Bosons in a double well: two-mode approximation and fluctuations

TL;DR

This paper analyzes the ground state of many interacting bosons in a double-well potential, deriving an effective Hamiltonian and studying particle number fluctuations that indicate correlated quantum states.

Contribution

It derives an energy expansion including Bose-Hubbard and Bogoliubov corrections and provides a variance bound showing non-classical correlations in the ground state.

Findings

Energy expansion with Bose-Hubbard and Bogoliubov corrections

Variance bound indicating non-classical particle correlations

Violation of the central limit theorem in particle number fluctuations

Abstract

We study the ground state for many interacting bosons in a double-well potential, in a joint limit where the particle number and the distance between the potential wells both go to infinity. Two single-particle orbitals (one for each well) are macroscopically occupied, and we are concerned with deriving the corresponding effective Bose-Hubbard Hamiltonian. We prove (i) an energy expansion, including the two-modes Bose-Hubbard energy and two independent Bogoliubov corrections (one for each potential well), (ii) a variance bound for the number of particles falling inside each potential well. The latter is a signature of a correlated ground state in that it violates the central limit theorem.