Fragmentation of a trapped bosonic mixture

Fragmentation of bosons and pairs in a trapped imbalanced bosonic mixture is investigated analytically using an exactly solvable model, the generic harmonic-interaction model for mixtures. Closed-form expressions for the eigenvalues and eigenfunctions of the reduced one-particle and two-particle density matrices as a function of all parameters, the masses, numbers of bosons, and the intraspecies and interspecies interactions, are obtained and analyzed. As an application, we consider a system made of N1 = 100 non-interacting species 1 bosons embedded in a bath made of N2 = 10⁶ non-interacting species 2 bosons, and show how fragmentation of the system’s bosons and pairs emerges from the system–bath interaction only. Interestingly, the lighter the bosons comprising the bath are the stronger is the system’s fragmentation. Further applications are briefly discussed.