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

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

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