Fragmentation of a trapped bosonic mixture

TL;DR

This paper analytically investigates the fragmentation phenomena in a trapped bosonic mixture using an exactly solvable model, deriving explicit expressions for eigenvalues and eigenfunctions related to the system's density matrices.

Contribution

It provides closed-form solutions for the eigenvalues and eigenfunctions of reduced density matrices in a bosonic mixture, revealing how system-bath interactions induce fragmentation.

Findings

Fragmentation increases with lighter bath bosons.

Explicit formulas for density matrices are derived.

System-bath interaction drives the fragmentation process.

Abstract

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 $N_1=100$ non-interacting species $1$ bosons embedded in a bath made of $N_2=10^6$ 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.