We study systems of two identical dipolar particles confined in quasi one-dimensional harmonic traps. Numerical results for the dependencies of the entanglement on the control parameters of the systems are provided and discussed in detail. In the limit of a strong interaction between the particles, the occupancies and the von Neumann entropies of the bosonic and fermionic ground states are derived in closed analytic forms by applying the harmonic approximation. The strong correlation regimes of the system with the dipolar bosons and the system with the charged ones are compared with each other in regard to aspects of their entanglement.
Exact solutions to many-body interacting systems of both bosonic and fermionic particles confined to harmonic potential in an arbitrary number of dimensions are given. Energy levels and their degeneracies for trapped identical particles interacting via harmonic forces are calculated. This specific form of the interaction allows for analytical solutions. The mutual interaction, attractive or repulsive, modifies significantly the properties of the considered system. For a large number of particles the interaction essentially results in a frequency shift. Statistical properties (e.g., microcanonical and grand canonical partition functions) as well as some illustrative, physically relevant examples are discussed. Our results give an unusual opportunity for further studies of interacting systems in the framework of the exactly soluble model.
The ground-state entanglement of a single particle of the N-harmonium system (i.e., a completely-integrable model of
N particles where both the confinement and the two-particle interaction are harmonic) is shown to be analytically determined in terms of
N and the relative interaction strength. For bosons, we compute the von Neumann entropy of the one-body reduced density matrix by using the corresponding natural occupation numbers. There exists a critical number
Nc of particles so that below it, for positive values of the coupling constant, the entanglement grows when the number of particles is increasing; the opposite occurs for
N>Nc. For fermions, we compute the one-body reduced density matrix for the closed-shell spinned case. In the strong coupling regime, the linear entropy of the system decreases when
N is growing. For fixed
N, the entanglement is found (a) to decrease (increase) for negatively (positively) increasing values of the coupling constant, and (b) to grow when the energy is increasing. Moreover, the spatial and spin contributions to the total entanglement are found to be of comparable size.
Following up on a recent analysis of two cold atoms in a time-dependent harmonic trap in one dimension, we explore the entanglement entropy of two and three fermions in the same situation when driven through a parametric resonance. We find that the presence of such a resonance in the two-particle system leaves a clear imprint on the entanglement entropy. We show how the signal is modified by attractive and repulsive contact interactions, and how it remains present for the three-particle system. Additionaly, we extend the work of recent experiments to demonstrate how restricting observation to a limited subsystem gives rise to locally thermal behavior.