Nanomechanical engine with tunable operation

(A) Experimental scheme to cool down a mechanical mode. The system is driven with a frequency red detained by an order of magnitude of the fundamental frequency of graphene-SiNx hybridized mode. (C) Experimentally we observe Lorentzian peak at fundamental frequency of the resonator (blue curve) for zero driving strength.  Red curve represents recorded spectra for maximum driving strength. The phonon occupancy of the mode can be determined from the equipartition theorem by evaluating area under the peak. Recorded spectra for increasing drive strength is shown in (D). We observe reduction in thermal phonon number of the central peak along with emergence of first and second order peaks separated by drive frequency which follow Bessel’s function of first kind according to it’s order. (B) shows theoretical plot of frequency modulated spectrum for zero (blue) and nonzero (red) value of modulation parameter. Frequency of the fundamental mode also gets shifted depending on the value of drive strength. (E) Lock-in measurement data shows an equal reduction in both quadratures of circularly distributed thermal noise fluctuations, hence phonon number reduction of central mode with increasing drive strength. Undriven thermal peak quadratures (red) have higher standard deviation (see histograms) than driven quadratures (blue). (F) Relative area (blue circles with error bars) of central peak follows 0th order of Bessel’s function of first kind (black curve) till hits the measurement noise floor. The extrapolated curve (red) shows possibility of reaching close to zero. (G) Peak frequency shifts (decreases) non-linearly with increasing drive strength following a parabolic curve. (H) Numerically we observe similar behaviour with increasing drive strength akin to experiments. (I) Numerical results indicate exponential dependence of maximum value of noise reduction on linear damping of the system. Red data point represents maximum value of noise reduction of our experimental setup, which is limited by 15.39 dB. (J) Several works suggest possible realization of a heat engine if we have control over the number of harmonic oscillators and frequency of the oscillators. To understand the timescales corresponding to these two processes, we turn on and off the drive in a periodic manner. (K)  quadrature fluctuations close to the thermal peak (black arrow) has been measured. A schematic diagram of the thermal peak at different times is shown here. (L) Average fluctuation around black peak  is plotted against time which shows different timescales present in system. (M) For red shift in frequency, system works in refrigeration mode as it absorbs low frequency phonons and releases high frequency phonons. Resulting engine cycle is plotted with relative area (proportional to phonon number) and fundamental mode frequency (Lines between data points are guides to the eye). Here, the vertical lines represent transition corresponding to phonon number change and horizontal lines represent transitions corresponding to frequency shift. Area inside the cycle (proportional to work done) increases with increasing modulation strength. (N) Red shift of the frequency of the fundamental mode is plotted with increasing modulation power at zero gate voltage. Red curve represents linear fitting of the data set. In the upper panel schematic, red and cyan Lorentzian peak represents central peak with and without low frequency modulation strength respectively. (O)  Displacement spectral density of a thermally driven 20 um diameter graphene membrane as a function of DC gate voltage, where frequency of the fundamental mode increases following an initial decrease with increasing tension.(P) Blue shift of the frequency of the fundamental mode is plotted with increasing modulation power at higher gate voltage (139V). Blue curve represents linear fitting of the data set. In the schematic in the upper panel, blue and cyan Lorentzian peak represents central peak with and without low frequency modulation strength respectively. (Q) For blue shift in frequency, system works in heat engine mode as it absorbs high frequency phonons and releases low frequency phonons. Resulting engine cycle is plotted with relative area (proportional to phonon number) and fundamental mode frequency where horizontal and vertical lines represents same transitions as mentioned above. Area inside the cycle (proportional to work done) increases with increasing modulation strength. Lines between data points are guides to the eye.