Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

APS Open Science

Entanglement control in confined two-particle systems: Mass imbalance, trap asymmetry, interaction range, and localized potentials

Anonymous, Daniel Vieira, Mateus B. P. Querne

Published Oct 6, 2026• 0 citations
Publisher

Abstract

We present a systematic study of entanglement control in one-dimensional systems of two distinguishable interacting particles in harmonic confinement. Using density matrix renormalization group calculations, we examine how the von Neumann entropy evolves under variations of mass ratio, trap-frequency asymmetry, interaction range, and localized external fields. Our results reveal a consistent picture connecting the real-space density overlap, the redistribution of quantum fluctuations, and the resulting entanglement. Within the parameter regimes investigated, mass imbalance produces more pronounced changes in entanglement than trap-frequency asymmetry. Furthermore, the competition between interaction range and field-induced polarization determines whether short- or long-range correlations dominate. By connecting the von Neumann entropy with measurable quantities such as the density difference Δ n ( x ) and the phase-space products 〈 x i 2 〉 〈 p x i 2 〉 , we establish experimentally accessible fingerprints of quantum correlation. Our analysis demonstrates how external and geometrical parameters can tune entanglement in confined two-particle models, providing a basis for exploring related control protocols in suitable experimental settings.

DOI
10.1103/rdby-pn24

Related papers

Entanglement in Bound States of Two Particles with a Localized Center-of-Mass Wave-Function

B. Nogales, Sergio Curilef, Angelo Plastino

Abstract We explore some entanglement-related features of systems consisting of two particles coupled through a central potential. We consider two types of systems, constituted by particles in one spatial dimension interacting through an attractive Dirac Delta potential, or through a harmonic quadratic potential. The degree of freedom corresponding to the system’s center of mass is either regarded as confined within a one dimensional box, or described by a localized Gaussian wave-packet. As a quantitative indicator of the degree of entanglement between the particles, we use the linear entropy of the one-particle marginal density matrix. In general, this quantity cannot be calculated analytically (except in some special cases related to the Harmonic interaction). Consequently, the linear entropy has to be evaluated numerically. Since the concomitant numerical problem consist in evaluating a multi-dimensional integral in four dimensions, the Monte Carlo integration method is an appropriate one for this task. We explore numerically how the system’s entanglement depends on the different interaction potentials, on the different types of confinement for the system’s center of mass, and on the associated parameters describing the size and geometry of the system.

Journal of Physics Conference Series•Sep 1, 2024•1 citation

Quantum Entanglement of Two Harmonically Trapped Dipolar Particles

Przemysław Kościk

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.

arXiv:1410.0578•Few-Body Systems•Jan 11, 2015•6 citations

Entanglement-related features of hydrogenic systems and other systems described by bound states of two interacting particles

Benny Nogales, Sergio Curilef, Angel Ricardo Plastino

This paper delves into entanglement-related features of one-dimensional and three-dimensional systems comprising two particles interacting through an attractive potential, such as the delta, harmonic, and Coulomb ones. As a quantitative indicator of the amount of entanglement between the particles, we employ the linear entropy of the system's one-particle marginal density matrices. Except in some particular instances involving the harmonic potential, this quantity is not analytically tractable and requires numerical evaluation. Our aim is to elucidate some aspects of entanglement in hydrogenic systems. Hydrogenic systems, consisting of two particles interacting through the Coulomb potential, are of clear importance in physics and chemistry, but their entanglement properties have started to be explored only recently. To better understand entanglement in those systems, we first analyze one-dimensional systems interacting via Dirac delta and harmonic potentials. Insights gained from these one-dimensional cases provide valuable guidelines for studying entanglement in hydrogenic systems. We numerically investigate, for the interaction potentials already mentioned, and for different types of confinement for the center of mass, how the system's entanglement varies with the parameters that determine the size and geometry of the system's quantum state. We find that entanglement depends on a dimensionless quantity given by the quotient of two parameters characterizing the length scales associated with the interaction potential and the center of mass confinement. Entanglement approaches its maximum when the above-mentioned dimensionless quotient tends to its extreme values and adopts its minimum at an intermediate value of the dimensionless quotient. We find that the same general qualitative features of entanglement behavior are observed for different attractive interactions.

