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

References in corpus (3)

• Derivation of Effective Evolution Equations from Microscopic Quantum Dynamics
• Théorèmes de de Finetti, limites de champ moyen et condensation de Bose-Einstein
• Propagation of Chaos and Effective Equations in Kinetic Theory: a Brief Survey

Cited by in corpus (3)

• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• The diatomic Hartree model at dissociation
• Reduced fluctuations for bosons in a double well