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

arXiv:1508.04452 · Physical Review A

Number-parity effect for confined fermions in one dimension

Christian Schilling, R. Schilling

Published Feb 1, 2016• 27 citations
arXivHTMLPDF

Abstract

For $N$ spin-polarized fermions with harmonic pair interactions in a one-dimensional trap an odd-even effect is found. The spectrum of the one-particle reduced density matrix of the system's ground state differs qualitatively for $N$ odd and $N$ even. This effect only occurs for strong attractive and repulsive interactions. Since it does not exist for bosons, it must originate from the repulsive nature implied by the fermionic exchange statistics. In contrast to the spectrum, the one-particle density and correlation function for strong attractive interactions do not show any sensitivity on the number parity. This also suggests that reduced-density-matrix-functional theory has a more subtle $N$ dependency than density-functional theory.

DOI
10.1103/physreva.93.021601

Related papers

Pairing in a system of a few attractive fermions in a harmonic trap

Tomasz Sowiński, Mariusz Gajda, Kazimierz Rza̧żewski

We study a strongly attractive system of a few spin-(1/2) fermions confined in a one-dimensional harmonic trap, interacting via two-body contact potential. Performing exact diagonalization of the Hamiltonian we analyze the ground state and the thermal state of the system in terms of one- and two-particle reduced density matrices. We show how for strong attraction the correlated pairs emerge in the system. We find that the fraction of correlated pairs depends on temperature and we show that this dependence has universal properties analogous to the gap function known from the theory of superconductivity. In contrast to the standard approach based on the variational ansatz and/or perturbation theory, our predictions are exact and are valid also in a strong-attraction limit. Our findings contribute to the understanding of strongly correlated few-body systems and can be verified in current experiments on ultra-cold atoms.

arXiv:1406.0400•Europhysics Letters (EPL)•Jan 1, 2015•46 citations

Ground-state properties of a one-dimensional strongly interacting Bose-Fermi mixture in a double-well potential

Karlo Lelas, Dario Jukić, Hrvoje Buljan

We calculate the reduced single-particle density matrix (RSPDM), momentum distribution, natural orbitals and their occupancies, for a strongly repulsive one-dimensional Bose-Fermi mixture in a double-well potential with a large central barrier. We assume that all particles have the same mass, and fermions are spin polarized. For mesoscopic systems, we find that the ground-state properties qualitatively differ for mixtures with even number of particles (both odd-odd and even-even mixtures) in comparison to mixtures with odd particle numbers (odd-even and even-odd mixtures). For even mixtures the momentum distribution is smooth, whereas the momentum distribution of odd mixtures possesses distinct modulations; the differences are observed also in the off-diagonal correlations of the RSPDM, and in the occupancies of natural orbitals. The calculation is based on a formula which enables efficient calculation of the RSPDM for mesoscopic mixtures in various potentials.

arXiv:0907.4580•Physical Review A•Nov 19, 2009•12 citations

Density-functional theory for the spin-1 bosons in a one-dimensional harmonic trap

Hongmei Wang, Yunbo Zhang

We propose the density-functional theory for one-dimensional harmonically trapped spin-1 bosons in the ground state with repulsive density-density interaction and antiferromagnetic spin-exchange interaction. The density distributions of spin-singlet-paired bosons and polarized bosons with different total polarization for various interaction parameters are obtained by solving the Kohn-Sham equations, which are derived based on the local density approximation and the Bethe ansatz exact results for a homogeneous system. Nonmonotonicity of the central densities is attributed to the competition between the density interaction and spin-exchange. The results reveal the phase separation of the paired and polarized bosons, the density profiles of which respectively approach the Tonks-Girardeau gases of Bose-Bose pairs and scalar bosons in the case of strong interaction. We give the radius-polarization phase diagram at strong interaction and find the critical polarization, which paves the way to directly observe the exotic singlet pairing in spinor gas experimentally.

