passed through the heater at half the detector resonance frequency. The generated emf on the detector beam is monitored by a spectrum analyzer.

Figure 3

(a) The power spectral density (PSD) of the generated emf signal as a function of frequency for three different values of the heater power. (b) The integrated emf power, $P_{\mathcal{E}}$, from the detector as a function of the heater power, $P_{\mathcal{H}}$. The orange band represents the uncertainty values for the experimental points. The black dashed line shows the theoretical model corresponding to Eq. (3) for diffuse scattering ($\alpha =1$). The blue band accounts for uncertainty in the scattering mechanism and possible impedance mismatch. The theoretical dependence assumes $100\%$ energy transfer from the heater to the ${}^4\mathrm{He}$.