1206.0957 (T. J. Volkoff et al.)

Quantum dynamics of local phase differences between reservoirs of driven
interacting bosons separated by simple aperture arrays    [PDF]

T. J. Volkoff, K. Birgitta Whaley

We present a microscopic derivation of the effective action for the relative phase of coupled, driven reservoirs of interacting condensed bosons, where the coupling is given by tunneling through nanometer sized apertures. The presence of an external driving velocity field and local chemical potential field require imposition of a local U(1) gauge symmetry on the microscopic model. We use the resulting locally gauge invariant effective action to derive the central equations of superfluid hydrodynamics for flow through a single nanoaperture junction from the stationary-phase approximation to the coherent state path-integral at first and second orders of perturbation theory. For a single junction, the resulting current-phase equation is shown to be consistent with dynamics in a tilted washboard potential. We compute the renormalization group (RG) beta function of the periodic potential component of the effective action for small tunneling amplitudes and use this to analyze the temperature dependence of the low-energy current-phase relation, with application to the transition from linear to sinusoidal current-phase behavior observed in experiments by Hoskinson et al. for liquid $^{4}$He driven through nanoaperture arrays. Extension of the microscopic theory to a two-aperture array shows that interference between the microscopic tunneling contributions for individual apertures leads to a effective coupling between apertures. The resulting multi-aperture current-phase equations are equivalent to a set of equations of coupled pendula, with microscopically derived couplings.

View original: http://arxiv.org/abs/1206.0957