Signatures of Dynamical Tunneling in the Wave function of a Soft-Walled Open Microwave Billiard

Evidence for dynamical tunneling is observed in studies of the transmission, and wave functions, of a soft-walled microwave cavity resonator. In contrast to previous work, we identify the conditions for dynamical tunneling by monitoring the evolution of the wave function phase as a function of energy, which allows us to detect the tunneling process even under conditions where its expected level splitting remains irresolvable.