Phonon Lasing in an Electromechanical Resonator

An electromechanical resonator harboring an atomlike spectrum of discrete mechanical vibrations, namely, phonon modes, has been developed. A purely mechanical three-mode system becomes available in the electromechanical atom in which the energy difference of the two higher modes is resonant with a long-lived lower mode. Our measurements reveal that even an incoherent input into the higher mode results in coherent emission in the lower mode that exhibits all the hallmarks of phonon lasing in a process that is reminiscent of Brillouin lasing.

Figure 1

(a) An electron micrograph of the electromechanical resonator which incorporates a two-dimensional electron gas (ii and iv) above which Schottky-contacted gold electrodes are placed (i, iii, and v). The mechanical vibrations are piezoelectrically excited by gate (i) which are then detected by the motion induced piezovoltage from gate (iii) at 2.0 K and ${10}^{-7}\mathrm{mbar}$, where contacts (ii), (iv), and (v) are grounded. The inset schematically depicts the phonon-lasing protocol. (b) Harmonically probing the electromechanical resonator reveals almost 200 resonances up to 4 MHz, where each line in this plot corresponds to a mechanical vibration. The three-mode system consists of the fundamental flexural oscillation as the lower mode ${\omega }_L$ (c) where the middle mode ${\omega }_M$ (d) and the higher mode ${\omega }_H$ (e) are composite oscillations [24]. The three modes are harmonically probed with amplitudes of $100\mu {\mathrm{V}}_{\mathrm{rms}}$, $5{\mathrm{mV}}_{\mathrm{rms}}$, and $8{\mathrm{mV}}_{\mathrm{rms}}$, respectively.

Figure 2

(a) The application of dc bias to electrode (i) in addition to a $100\mu {\mathrm{V}}_{\mathrm{rms}}$ harmonic probe can be used to tune the frequency of the lower mode. Although the flexural and torsional modes can be affected by the resultant piezoelectric strain, the composite modes (${\omega }_M$ and ${\omega }_H$) show no discernible response possibly due to their larger bandwidths. (b) and (c) The current noise spectral density around the lower and middle modes in response to a $60{\mathrm{mV}}_{\mathrm{rms}}$ harmonic tone applied at exactly ${\omega }_H$ reveals the creation of mechanical vibrations namely phonon emission as dc bias is applied to the eletromechanical resonator to reduce ${\omega }_L$.

Figure 3

(a) and (b) The current noise spectral density around the lower and middle modes, respectively in response to a $0–100{\mathrm{mV}}_{\mathrm{rms}}$ harmonic tone applied at exactly ${\omega }_H$. The spectra are offset for clarity with the bottom (top) spectrum corresponding to $0{\mathrm{mV}}_{\mathrm{rms}}$ ($100{\mathrm{mV}}_{\mathrm{rms}}$) where the amplitude of the tone is nonuniformly varied. (c) The corresponding amplitudes of the phonon emission in the lower and middle modes. (d) The calculated amplitudes of the phonon emission in the lower and middle modes in response to the harmonic tone. (e) The sum frequency of the phonon emission in the lower and middle modes. (f) The phonon emission in the lower mode is confined within 175 mHz (the inset shows the phonon emission when the detuning is ${\omega }_H\pm 2\mathrm{Hz}$), which is much less than ${\gamma }_L/2\pi$ when the harmonic tone with an amplitude of $36{\mathrm{mV}}_{\mathrm{rms}}$ is detuned around ${\omega }_H$ with a measurement resolution bandwidth of 25 mHz.

Figure 4

(a) The noise power density around the lower mode in response to a white-noise voltage injected into the higher mode with a measurement resolution bandwidth of 25 mHz. (b) The corresponding full widths at half maximum (FWHM) extracted from Gaussian fits for noise amplitudes $<60{\mathrm{mV}}_{\mathrm{rms}}$. For amplitudes $\ge 60{\mathrm{mV}}_{\mathrm{rms}}$, a composite function composed of a Gaussian and Lorentzian was used. (c) The experimental data and theoretical analysis [24] indicate the line shapes at larger noise amplitudes ($60{\mathrm{mV}}_{\mathrm{rms}}$) originate from both the lasing ($58.5{\mathrm{mV}}_{\mathrm{rms}}$) and the bandwidth of the lower mode (ref.). The ref. line shape of the lowest mode is measured by injecting white-noise voltage over ${\omega }_L\pm 25{\gamma }_L$ with an amplitude of only $100\mu {\mathrm{V}}_{\mathrm{rms}}$ which also yields the $0{\mathrm{mV}}_{\mathrm{rms}}$ data point in Fig. 4b.