dc to ac Josephson transition in a dc atom superconducting quantum interference device

Abstract

We analyze the effect of the barrier motion on the Bose-Hubbard Hamiltonian of a ring-shaped Bose-Einstein condensate interrupted by a pair of Josephson junctions, a configuration which is the cold atom analog of the well-known dc superconducting quantum interference device (SQUID).Such an effect is also shown to modify the Heisenberg equation of motion of the boson field operator in the two-mode approximation, where a hysteretic contribution that could affect the dynamics for accelerated or overlapping barriers is identified. By studying the energy landscape as a function of order and control parameters, we determine the diagram with the location of the dc and ac Josephson regimes, along with the critical points that are shown to depend on the junctions position. We analyze the dc to ac Josephson transition for adiabatic barrier trajectories that lead to a final uniform velocity, or which perform symmetric velocity paths. We show that such symmetric trajectories may induce, when reaching the critical point, highly hysteretic oscillating return paths within the dc regime, similar to the underdamped hysteresis loops arising from the action of a resistive flow in the ac regime. We also consider nonequilibrium initial conditions resulting from a finite phase difference on either side of the junctions, along with the critical features of such a parameter. An excellent agreement between the Gross-Pitaevskii simulations and the two-mode results is found in all cases.

Rotation-driven transition into coexistent Josephson modes in an atomtronic dc-SQUID

“…In the Thomas-Fermi approximation, it has been shown that the effective interaction energy parameter becomes reduced with respect to the standard one by a factor of 7/10, 3/4, or 5/6, depending on the dimensionality of the system. Such an effective TM model has shown to accurately describe the exact dynamics in double-well [24,25], asymmetric twowell [26,27] and, in the multimode version, multiple-well [28,29] condensates. A multimode model, which includes all the type of corrections introduced in the TM model, was recently proposed for describing the dynamics of cold atoms confined by a rotating ring-shaped optical lattice forming a weakly linked array of condensates [30].…”