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

TL;DR

This paper investigates the transition from dc to ac Josephson effects in a cold atom SQUID analog, analyzing how barrier motion influences the system's dynamics, hysteresis, and phase transitions through theoretical and simulation methods.

Contribution

It introduces a detailed analysis of the dc to ac Josephson transition in a cold atom SQUID, highlighting the effects of barrier motion and hysteresis, with validation via simulations.

Findings

Identification of the energy landscape and critical points for Josephson regimes.

Observation of hysteretic oscillations during the transition.

Excellent agreement between Gross-Pitaevskii simulations and two-mode theory.

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.