Phase engineering of controlled entangled number states in a single component Bose-Einstein condensate in a double well

TL;DR

This paper introduces a method to generate entangled number states, or Schrödinger cat states, in a Bose-Einstein condensate within a double well by using phase engineering and barrier height control.

Contribution

It presents a novel phase engineering approach to produce controlled entangled states in a BEC double-well system, linking classical phase space dynamics to quantum state formation.

Findings

Successful creation of entangled number states via phase imprinting.

Controlled entanglement depends on initial barrier height and ramping rate.

The process is explained through classical phase space analysis.

Abstract

We propose a model for the creation of entangled number states (Schr\"odinger cat states) of a Bose-Einstein condensate in a double well through simple phase engineering. We show that a $\pi$-phase imprinted condensate in a double-well evolves, with a simultaneous change of barrier height, to number states with well defined and controlled entanglement. The cat state generation is understood in terms of the underlying classical phase space dynamics of a $\pi$-phase displaced coherent state put at the hyperbolic fixed point of the separatrix of a physical pendulum. The extremity and sharpness of the final cat state is determined by the initial barrier height and the rate at which it is ramped during the evolution.