Direct verification of the relation v s = h̄ m 5 φ

We describe an experiment in which we induce a heat-driven superfluid flow in a straight tube and monitor the phase difference across the tube’s ends with a superfluid He quantum interference device (SHeQUID). We quantitatively verify the relation vs = (h̄/m)5φ. We also demonstrate the linearization of a SHeQUID using the heat injection method. Superfluid is described by a macroscopic wavefunction of the form Ψ = √ ρse iφ, where ρs is the superfluid density and φ is the quantum mechanical phase. Applying a momentum operator (p̂Ψ = −ih̄5Ψ = pΨ) with p = mvs immediately gives [1] the relation