arXiv:1304.1328•Physical Review A•Aug 30, 2013•9 citations

Treatment of backscattering in a gas of interacting fermions confined to a one-dimensional harmonic atom trap

Gao Xianlong, F. Gleisberg, F. Lochmann +1 more

An asymptotically exact many-body theory for spin-polarized interacting fermions in a one-dimensional harmonic atom trap is developed using the bosonization method and including backward scattering. In contrast to the Luttinger model, backscattering in the trap generates one-particle potentials which must be diagonalized simultaneously with the two-body interactions. Inclusion of backscattering becomes necessary because backscattering is a dominant interaction process between confined identical one-dimensional fermions. The bosonization method is applied to the calculation of one-particle matrix elements at zero temperature. A detailed discussion of the validity of the results from bosonization is given, including a comparison with direct numerical diagonalization in fermionic Hilbert space. A model for the interaction coefficients is developed along the lines of the Luttinger model with only one coupling constant K. With these results, particle densities, the Wigner function, and the central pair-correlation function are calculated and displayed for large fermion numbers. It is shown how interactions modify these quantities. The anomalous dimension of the pair-correlation function in the center of the trap is also discussed and found to be in accord with the Luttinger model.

arXiv:cond-mat/0206337•Physical Review A•Feb 24, 2003•13 citations

Low-density, one-dimensional quantum gases in the presence of a localized attractive potential

John Goold, D O'Donoghue, Thomas Busch

We investigate low-density, quantum-degenerate gases in the presence of a localized attractive potential in the centre of a one-dimensional harmonic trap. The attractive potential is modelled using a parameterized δ-function, allowing us to determine all single-particle eigenfunctions analytically. From these we calculate the ground-state many-body properties for a system of spin-polarized fermions and, using the Bose–Fermi mapping theorem, extend the results to strongly interacting bosonic systems. We discuss the single-particle densities, the pair-correlation functions, the reduced single-particle density matrices and the momentum distributions as a function of the particle number and strength of the attractive point potential. As an important experimental observable, we place special emphasis on spatial coherence properties of such samples.

Journal of Physics B Atomic Molecular and Optical Physics•Oct 15, 2008•12 citations

Pairing in Few-Fermion Systems with Attractive Interactions

G. Zürn, A. N. Wenz, Simon Murmann +3 more

We study quasi-one-dimensional few-particle systems consisting of one to six ultracold fermionic atoms in two different spin states with attractive interactions. We probe the system by deforming the trapping potential and by observing the tunneling of particles out of the trap. For even particle numbers, we observe a tunneling behavior that deviates from uncorrelated single-particle tunneling indicating the existence of pair correlations in the system. From the tunneling time scales, we infer the differences in interaction energies of systems with different number of particles, which show a strong odd-even effect, similar to the one observed for neutron separation experiments in nuclei.

