A HBAR-oscillator-based 4.596~GHz frequency source: Application to a coherent population trapping Cs vapor cell atomic clock

This article reports on the design and characterization of a high-overtone bulk acoustic wave resonator (HBAR)-oscillator-based 4.596~GHz frequency source. A 2.298~GHz signal, generated by an oscillator constructed around a thermally-controlled two-port AlN-sapphire HBAR resonator with a Q-factor of 24000 at 68$^{\circ}$C, is frequency multiplied by 2 to 4.596~GHz, half of the Cs atom clock frequency. The temperature coefficient of frequency (TCF) of the HBAR is measured to be $-23$~ppm/$^{\circ}$C at 2.298~GHz. The measured phase noise of the 4.596~GHz source is $-105$~dBrad$^2$/Hz at 1~kHz offset and $-150$~dBrad$^2$/Hz at 100~kHz offset. The 4.596~GHz output signal is used as a local oscillator (LO) in a laboratory-prototype Cs microcell-based coherent population trapping (CPT) atomic clock. The signal is stabilized onto the atomic transition frequency by tuning finely a voltage-controlled phase shifter (VCPS) implemented in the 2.298~GHz HBAR-oscillator loop, preventing the need for a high-power-consuming direct digital synthesis (DDS). The short-term fractional frequency stability of the free-running oscillator is 1.8 $\times$ 10$^{-9}$ at one second integration time. In locked regime, the latter is improved in a preliminary proof-of-concept experiment at the level of 6.6 $\times$ 10$^{-11}~\tau^{-1/2}$ up to a few seconds and found to be limited by the signal-to-noise ratio of the detected CPT resonance.