Two particles in one-dimensional confinement: the role of mass imbalance and Pauli's exclusion principle within short and long range interactions

Abstract

Abstract We consider the problem of two interacting particles in one-dimensional harmonic confinement. By considering both particles are subject to the same harmonic curvature, we obtain exact numerical solutions in a straightforward way for any choice of interaction potential. The formulation is then applied in the situations of ({\it i}) non-identical particles with different masses $m_1$ and $m_2$; ({\it ii}) bosons and fermions; ({\it iii}) short and long range interactions; and ({\it iv}) combining all these ingredients within a time-dependent applied electric field. We analyze the role of the mass imbalance and Pauli's exclusion principle by investigating the formation of bound pairs, the expected value of the separation between the particles and the effects of interaction and exclusion principle on the density distributions.