Coherent phase slips in coupled rings: from weak to strong interactions

Abstract

We study the coherent transfer of circulation between two weakly coupled lattice rings of ultracold bosons, in which a persistent current initially prepared in one ring oscillates back and forth between the rings without net transfer of particles. Combining Bose--Hubbard simulations with their Gross--Pitaevskii and quantum phase model limits, we show that similar current oscillations arise from two distinct microscopic mechanisms. At weak interactions, particles in each occupied momentum mode tunnel independently between the rings, leading to a transfer time inversely proportional to the inter-ring tunnelling, extensive particle-number fluctuations and entanglement distributed over many Schmidt components; this mode-exchange dynamics is suppressed by self-trapping as the interactions increase. At stronger interactions and large filling, in the phase-dominated regime, circulation is instead transferred through a second-order collective process between many-body persistent-current states, with a transfer time scaling as the inverse square of the inter-ring tunnelling in the weak-link limit. Number fluctuations then remain of order one instead of growing with the particle number, and within each number sector the system evolves into coherent superpositions of two many-body configurations, distinguished by which ring carries the circulation. The entanglement accessible under number-conserving operations therefore reaches up to approximately one bit. We propose a quench protocol to prepare the initial state and estimate transfer times within reach of current ring-lattice experiments, identifying coupled rings as a platform to study coherent quantum phase slips and to manipulate persistent-current states.