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The properties of phase escape in a dc SQUID at 25 mK, which is well belowquantum-to-classical crossover temperature $T_{cr}$, in the presence of strongresonant ac driving have been investigated. The SQUID contains twoNb/Al-AlO$_{x} $/Nb tunnel junctions with Josephson inductance much larger thanthe loop inductance so it can be viewed as a single junction having adjustablecritical current. We find that with increasing microwave power $W$ and atcertain frequencies $\nu $ and $\nu $/2, the single primary peak in theswitching current distribution, \textrm{which is the result of macroscopicquantum tunneling of the phase across the junction}, first shifts toward lowerbias current $I$ and then a resonant peak develops. These results are explainedby quantum resonant phase escape involving single and two photons withmicrowave-suppressed potential barrier. As $W$ further increases, the primarypeak gradually disappears and the resonant peak grows into a single one whileshifting 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 $. Analysisbased on the classical equation of motion shows that such resonant peak canarise from the resonant escape of the phase particle with extremely largeoscillation amplitude resulting from bifurcation of the nonlinear system. Ourexperimental result and theoretical analysis demonstrate that at $T\ll T_{cr}$,escape of the phase particle could be dominated by classical process, such asdynamical bifurcation of nonlinear systems under strong ac driving.

Quantum and classical resonant escapes of a strongly-driven Josephson junction