Chaos An Interdisciplinary Journal of Nonlinear Science•Jul 1, 2025•1 citation

Entanglement and particle correlations of Fermi gases in harmonic traps

Ettore Vicari

We investigate quantum correlations in the ground state of noninteracting Fermi gases of $N$ particles trapped by an external space-dependent harmonic potential, in any dimension. For this purpose we compute one-particle correlations, particle fluctuations, and bipartite entanglement entropies of extended space regions, and study their large-$N$ scaling behaviors. The half-space von Neumann entanglement entropy is computed for any dimension, obtaining ${S}_{\mathrm{HS}}\ensuremath{\approx}{c}_{l}{N}^{(d\ensuremath{-}1)/d}\mathrm{ln}N$ analogously to homogenous systems, with ${c}_{l}=1/6,\phantom{\rule{0.222222em}{0ex}}1/(6\sqrt{2}),\phantom{\rule{0.222222em}{0ex}}1/(6\sqrt{6})$ in one, two, and three dimensions, respectively. We show that the asymptotic large-$N$ relation ${S}_{A}\ensuremath{\approx}{\ensuremath{\pi}}^{2}{V}_{A}/3$, between the von Neumann entanglement entropy ${S}_{A}$ and particle variance ${V}_{A}$ of an extended space region $A$, holds for any subsystem $A$ and in any dimension, analogously to homogeneous noninteracting Fermi gases.

arXiv:1204.2155•Physical Review A•Jun 5, 2012•51 citations

Exact spectral decomposition of a time-dependent one-particle reduced density matrix

István Nagy, Jānos Pipek, M. L. Glasser

We determine the exact time-dependent non-idempotent one-particle reduced density matrix and its spectral decomposition for a harmonically confined two-particle correlated one-dimensional system when the interaction terms in the Schrödinger Hamiltonian are changed abruptly. Based on this matrix in coordinate space we derivea precise condition for the equivalence of the purity and the overlap-square of the correlated and non-correlated wave functions as the system evolves in time. This equivalence holds only if the interparticle interactions are affected, while the confinement terms are unaffected within the stability range of the system. Under this condition we also analyze various time-dependent measures of entanglement and demonstrate that, depending on the magnitude of the changes made in the Schrödinger Hamiltonian, periodic, logarithmically incresing or constant value behavior of the von Neumann entropy can occur.

arXiv:1701.09030•Jan 31, 2017•0 citations

Entanglement between two fermionic atoms inside a cylindrical harmonic trap

Baoqing Sun, Li You, D. L. Zhou

We investigate quantum entanglement between two (spin-$1∕2$) fermions inside a cylindrical harmonic trap, making use of the von Neumann entropy for the reduced single-particle density matrix as the pure-state entanglement measure. We explore the dependence of pair entanglement on the geometry and strength of the trap and on the strength of the pairing interaction over the complete range of the effective BCS to BEC crossover. Our result elucidates an interesting connection between our model system of two fermions and that of two interacting bosons.

