Exact quantum dynamics of bosons with finite-range time-dependent interactions of harmonic type

TL;DR

This paper extends an exactly solvable bosonic quantum model to include time-dependent interactions and potentials, and uses it to benchmark the MCTDHB method's accuracy in dynamic scenarios involving ultracold Bose-Einstein condensates.

Contribution

The authors derive exact solutions for a time-dependent bosonic model with finite-range interactions, enabling precise benchmarking of the MCTDHB method for dynamic many-body quantum systems.

Findings

MCTDHB shows excellent convergence for ground state and dynamics.

Self-consistency and time-adaptivity are crucial for accurate predictions.

The model's results are relevant for ultra-cold Bose-Einstein condensates.

Abstract

The exactly solvable quantum many-particle model with harmonic one- and two-particle interaction terms is extended to include time-dependency. We show that when the external trap potential and finite-range interparticle interaction have a time-dependency the exact solutions of the corresponding time-dependent many-boson Schr\"odinger equation are still available. We use these exact solutions to benchmark the recently developed multiconfigurational time-dependent Hartree method for bosons (MCTDHB) [Phys. Rev. Lett. {\bf 99}, 030402 (2007), Phys. Rev. A {\bf 77}, 033613 (2008)]. In particular, we benchmark the MCTDHB method for: (i) the ground state; (ii) the breathing many-body dynamics activated by a quench scenario where the interparticle interaction strength is suddenly turned on to a finite value; (iii) the non-equilibrium dynamic for driven scenarios where both the trap- and interparticle-interaction potentials are {\it time-dependent}. Excellent convergence of the ground state and dynamics is demonstrated. The great relevance of the self-consistency and time-adaptivity, which are the intrinsic features of the MCTDHB method, is demonstrated by contrasting the MCTDHB predictions and those obtained within the standard full configuration interaction method spanning the Fock space of the same size, but utilizing as one-particle basis set the fixed-shape eigenstates of the one-particle potential. Connections of the model's results to ultra-cold Bose-Einstein condensed systems are addressed.