Macroscopic superposition states of ultracold bosons in a double-well potential

TL;DR

This paper thoroughly analyzes macroscopic superpositions of ultracold bosons in double-well potentials, extending the traditional two-mode model to include multiple modes and revealing new regimes and properties of these quantum states.

Contribution

It generalizes the Lipkin-Meshkov-Glick Hamiltonian to include up to eight modes, providing a comprehensive framework for understanding complex macroscopic superpositions beyond the two-mode approximation.

Findings

Identification of new macroscopic superposition regimes

Demonstration of limitations of the two-mode LMG model

Introduction of angular degrees of freedom in superposition states

Abstract

We present a thorough description of the physical regimes for ultracold bosons in double wells, with special attention paid to macroscopic superpositions (MSs). We use a generalization of the Lipkin-Meshkov-Glick Hamiltonian of up to eight single particle modes to study these MSs, solving the Hamiltonian with a combination of numerical exact diagonalization and high-order perturbation theory. The MS is between left and right potential wells; the extreme case with all atoms simultaneously located in both wells and in only two modes is the famous NOON state, but our approach encompasses much more general MSs. Use of more single particle modes brings dimensionality into the problem, allows us to set hard limits on the use of the original two-mode LMG model commonly treated in the literature, and also introduces a new mixed Josephson-Fock regime. Higher modes introduce angular degrees of freedom and MS states with different angular properties.