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Collective excitations reveal fundamental properties and potentialapplications of superconducting states. We theoretically study macroscopicquantum tunneling (MQT) in a Josephson junction composed of multi-bandsuperconductors, focusing on a phase mode induced by inter-band fluctuations:the Josephson-Leggett (JL) collective excitation mode. Using the imaginary-timepath-integral method, we derive a formula for the MQT escape rate forlow-temperature switching events. We clarify that the JL mode has two majoreffects on the MQT: (i) the zero-point fluctuations enhance the escape rate,and (ii) the quantum dissipation induced by the couplings to thegauge-invariant phase difference suppresses the quantum tunneling. We show thatthe enhancement exceeds the suppression for a wide range of junctionparameters. This enhancement originates from the single-mode interactionbetween the tunneling variable and the inter-band fluctuations.

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