Entanglement in N-harmonium: bosons and fermions

Abstract

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 N c 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 > N c . 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.

Entropic measures of Rydberg‐like harmonic states

“…Let us just highlight that the oscillator wave functions saturate the most important mathematical realizations of the quantum uncertainty principle such as the Heisenberg‐like uncertainty relations, which are based on the variance and/or higher‐order moments, and the entropic uncertainty relations based on the Shannon entropy, the Rényi entropy, or the Fisher information . Furthermore, they have been used in numerous scientific fields ranging from quantum many‐body physics, heat transport, quantum entanglement, Keppler systems, quantum dots and cold atomic gases to fractional and quantum statistics, and black‐holes thermodynamics . However, the information‐theoretic properties of the three (or higher)‐dimensional harmonic oscillator are not yet settled down in spite of numerous efforts (see e.g., Refs.…”

The von Neumann entanglement entropy for Wigner-crystal states in one dimensional N-particle systems

“…In particular, a few attempts have been made recently towards understanding the entanglement in systems of interacting particles. For example, some light has been shed on entanglement both in quantum dot systems [6][7][8][9][10][11][12][13][14][15] and in systems of harmonically interacting particles in a harmonic trap (the so-called Moshinsky atom) [16][17][18][19][20][21][22][23]. Special attention has also been paid to the study of entanglement in the helium atoms and helium ions [24][25][26][27][28][29][30][31][32].…”

“…The reason for this lies in the fact that in most cases the determination of the wavefunction of a few-body state requires performing numerical calculations, which is a major problem in general. According to our best knowledge, the only N particle system of which the entanglement properties have been fully explored so far is the Moshinsky model system [17,18] The model on which we focus here is a system composed of N particles interacting via a long-range inverse power-law potential, which are confined by an external one-dimensional (1D) harmonic potential…”

Quantum correlations in one-dimensional Wigner molecules

“…In particular, the study of the manybody properties of various quantum composite systems is nowadays one of the most active areas of theoretical physics [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. Investigating quantum correlations in systems of interacting particles trapped in external potentials is not only important in view of the context of quantum information technology [24] but also a key to improving our understanding of quantum matter.…”