Josephson effect in coherent roton aggregates

A localized microwave electromagnetic field in liquid helium behaves as a laser of rotons: it produces a coherent roton aggregate. We show that the whispering gallery mode of the dielectric resonator excites multiple coherent aggregates simultaneously and predict a Josephson effect between them. The superfluid velocity around the resonator acts as a “voltage across the weak link” in superconducting Josephson junctions. Josephson frequency-velocity relation agrees with existing experimental data.