Dynamical creation of entangled bosonic states in a double well

TL;DR

This paper investigates how a Bose-Hubbard Hamiltonian can dynamically generate entangled bosonic N00N states in a double well, highlighting the role of spectral degeneracy and interactions in state formation.

Contribution

It reveals the spectral mechanisms that facilitate the dynamical creation of N00N states in symmetric double wells under moderate interactions.

Findings

Degeneracy suppresses transitions to high-energy states.

Moderate interactions support N00N state formation.

Asymmetry inhibits N00N state creation.

Abstract

We study the creation of a bosonic N00N state from the evolution of a Fock state in a double well. While noninteracting bosons disappear quickly in the Hilbert space, the evolution under the influence of a Bose-Hubbard Hamiltonian is much more restricted. This restriction is caused by the fragmentation of the spectrum into a high-energy part with doubly degenerate levels and a nondegenerate low-energy part. This degeneracy suppresses transitions to states of the high-energy part of the spectrum. At a moderate interaction strength this effect supports strongly the dynamical formation of a N00N state. The N00N state is suppressed in an asymmetric double well, where the double degeneracy is absent.