Theory of Josephson flow oscillations in superfluid³He-B

Abstract

Avenel and Varoquaux have proposed an experiment for observing pressure-induced Josephson flow oscillations across an orifice connecting two reservoirs of³He-B. The aim of the present work is to specify the conditions for the observability of this effect. First the six coupled Ginzburg-Landau (GL) equations for the order parameter components within the orifice are solved, subject to rigid boundary conditions at the ends (fixed phase difference ф between the bulk order parameters) and specular reflection boundary conditions at the walls. The longitudinal component is depressed and one of the transverse components is enhanced toward the middle of the orifice. From the order parameter functions the supercurrent through the orifice I(ф), and the GL energyF(ф) are calculated for 0≤ф≤ 2π and for different lengths and cross sections of the orifice. A new feature of the functionI(ф) in comparison to the current-phase relationship for superconducting microbridges is its multivaluedness and the occurrence of two nontrivial zeros ofI(ф). The functionF(ф) exhibits two local maxima besides the absolute maximum at ф=π. The optimal length of the orifice for the observability of the ac Josephson effect turns out to be about seven GL coherence lengths ξ. Then the frequency ω of the Josephson flow oscillations, which follow the sudden application of a force ΔF on a diaphragm, depends on ΔF in a way similar to that in which the frequency of the parallel ringing experiment in³He-A depends on the field step ΔH.