Coherent phonon generation in optomechanical crystals

Phonons represent collective excitation states that occur in periodic elastic arrangements of atoms or molecules. High-frequency (more than 10GHz) phonons are less sensitive to thermal decoherence than lower-frequency phonons. These high-frequency phonons, however, are outside the range of most piezoelectric actuators, and alternative means of control are therefore required. In optomechanical (OM) systems, light interacts with mechanical objects.1 Radiation pressure forces are thus commonly used to activate coherent mechanical oscillations.2 So-called phonon lasing is the regime in which mechanical oscillations are self-sustained, monochromatic, coherent, and have high amplitudes. The phonon lasing regime in OM systems is commonly achieved by means of dynamical back-action (i.e, the radiation pressure force is delayed in response to a mechanical deformation), at frequencies of up to a few gigahertz.3 To be efficient, however, these methods require high-quality factor modes and high OM coupling rates. The requirements of phonon lasing techniques are thus difficult to fulfill.Phonons play an important role in the physical properties of condensed matter (e.g., thermal or electrical conductivity), and over the past few years there has been a steady increase in the amount of research on phonons.4 The term 'phononics' has now entered the scientific vocabulary to indicate a platform where coherent phonons can be generated, harnessed, and detected. Mechanical (i.e., phonon) lasing can only be achieved if the mechanical losses of the OM system can be neutralized, no matter what pumping mechanism is used. Although dynamical back-action can be used to achieve mechanical lasing, the field-enhanced cooperativity (a figure of merit) must be at least one, and the system must be in the sideband resolved regime. We recently reported a new lasing method for phonon control. In our approach, coherent high-amplitude mechanical oscillations within a one-dimensional OM crystal are produced in response to an anharmonic modulation of the intracavity radiation pressure force.6 This modulation is a consequence of spontaneous triggering in the optical cavity of a self-pulsing limit cycle (i.e., a closed trajectory along which the system oscillates in a periodic manner). In other words, there is a stable and dynamic interplay between the thermo-optic effects and dispersion of free carriers (i.e., electrons and electron holes) in the OM crystal.7 With our self-pulsing laser mechanism we are able to achieve phonon lasing under more relaxed configurations than with conventional methods. Namely, we operate our devices deep within the unresolved regime (where the mechanical period is greater than the radiative lifetime and dynamical back-action is very inefficient) and with field-enhanced cooperativity values within the 10-2 range. We therefore use relatively low-quality factor modes (102), and single-particle OM coupling rates as low as a few tens of kilohertz, for our phonon lasing technique. We do not require extreme optimization of designs, nor top-class fabrication facilities, competencies, or techniques to achieve these performances. Instead, we fabricate our devices out of standard silicon-on-insulator wafers. In addition, the patterns for these devices are written using an electron beam and are transferred to the silicon using a reactive ion etching technique. We use wet etching in buffered hydrofluoric acid to remove the buried oxide layer and to release the beam structures (see Figure 1). The feedback produced by the coherent mechanical oscillations on the self-pulsing mechanism makes our coupled system a frequency-entrained self-stabilized oscillator. Because of this self-stabilizing feature, our device is extraordinarily robust to wavelength or power