  We demonstrate a previously unobserved nonlinear phenomenon in an ultra-low
loss quartz Bulk Acoustic Wave cavity ($Q>3\times10^9$), which only occurs
below 20 milli-Kelvin in temperature and under relatively weak pumping. The
phenomenon reveals the emergence of several stable equilibria (at least two
foci and two nodes) and jumps between these quasi states at random times. The
degree of this randomness as well as separations between levels can be
controlled by the frequency of the incident carrier signal. It is demonstrated
that the nature of the effect lays beyond the standard Duffing model.
