Closed system approach to open systems: Tunneling decay of interacting cold bosons in an optical lattice

TL;DR

This paper models the decay of interacting cold bosons in an optical lattice using a closed system approach, comparing exact dynamics with effective non-Hermitian and Lindblad models, and introduces a lattice Siegert approximation for decay rates.

Contribution

It presents a novel closed system framework for simulating open quantum system dynamics and introduces a lattice Siegert approximation method for decay rate calculations.

Findings

Effective models with constant decay rates are validated for single and double well decays.

The approach avoids the need for baths or absorbing boundaries in simulations.

The lattice Siegert approximation provides a new tool for decay rate estimation.

Abstract

A Bose-Hubbard Hamiltonian, modeling cold bosons in an optical lattice, is used to simulate the dynamics of interacting open quantum systems as subsystems a larger closed system, avoiding complications like the introduction of baths, complex absorbing potentials or absorbing boundaries. The numerically exact unitary dynamics is compared with effective descriptions of the subsystems based on non-Hermitian Hamiltonians or Lindblad master equations. The validity of popular models with constant decay rates is explicitly analyzed for decaying single and double wells. In addition we present a discrete lattice version of the Siegert approximation method for calculating decay rates.