Dynamical studies of macroscopic superposition states: Phase engineering of controlled entangled number states of Bose-Einstein condensate in multiple wells

TL;DR

This paper proposes a phase engineering scheme to generate controllable macroscopic superposition states of Bose-Einstein condensates across multiple wells, extending the concept of NOON states to complex multi-well systems.

Contribution

It introduces a novel method for creating entangled number states in multi-well BECs through phase engineering, demonstrating its effectiveness via numerical simulations.

Findings

Successful creation of entangled states in three and four wells

Entanglement complexity increases with particle number and interactions

Novel behavior observed in entanglement as system parameters vary

Abstract

We provide a scheme for the generation of entangled number states of Bose-Einstein condensates in multiple wells with cyclic pairwise connectivity. The condensate ground state in a multiple well trap can self-evolve, when phase engineered with specific initial phase differences between the neighboring wells, to a macroscopic superposition state with controllable entanglement -- to multiple well generalization of double well NOON states. We demonstrate through numerical simulations the creation of entangled states in three and four wells and then explore the creation of "larger" entangled states where there are either a larger number of particles in each well or a larger number of wells. The type of entanglement produced as the particle numbers, or interaction strength, increases changes in a novel and initially unexpected manner.