Exact Solution of Strongly Interacting Quasi-One-Dimensional Spinor Bose Gases

Abstract

We present an exact analytical solution of the fundamental system of quasi-one-dimensional spin-1 bosons with infinite delta-repulsion. The eigenfunctions are constructed from the wave functions of non-interacting spinless fermions, based on Girardeau's Fermi-Bose mapping, and from the wave functions of distinguishable spins. We show that the spinor bosons behave like a compound of non-interacting spinless fermions and non-interacting distinguishable spins. This duality is especially reflected in the spin densities and the energy spectrum. We find that the momentum distribution of the eigenstates depends on the symmetry of the spin function. Furthermore, we discuss the splitting of the ground state multiplet in the regime of large but finite repulsion.

arXiv commentRevised to discuss large but finite interactions

References in corpus (24)

• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• Spinor Bose Condensates in Optical Traps
• Spin domains in ground state spinor Bose-Einstein condensates
• Bose-Einstein condensation with internal degrees of freedom in alkali atom gases
• Quantum spins mixing in spinor Bose-Einstein condensates
• Dynamical response of a Bose-Einstein condensate to a discontinuous change in internal state
• Stability and phase coherence of trapped 1D Bose gases
• Ground state properties of a one-dimensional condensate of hard core bosons in a harmonic trap
• Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction
• Realizing Discontinuous Wave Functions with Renormalized Short-Range Potentials
• Tuning the interactions of spin-polarized fermions using quasi-one-dimensional confinement
• Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides
• Polarization of interacting bosons with spin
• Pathway from condensation via fragmentation to fermionization of cold bosonic systems
• Ultracold Few-Boson Systems in a Double-Well Trap
• Ground-state properties of one-dimensional ultracold Bose gases in a hard-wall trap
• Evolution from a Bose-Einstein condensate to a Tonks-Girardeau gas: An exact diagonalization study
• Correlations in Ultracold Trapped Few-Boson Systems: Transition from Condensation to Fermionization
• Theory of spinor Fermi and Bose gases in tight atom waveguides
• Ferromagnetic behaviour in the strongly interacting two-component Bose gas
• Ground-state properties of hard core bosons in one-dimensional harmonic traps
• Crystalline boson phases in harmonic traps: Beyond the Gross-Pitaevskii mean field
• Exponentially decaying correlations in a gas of strongly interacting spin-polarized 1D fermions with zero-range interactions
• Ramsey interferometry with a two-level Tonks-Girardeau gas

Cited by in corpus (103)

