## 1 Introduction  
In the past ultra-stable low phase noise photonic frequency sources have been implemented for a range of applications including very high precision probes of fundamental physics, high precision oscillators as local oscillators for atomic clocks and advanced radar systems [1; 2; 3; 4]. The best results at microwave and radio frequencies to date have been those derived from sapphire oscillators at room [3; 4] and cryogenic temperatures [1; 2; 5] as well as lasers locked to optical cavities down converted through a frequency comb [6; 7; 8; 9; 10]. For example, such oscillators have been exploited to demonstrate possible violation of the Lorentz symmetry in the photon sector [1]. Though the photonic devices have extraordinary stability, they can be used to test only certain range of physical phenomena, and devices where the resonance conditions depend upon mechanical motion of matter can test totally different sectors including frequencies of the bulk elastic waves, which are sensitive to the photon-, electron-, proton- and the neutron-sector. Moreover, recently new oscillator systems with rival performance of pure photonic systems have been demonstrated involving high-Q frequency stable phonon systems. Such systems include but are not limited to, phonon lasers [11], optomechanical systems [12; 13; 14] and phonon induced Brillouin scattering devices [15; 16; 17; 18; 19]. Traditionally, the most stable oscillators based on acoustic resonance have been realised from technology based on Bulk Acoustic Wave (BAW) resonators, which trap phonons in a cavity in a similar way to a [PERSON] cavity. These techniques have been perfected for decades allowingprecision room temperature oscillators and related devices, culminating in \(Q\times f\) products as high \(2\times 10^{13}\) Hz and oscillator frequency stability reaching below \(10^{-13}\) between 1 and 10 s of integration time [20]. Only recently has this technology has been extended to cryogenic temperatures attaining \(Q\times f\) products as high \(2\times 10^{18}\) Hz. Thus, such cryogenic BAW systems shows great potential for use in applications that require precision control, measurement, and sensing at the quantum limit. This is mainly due to the relatively high mechanical frequencies and extremely high \(Q\)-factors achievable at cryogenic temperatures (\(Q\approx 10^{10}\)) [21] for frequencies ranging from a MHz to tens of GHz, beyond the capability of any other competing technology compared in [PERSON] et al. and others [22; 23; 24; 25]. Such high-Q devices with nonlinear properties are very valuable in many areas of physics. This includes quantum metrological applications where nonlinearities are employed to perform quantum state preparation [26]. In regards to creating low noise oscillators, nonlinear processes are used to create a limit cycle in feedback frequency to maintain stable output power. The further improvement of BAW oscillators can only be achieved by cooling the resonators and reducing the resonator flicker phase self-noise, since this is the dominant noise source both at cryogenic and room temperature. The influence on the frequency stability of high-performance quartz oscillators on time scales of order 1-50 s is well-documented and it has been observed that the flicker self-noise decreases with decreasing power of the incident signal, and our recent results confirm that the resonators are thermal noise limited, and flicker-free without the carrier [27]. Thus, the noise in the quartz oscillator is dependent on power, with the white noise floor decreasing with power, while the flicker noise increases. The best quartz typically has frequency instabilities of better than \(10^{-13}\) limited by flicker fluctuations. However at cryogenic temperatures the white noise floor is reduced by 40 dB, allowing a much lower oscillator power and a large reduction of the flicker noise so the increased \(Q\)-factor may be exploited.