Theory of macroscopic quantum tunneling with Josephson-Leggett collective excitations in multi-band superconducting Josephson junctions

Collective excitations reveal fundamental properties and potential applications of superconducting states. We theoretically study macroscopic quantum tunneling (MQT) in a Josephson junction composed of multi-band superconductors, focusing on a phase mode induced by inter-band fluctuations: the Josephson-Leggett (JL) collective excitation mode. Using the imaginary-time path-integral method, we derive a formula for the MQT escape rate for low-temperature switching events. We clarify that the JL mode has two major effects on the MQT: (i) the zero-point fluctuations enhance the escape rate, and (ii) the quantum dissipation induced by the couplings to the gauge-invariant phase difference suppresses the quantum tunneling. We show that the enhancement exceeds the suppression for a wide range of junction parameters. This enhancement originates from the single-mode interaction between the tunneling variable and the inter-band fluctuations.