  Thermal Nyquist noise fluctuations of high-$Q$ Bulk Acoustic Wave (BAW)
cavities have been observed at cryogenic temperatures with a DC Superconducting
Quantum Interference Device (SQUID) amplifier. High $Q$ modes with bandwidths
of few tens of milliHz produce thermal fluctuations with a Signal-To-Noise
ratio of up to 23dB. The estimated effective temperature from the Nyquist noise
is in good agreement with the physical temperature of the device, confirming
the validity of the equivalent circuit model and the non-existence of any
excess resonator self-noise. The measurements also confirm that the quality
factor remains extremely high ($Q>10^8$ at low order overtones) for very weak
(thermal) system motion at low temperatures, when compared to values measured
with relatively strong external excitation. This result represents an enabling
step towards operating such a high-Q acoustic device at the standard quantum
limit.
