Collision dynamics and entanglement generation of two initially independent and indistinguishable boson pairs in one-dimensional harmonic confinement

Abstract

We investigate finite number effects in collisions between two states of an initially well known number of identical bosons with contact interactions, oscillating in the presence of harmonic confinement in one dimension. We investigate two N/2 (interacting) ground states, which are initially displaced from the trap center, and the effects of varying interaction strength. The numerics focus on the simplest case of N=4. In the non-interacting case, such a system would display periodic oscillation with a half harmonic oscillator period (due to the left-right symmetry). With the addition contact interactions between the bosons, collisions generate entanglement between each of the states and distribute energy into other modes of the oscillator. We study the system numerically via an exact diagonalization of the Hamiltonian with a finite basis, investigating left/right number uncertainty as our primary measure of entanglement. Additionally we study the time-evolution and equilibration of the single-body von Neumann entropy for both the attractive and repulsive cases. We identify parameter regimes for which attractive interactions create qualitatively different behavior to repulsive interactions, due to the presence of bound states (quantum solitons) and explain the processes behind this.

arXiv comment17 pages, 8 figures

References in corpus (34)

• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• Formation and Propagation of Matter Wave Soliton Trains
• Formation of a Matter-Wave Bright Soliton
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Collapse and Revival of the Matter Wave Field of a Bose-Einstein Condensate
• Matter-wave interferometry in a double well on an atom chip
• Bright gap solitons of atoms with repulsive interaction
• Effective wave-equations for the dynamics of cigar-shaped and disc-shaped Bose condensates
• Deterministic Preparation of a Tunable Few-Fermion System
• Formation of bright matter-wave solitons during the collapse of Bose-Einstein condensates
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Twin matter waves for interferometry beyond the classical limit
• The Mott insulator transition in two dimensions
• A lattice of double wells for manipulating pairs of cold atoms
• Fermionization of two distinguishable fermions
• Absence of Thermalization in Nonintegrable Systems
• Ground state properties of a one-dimensional condensate of hard core bosons in a harmonic trap
• Topological semimetal in a fermionic optical lattice
• Friction and diffusion of matter-wave bright solitons
• Quantum Entangled Dark Solitons Formed by Ultracold Atoms in Optical Lattices
• Strong Violations of Bell-type Inequalities for Path-Entangled Number States
• Bright Solitary-Matter-Wave Collisions in a Harmonic Trap: Regimes of Soliton-like Behaviour
• Entanglement robustness and geometry in systems of identical particles
• Scattering bright solitons: quantum versus mean-field behavior
• Invariant Correlation Entropy and Complexity of Quantum States
• Bright solitary waves and trapped solutions in Bose-Einstein condensates with attractive interactions
• Exact dynamics and decoherence of two cold bosons in a 1D harmonic trap
• Invariance of the Kohn (sloshing) mode in a conserving theory
• Second-order, number-conserving description of non-equilibrium dynamics in finite-temperature Bose-Einstein condensates
• Variational determination of approximate bright matter-wave soliton solutions in anisotropic traps
• Coherence and Instability in a Driven Bose-Einstein Condensate: A Fully Dynamical Number-Conserving Approach
• Quantum theory of bright matter wave solitons in harmonic confinement
• Nonlocal quantum superpositions of bright matter-wave solitons and dimers
• Internal One-Particle Density Matrix for Bose-Einstein Condensates with Finite Number of Particles in a Harmonic Potential

Cited by in corpus (9)

• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Equilibration in one-dimensional quantum hydrodynamic systems
• Correlated Quantum Dynamics of a Single Atom Collisionally Coupled to an Ultracold Finite Bosonic Ensemble
• Bright soliton quantum superpositions: signatures of high- and low-fidelity states
• Superballistic center-of-mass motion in one-dimensional attractive Bose gases: Decoherence-induced Gaussian random walks in velocity space
• Collision-induced frequency shifts in bright matter-wave solitons and soliton molecules
• Effects of interactions on the generalized Hong-Ou-Mandel effect
• Entangling two distinguishable quantum bright solitons via collisions
• Phase-matching condition for enhanced entanglement of colliding indistinguishable quantum bright solitons in a harmonic trap