  We investigate the electromechanical properties of quartz bulk acoustic wave
resonators at extreme cryogenic temperatures. By applying a DC bias voltage, we
demonstrate broad frequency tuning of high-Q phonon modes in a quartz bulk
acoustic wave cavity at cryogenic temperatures of 4 K and 20 mK. More than 100
line-widths of tuning of the resonance peak without any degradation in loaded
quality factor, which are as high as $1.73\times 10^9$, is seen for high order
overtone modes. For all modes and temperatures the observed coefficient of
frequency tuning is $\approx$ 3.5 mHz/V per overtone number $n$ corresponding
to a maximum of 255.5 mHz/V for the $n = 73$ overtone mode. No degradation in
the quality factor is observed for any value of applied biasing field.
