Ultra-subharmonic bifurcations in a driven nonlinear oscillator - Part 2/2: harmful and beneficial consequences in Josephson circuits*

Ultra-subharmonic (USH) bifurcation refers to a broad class of dynamical transitions wherein a driven nonlinear oscillator is resonantly excited to one of q equiprobable stable states by some p/q-th USH of a drive, for naturals p and q. In circuit quantum electrodynamics (cQED), particular USH processes have been employed in quantum devices such as amplifiers based on bifurcation thresholds and qubits based on Schrodinger Cat-like manifolds of degenerate driven-dissipative states. While these instances are well documented, mapping out where in parameter space generic USH processes occur in cQED experiments is of increasing importance. This is especially relevant in cases where unexpected bifurcations plague the driven-dissipative operations employed in quantum information processing. Moreover, controlled USH processes could lead to novel nonlinear interactions, like those involved in stabilizing higher-dimensional cat states. In this talk, basing ourselves on Part 1, we will discuss different experimental manifestations of USH processes. Their comprehensive map in parameter space will be shown. Finally, we will discuss how to mitigate the undesired side-effects of USH bifurcation and to harness it for quantum operations.