Accurate multi-boson long-time dynamics in triple-well periodic traps

TL;DR

This paper advances the simulation of many-boson quantum dynamics in triple-well traps by implementing a parallel MCTDHB method, enabling longer and larger system studies with detailed analysis of complex oscillatory behaviors.

Contribution

The authors develop a parallelized MCTDHB approach to efficiently simulate long-time dynamics of large bosonic systems in triple-well potentials, demonstrating convergence and the need for more orbitals at longer times.

Findings

Long-time dynamics show oscillations around a threefold fragmented state.

Quantum depletions strongly damp these oscillations.

Three orbitals suffice for short and intermediate times, but more are needed for long-term accuracy.

Abstract

To solve the many-boson Schr\"odinger equation we utilize the Multiconfigurational time-dependent Hartree method for bosons (MCTDHB). To be able to attack larger systems and/or to propagate the solution for longer times, we implement a parallel version of the MCTDHB method thereby realizing the recently proposed [Streltsov {\it et al.} arXiv:0910.2577v1] novel idea how to construct efficiently the result of the action of the Hamiltonian on a bosonic state vector. We study the real-space dynamics of repulsive bosonic systems made of N=12, 51 and 3003 bosons in triple-well periodic potentials. The ground state of this system is three-fold fragmented. By suddenly strongly distorting the trap potential, the system performs complex many-body quantum dynamics. At long times it reveals a tendency to an oscillatory behavior around a threefold fragmented state. These oscillations are strongly suppressed and damped by quantum depletions. In spite of the richness of the observed dynamics, the three time-adaptive orbitals of MCTDHB(M=3) are capable to describe the many-boson quantum dynamics of the system for short and intermediate times. For longer times, however, more self-consistent time-adaptive orbitals are needed to correctly describe the non-equilibrium many-body physics. The convergence of the MCTDHB($M$) method with the number $M$ of self-consistent time-dependent orbitals used is demonstrated.