Exact dynamics and decoherence of two cold bosons in a 1D harmonic trap

TL;DR

This paper provides an exact analysis of the quantum dynamics and decoherence of two interacting cold bosons in a 1D harmonic trap, highlighting the limitations of the Gross-Pitaevskii equation in certain entangled initial states.

Contribution

It introduces an exact solution approach for two bosons in a 1D harmonic trap and compares it with mean-field predictions, revealing entanglement effects missed by traditional methods.

Findings

Exact dynamics differ from Gross-Pitaevskii predictions when initial states are entangled.

Entanglement can be dynamically generated during evolution.

The results are experimentally verifiable in optical lattices.

Abstract

We study dynamics of two interacting ultra cold Bose atoms in a harmonic oscillator potential in one spatial dimension. Making use of the exact solution of the eigenvalue problem of a particle in the delta-like potential we study time evolution of initially separable state of two particles. The corresponding time dependent single particle density matrix is obtained and diagonalized and single particle orbitals are found. This allows to study decoherence as well as creation of entanglement during the dynamics. The evolution of the orbital corresponding to the largest eigenvalue is then compared to the evolution according to the Gross-Pitaevskii equation. We show that if initially the center of mass and relative degrees of freedom are entangled then the Gross-Pitaevskii equation fails to reproduce the exact dynamics and entanglement is produced dynamically. We stress that predictions of our study can be verified experimentally in an optical lattice in the low-tunneling limit.