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

Alessandro Olgiati (1) , Nicolas Rougerie (2) , Dominique Spehner (3, 4, 5)

1 Institute of Mathematics University of Zurich
2 ENS de Lyon - École normale supérieure de Lyon
3 Departamento de Ingenieria Matematica
4 IF - Institut Fourier
5 LPM2C - Laboratoire de physique et modélisation des milieux condensés

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.

Domaines: Physique mathématique [math-ph]; Théorie spectrale [math.SP]

Alessandro Olgiati, Nicolas Rougerie, Dominique Spehner. Bosons in a double well: two-mode approximation and fluctuations. 2021. ⟨hal-03117990v2⟩