Josephson effect and quantum phase slippage in superfluids

Abstract

We describe the operation of a hydromechanical resonator immersed in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathit{B}$ superfluids and opened on the main bath by two holes, a micro-orifice acting as a weak link and a long parallel channel. Transitions between adjacent quantum states differing by one hydrodynamic circulation quantum can be induced coherently, yielding a succession of steps arranged in a staircase pattern. In ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ at about 0.8 mK and 0 bar, a nearly ideal, nondissipative hydrodynamic Josephson effect can be observed.