Spectroscopy for a Few Atoms Harmonically-Trapped in One Dimension

Abstract

Spectroscopic labels for a few particles with spin that are harmonically trapped in one-dimension with effectively zero-range interactions are provided by quantum numbers that characterize the symmetries of the Hamiltonian: permutations of identical particles, parity inversion, and the separability of the center-of-mass. The exact solutions for the non-interacting and infinitely repulsive cases are reduced with respect to these symmetries. This reduction explains how states of single-component and multi-component fermions and bosons transform under adiabatic evolution from non-interacting to strong hard-core repulsion. These spectroscopic methods also clarify previous analytic and numerical results for intermediate values of interaction strength. Several examples, including adiabatic mapping for two-component fermionic states in the cases $N=3-5$, are provided.

version 3: 11 pages, 1 figure, 16 tables. Few corrections of v2 to match published form

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Exact Solution of Strongly Interacting Quasi-One-Dimensional Spinor Bose Gases
• Exact solution for infinitely strongly interacting Fermi gases in tight waveguides
• Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides
• Evolution from a Bose-Einstein condensate to a Tonks-Girardeau gas: An exact diagonalization study
• Symmetries of Three Harmonically-Trapped Particles in One Dimension
• Multicomponent Strongly Interacting Few-Fermion Systems in One Dimension
• Many-particle Systems in One Dimension in the Harmonic Approximation

Cited by in corpus (34)

• Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap
• One-dimensional mixtures of several ultracold atoms: a review
• Distinguishability, degeneracy and correlations in three harmonically trapped bosons in one-dimension
• High-momentum tails as magnetic structure probes for strongly-correlated $SU(\kappa )$ fermionic mixtures in one-dimensional traps
• Quantum correlations and spatial localization in one-dimensional ultracold bosonic mixtures
• Quenching small quantum gases: Genesis of the orthogonality catastrophe
• Pairing in a system of a few attractive fermions in a harmonic trap
• Momentum distributions and numerical methods for strongly interacting one-dimensional spinor gases
• Exact density profiles and symmetry classification for strongly interacting multi-component Fermi gases in tight waveguides
• One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: I. One, Two, and Three Particles
• A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap
• Strongly interacting mesoscopic systems of anyons in one dimension
• One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: II. $N$ Particles
• Impenetrable Mass-Imbalanced Particles in One-Dimensional Harmonic Traps
• Exploring the few- to many-body crossover using cold atoms in one dimension
• Strongly interacting Bose-Fermi mixtures in one dimension
• Integrable families of hard-core particles with unequal masses in a one-dimensional harmonic trap
• Strongly correlated one-dimensional Bose-Fermi quantum mixtures: symmetry and correlations
• Strongly interacting one-dimensional quantum gas mixtures with weak p-wave interactions
• Static and dynamic properties of a few spin $1/2$ interacting fermions trapped in an harmonic potential
• Strongly Interacting One-Dimensional Systems with Small Mass Imbalance
• Permutation symmetry in spinor quantum gases: selection rules, conservation laws, and correlations
• Optimized Configuration Interaction Approach for Trapped Multiparticle Systems Interacting Via Contact Forces
• Correlation properties of a three-body bosonic mixture in a harmonic trap
• Slightly imbalanced system of a few attractive fermions in a one-dimensional harmonic trap
• Entanglement production by statistical operators
• Ground-states of spin-1 bosons in asymmetric double-wells
• Spin-incoherent one-dimensional spin-1 Bose Luttinger liquid
• Sum rules for spin-$1/2$ quantum gases in states with well-defined spins: spin-independent interactions and spin-dependent external fields
• Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results
• Long-lived states with well-defined spins in spin-$1/2$ homogeneous Bose gases
• The Goldilocks model of separable, zero-range, few-body interactions in one-dimensional harmonic traps
• Dynamical resistivity of a few interacting fermions to the time-dependent potential barrier
• Sum rules for spin-$1/2$ quantum gases in states with well-defined spins: II. Spin-dependent two-body interactions