arXiv:quant-ph/0701130•Physical Review A•Jan 25, 2007•2 citations
We present a systematic study of entanglement control in one-dimensional systems of two distinguishable interacting particles in harmonic confinement. Using density matrix renormalization group calculations, we examine how the von Neumann entropy evolves under variations of mass ratio, trap-frequency asymmetry, interaction range, and localized external fields. Our results reveal a consistent picture connecting the real-space density overlap, the redistribution of quantum fluctuations, and the resulting entanglement. Within the parameter regimes investigated, mass imbalance produces more pronounced changes in entanglement than trap-frequency asymmetry. Furthermore, the competition between interaction range and field-induced polarization determines whether short- or long-range correlations dominate. By connecting the von Neumann entropy with measurable quantities such as the density difference Δ n ( x ) and the phase-space products 〈 x i 2 〉 〈 p x i 2 〉 , we establish experimentally accessible fingerprints of quantum correlation. Our analysis demonstrates how external and geometrical parameters can tune entanglement in confined two-particle models, providing a basis for exploring related control protocols in suitable experimental settings.
Abstract We explore some entanglement-related features of systems consisting of two particles coupled through a central potential. We consider two types of systems, constituted by particles in one spatial dimension interacting through an attractive Dirac Delta potential, or through a harmonic quadratic potential. The degree of freedom corresponding to the system’s center of mass is either regarded as confined within a one dimensional box, or described by a localized Gaussian wave-packet. As a quantitative indicator of the degree of entanglement between the particles, we use the linear entropy of the one-particle marginal density matrix. In general, this quantity cannot be calculated analytically (except in some special cases related to the Harmonic interaction). Consequently, the linear entropy has to be evaluated numerically. Since the concomitant numerical problem consist in evaluating a multi-dimensional integral in four dimensions, the Monte Carlo integration method is an appropriate one for this task. We explore numerically how the system’s entanglement depends on the different interaction potentials, on the different types of confinement for the system’s center of mass, and on the associated parameters describing the size and geometry of the system.
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.
This paper delves into entanglement-related features of one-dimensional and three-dimensional systems comprising two particles interacting through an attractive potential, such as the delta, harmonic, and Coulomb ones. As a quantitative indicator of the amount of entanglement between the particles, we employ the linear entropy of the system's one-particle marginal density matrices. Except in some particular instances involving the harmonic potential, this quantity is not analytically tractable and requires numerical evaluation. Our aim is to elucidate some aspects of entanglement in hydrogenic systems. Hydrogenic systems, consisting of two particles interacting through the Coulomb potential, are of clear importance in physics and chemistry, but their entanglement properties have started to be explored only recently. To better understand entanglement in those systems, we first analyze one-dimensional systems interacting via Dirac delta and harmonic potentials. Insights gained from these one-dimensional cases provide valuable guidelines for studying entanglement in hydrogenic systems. We numerically investigate, for the interaction potentials already mentioned, and for different types of confinement for the center of mass, how the system's entanglement varies with the parameters that determine the size and geometry of the system's quantum state. We find that entanglement depends on a dimensionless quantity given by the quotient of two parameters characterizing the length scales associated with the interaction potential and the center of mass confinement. Entanglement approaches its maximum when the above-mentioned dimensionless quotient tends to its extreme values and adopts its minimum at an intermediate value of the dimensionless quotient. We find that the same general qualitative features of entanglement behavior are observed for different attractive interactions.
We investigate quantum correlations in the ground state of noninteracting Fermi gases of NNN particles trapped by an external space-dependent harmonic potential, in any dimension. For this purpose we compute one-particle correlations, particle fluctuations, and bipartite entanglement entropies of extended space regions, and study their large-NNN scaling behaviors. The half-space von Neumann entanglement entropy is computed for any dimension, obtaining ${S}_{\mathrm{HS}}\ensuremath{\approx}{c}_{l}{N}^{(d\ensuremath{-}1)/d}\mathrm{ln}N$ analogously to homogenous systems, with cl=1/6,1/(62),1/(66){c}_{l}=1/6,\phantom{\rule{0.222222em}{0ex}}1/(6\sqrt{2}),\phantom{\rule{0.222222em}{0ex}}1/(6\sqrt{6})cl​=1/6,1/(62​),1/(66​) in one, two, and three dimensions, respectively. We show that the asymptotic large-NNN relation ${S}_{A}\ensuremath{\approx}{\ensuremath{\pi}}^{2}{V}_{A}/3$, between the von Neumann entanglement entropy SA{S}_{A}SA​ and particle variance VA{V}_{A}VA​ of an extended space region AAA, holds for any subsystem AAA and in any dimension, analogously to homogeneous noninteracting Fermi gases.
We determine the exact time-dependent non-idempotent one-particle reduced density matrix and its spectral decomposition for a harmonically confined two-particle correlated one-dimensional system when the interaction terms in the Schrödinger Hamiltonian are changed abruptly. Based on this matrix in coordinate space we derivea precise condition for the equivalence of the purity and the overlap-square of the correlated and non-correlated wave functions as the system evolves in time. This equivalence holds only if the interparticle interactions are affected, while the confinement terms are unaffected within the stability range of the system. Under this condition we also analyze various time-dependent measures of entanglement and demonstrate that, depending on the magnitude of the changes made in the Schrödinger Hamiltonian, periodic, logarithmically incresing or constant value behavior of the von Neumann entropy can occur.
We investigate quantum entanglement between two (spin-1∕21∕21∕2) fermions inside a cylindrical harmonic trap, making use of the von Neumann entropy for the reduced single-particle density matrix as the pure-state entanglement measure. We explore the dependence of pair entanglement on the geometry and strength of the trap and on the strength of the pairing interaction over the complete range of the effective BCS to BEC crossover. Our result elucidates an interesting connection between our model system of two fermions and that of two interacting bosons.