arXiv:1307.5153•Physical Review Letters•Oct 22, 2013•179 citations
For NNN spin-polarized fermions with harmonic pair interactions in a one-dimensional trap an odd-even effect is found. The spectrum of the one-particle reduced density matrix of the system's ground state differs qualitatively for NNN odd and NNN even. This effect only occurs for strong attractive and repulsive interactions. Since it does not exist for bosons, it must originate from the repulsive nature implied by the fermionic exchange statistics. In contrast to the spectrum, the one-particle density and correlation function for strong attractive interactions do not show any sensitivity on the number parity. This also suggests that reduced-density-matrix-functional theory has a more subtle NNN dependency than density-functional theory.
We study a strongly attractive system of a few spin-(1/2) fermions confined in a one-dimensional harmonic trap, interacting via two-body contact potential. Performing exact diagonalization of the Hamiltonian we analyze the ground state and the thermal state of the system in terms of one- and two-particle reduced density matrices. We show how for strong attraction the correlated pairs emerge in the system. We find that the fraction of correlated pairs depends on temperature and we show that this dependence has universal properties analogous to the gap function known from the theory of superconductivity. In contrast to the standard approach based on the variational ansatz and/or perturbation theory, our predictions are exact and are valid also in a strong-attraction limit. Our findings contribute to the understanding of strongly correlated few-body systems and can be verified in current experiments on ultra-cold atoms.
We calculate the reduced single-particle density matrix (RSPDM), momentum distribution, natural orbitals and their occupancies, for a strongly repulsive one-dimensional Bose-Fermi mixture in a double-well potential with a large central barrier. We assume that all particles have the same mass, and fermions are spin polarized. For mesoscopic systems, we find that the ground-state properties qualitatively differ for mixtures with even number of particles (both odd-odd and even-even mixtures) in comparison to mixtures with odd particle numbers (odd-even and even-odd mixtures). For even mixtures the momentum distribution is smooth, whereas the momentum distribution of odd mixtures possesses distinct modulations; the differences are observed also in the off-diagonal correlations of the RSPDM, and in the occupancies of natural orbitals. The calculation is based on a formula which enables efficient calculation of the RSPDM for mesoscopic mixtures in various potentials.
We propose the density-functional theory for one-dimensional harmonically trapped spin-1 bosons in the ground state with repulsive density-density interaction and antiferromagnetic spin-exchange interaction. The density distributions of spin-singlet-paired bosons and polarized bosons with different total polarization for various interaction parameters are obtained by solving the Kohn-Sham equations, which are derived based on the local density approximation and the Bethe ansatz exact results for a homogeneous system. Nonmonotonicity of the central densities is attributed to the competition between the density interaction and spin-exchange. The results reveal the phase separation of the paired and polarized bosons, the density profiles of which respectively approach the Tonks-Girardeau gases of Bose-Bose pairs and scalar bosons in the case of strong interaction. We give the radius-polarization phase diagram at strong interaction and find the critical polarization, which paves the way to directly observe the exotic singlet pairing in spinor gas experimentally.
An asymptotically exact many-body theory for spin-polarized interacting fermions in a one-dimensional harmonic atom trap is developed using the bosonization method and including backward scattering. In contrast to the Luttinger model, backscattering in the trap generates one-particle potentials which must be diagonalized simultaneously with the two-body interactions. Inclusion of backscattering becomes necessary because backscattering is a dominant interaction process between confined identical one-dimensional fermions. The bosonization method is applied to the calculation of one-particle matrix elements at zero temperature. A detailed discussion of the validity of the results from bosonization is given, including a comparison with direct numerical diagonalization in fermionic Hilbert space. A model for the interaction coefficients is developed along the lines of the Luttinger model with only one coupling constant K. With these results, particle densities, the Wigner function, and the central pair-correlation function are calculated and displayed for large fermion numbers. It is shown how interactions modify these quantities. The anomalous dimension of the pair-correlation function in the center of the trap is also discussed and found to be in accord with the Luttinger model.
We investigate low-density, quantum-degenerate gases in the presence of a localized attractive potential in the centre of a one-dimensional harmonic trap. The attractive potential is modelled using a parameterized δ-function, allowing us to determine all single-particle eigenfunctions analytically. From these we calculate the ground-state many-body properties for a system of spin-polarized fermions and, using the Bose–Fermi mapping theorem, extend the results to strongly interacting bosonic systems. We discuss the single-particle densities, the pair-correlation functions, the reduced single-particle density matrices and the momentum distributions as a function of the particle number and strength of the attractive point potential. As an important experimental observable, we place special emphasis on spatial coherence properties of such samples.
We study quasi-one-dimensional few-particle systems consisting of one to six ultracold fermionic atoms in two different spin states with attractive interactions. We probe the system by deforming the trapping potential and by observing the tunneling of particles out of the trap. For even particle numbers, we observe a tunneling behavior that deviates from uncorrelated single-particle tunneling indicating the existence of pair correlations in the system. From the tunneling time scales, we infer the differences in interaction energies of systems with different number of particles, which show a strong odd-even effect, similar to the one observed for neutron separation experiments in nuclei.