• Shortcuts to adiabaticity
• Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap
• Strongly interacting confined quantum systems in one dimension
• Quantum magnetism without lattices in strongly interacting one-dimensional spinor gases
• One-dimensional mixtures of several ultracold atoms: a review
• Exact solution for infinitely strongly interacting Fermi gases in tight waveguides
• Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential
• Fermionization of two-component few-fermion systems in a one-dimensional harmonic trap
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Strongly Interacting Quantum Gases in One-Dimensional Traps
• Ground-State Ferromagnetic Transition in Strongly Repulsive One-Dimensional Fermi Gases
• Effective spin-chain model for strongly interacting one-dimensional atomic gases with an arbitrary spin
• Distinguishability, degeneracy and correlations in three harmonically trapped bosons in one-dimension
• Exact solution for the degenerate ground-state manifold of a strongly interacting one-dimensional Bose-Fermi mixture
• 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
• Spectroscopy for a Few Atoms Harmonically-Trapped in One Dimension
• 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
• Bose-Fermi dualities for arbitrary one-dimensional quantum systems in the universal low energy regime
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap
• Density-functional theory of two-component Bose gases in one-dimensional harmonic traps
• Ground-state properties of interacting two-component Bose gases in a one-dimensional harmonic trap
• Magnetic ordering and quantum statistical effects in strongly repulsive Fermi-Fermi and Bose-Fermi mixtures
• Spin-chain model for strongly interacting one-dimensional Bose-Fermi mixtures
• Fractional energy states of strongly-interacting bosons in one dimension
• Excitations of attractive 1-D bosons: Binding vs. fermionization
• Impenetrable Mass-Imbalanced Particles in One-Dimensional Harmonic Traps
• One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: II. $N$ Particles
• Exploring the few- to many-body crossover using cold atoms in one dimension
• Engineering quantum magnetism in one-dimensional trapped Fermi gases with p-wave interactions
• Topological Mott insulators of ultracold atomic mixtures induced by interactions in one-dimensional optical superlattices
• Ground-state properties of interacting two-component Bose gases in a hard-wall trap
• Exact Solution for 1D Spin-Polarized Fermions with Resonant Interactions
• CONAN -- the cruncher of local exchange coefficients for strongly interacting confined systems in one dimension
• Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions
• Bose-Fermi Mapping and Multi-Branch Spin Chain Model for Strongly Interacting Quantum Gases in One-Dimension: Dynamics and Collective Excitations
• Universal duality transformations in interacting one-dimensional quantum systems
• Tonks-Girardeau and Super Tonks-Girardeau States of a Trapped 1D Spinor Bose Gas
• Strongly interacting Bose-Fermi mixtures in one dimension
• Ultracold few fermionic atoms in needle-shaped double wells: spin chains and resonating spin clusters from microscopic Hamiltonians emulated via antiferromagnetic Heisenberg and t-J models
• Strongly correlated one-dimensional Bose-Fermi quantum mixtures: symmetry and correlations
• Strongly interacting one-dimensional quantum gas mixtures with weak p-wave interactions
• Spectral properties and breathing dynamics of a few-body Bose-Bose mixture in a 1D harmonic trap
• Realizing time crystals in discrete quantum few-body systems
• Analytical and numerical studies of Bose-Fermi mixtures in a one-dimensional harmonic trap
• Strongly Interacting One-Dimensional Systems with Small Mass Imbalance
• Infinite Barriers and Symmetries for a Few Trapped Particles in One Dimension
• Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps
• Equilibrium thermodynamic properties of interacting two-component bosons in one dimension
• Mesoscopic superpositions of Tonks-Girardeau states and the Bose-Fermi mapping
• Spin-Orbit Coupled One-Dimensional Fermi Gases with Infinite Repulsion
• Two interacting ultracold molecules in a one-dimensional harmonic trap
• Universal scaling of spin mixing dynamics in a strongly interacting one-dimensional Fermi gas
• Dynamical Fermionization in One Dimensional Spinor Gases
• Exact ordering of energy levels for one-dimensional interacting Fermi gases with $SU(n)$ symmetry
• One-Body Density Matrix and Momentum Distribution of Strongly Interacting One-Dimensional Spinor Quantum Gases
• Entanglement of an Impurity in a Few-Body One-Dimensional Ideal Bose System
• Quantum phase transition in a multicomponent anyonic Lieb-Liniger model
• Tan's contact scaling behaviour for trapped Lieb-Liniger bosons: from two to many
• Hard-core Bose-Fermi mixture in one-dimensional split traps
• Dynamical fermionization in a one-dimensional Bose-Fermi mixture
• Exact solution for $SU(2)$-symmetry breaking bosonic mixtures at strong interactions
• Engineering entanglement Hamiltonians with strongly interacting cold atoms in optical traps
• Density-functional theory for the spin-1 bosons in a one-dimensional harmonic trap
• Spin-incoherent Luttinger liquid of one-dimensional spin-1 Tonks-Girardeau Bose gas: Spin-dependent properties
• Spin-incoherent Luttinger liquid of one-dimensional SU($\kappa$) fermions
• Dynamical realization of magnetic states in a strongly interacting Bose mixture
• Effects of interaction imbalance in a strongly repulsive one-dimensional Bose gas
• Spin-incoherent one-dimensional spin-1 Bose Luttinger liquid
• Tuning an effective spin chain of three strongly interacting one-dimensional fermions with the transversal confinement
• Tailoring Dynamical Fermionization: Delta kick cooling of a Tonks-Girardeau gas
• Symmetry oscillations in strongly interacting one-dimensional mixtures
• Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results
• High-momentum oscillating tails of strongly interacting 1D gases in a box
• Mixture of Tonks-Girardeau gas and Fermi gas in one-dimensional optical lattices
• Identical Wells, Symmetry Breaking, and the Near-Unitary Limit
• Are smooth pseudopotentials a good choice for representing short-range interactions?
• A generalized effective spin-chain formalism for strongly interacting spinor gases in optical lattice
• Multiple-Channel Scattering Resonance of One-Dimensional Ultracold Spinor Bosons
• Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture
• The Goldilocks model of separable, zero-range, few-body interactions in one-dimensional harmonic traps
• Emergence of junction dynamics in a strongly interacting Bose mixture
• Dynamical fermionization in one-dimensional spinor gases at finite temperature
• Spectroscopy and spin dynamics for strongly interacting few spinor bosons in one-dimensional traps
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• Ground State Properties of Anti-Ferromagnetic Spinor Bose gases in One Dimension
• The weakening of fermionization of one dimensional spinor Bose gases induced by spin-exchange interaction
• Fermi super-Tonks-Girardeau state for attractive Fermi gases in an optical lattice
• Exact spectral function and nonequilibrium dynamics of the strongly interacting Hubbard model
• Nonequilibrium dynamics in one-dimensional strongly interacting two-component gases
• Dynamical probing of high-order spin coherence in one-dimensional mixtures
• Numerical methods and analytic results for one-dimensional strongly interacting spinor gases
• Space-time first-order correlations of an open Bose-Hubbard model with incoherent pump and loss
• Ferromagnetic to antiferromagnetic transition of one-dimensional spinor Bose gases with spin-orbit coupling
• Loschmidt echo and Momentum Distribution in a Kitaev Spin Chain
• Shortcut to spin dynamics for quantum mixtures
• Necklace Ansatz for strongly repulsive spin mixtures on a ring
• Symmetry oscillations sensitivity to SU(2)-symmetry breaking in quantum mixtures
• Generation of spin currents by a temperature gradient in a two-terminal device
• Impenetrability in Floquet scattering in one dimension