  The properties of phase escape in a dc SQUID at 25 mK, which is well below
quantum-to-classical crossover temperature $T_{cr}$, in the presence of strong
resonant ac driving have been investigated. The SQUID contains two
Nb/Al-AlO$_{x} $/Nb tunnel junctions with Josephson inductance much larger than
the loop inductance so it can be viewed as a single junction having adjustable
critical current. We find that with increasing microwave power $W$ and at
certain frequencies $\nu $ and $\nu $/2, the single primary peak in the
switching current distribution, \textrm{which is the result of macroscopic
quantum tunneling of the phase across the junction}, first shifts toward lower
bias current $I$ and then a resonant peak develops. These results are explained
by quantum resonant phase escape involving single and two photons with
microwave-suppressed potential barrier. As $W$ further increases, the primary
peak gradually disappears and the resonant peak grows into a single one while
shifting further to lower $I$. At certain $W$, a second resonant peak appears,
which can locate at very low $I$ depending on the value of $\nu $. Analysis
based on the classical equation of motion shows that such resonant peak can
arise from the resonant escape of the phase particle with extremely large
oscillation amplitude resulting from bifurcation of the nonlinear system. Our
experimental result and theoretical analysis demonstrate that at $T\ll T_{cr}$,
escape of the phase particle could be dominated by classical process, such as
dynamical bifurcation of nonlinear systems under strong ac driving.
