  We investigate the quantum dynamics of a quadratic-quartic anharmonic
oscillator formed by a potential well between two potential barriers. We
realize this novel potential shape with a superconducting circuit comprised of
a loop interrupted by two Josephson junctions, with near-zero current bias and
flux bias near half a flux quantum. We investigate escape out of the central
well, which can occur via tunneling through either of the two barriers, and
find good agreement with a generalized double-path macroscopic quantum
tunneling theory. We also demonstrate that this system exhibits an "optimal
line" in current and flux bias space along which the oscillator, which can be
operated as a phase qubit, is insensitive to decoherence due to low-frequency
current fluctuations.
