Protecting coherence by environmental decoherence: A solvable paradigmatic model

TL;DR

This paper presents an exactly solvable model demonstrating how coupling to a far environment can preserve quantum coherence in a qubit, with analytical results covering all coupling regimes.

Contribution

It introduces a simple, exactly solvable model using the Jaynes-Cummings Hamiltonian within a Lindblad master equation to analytically study coherence preservation.

Findings

Coupling to a far environment can conserve coherence across all coupling strengths.

The model confirms the coherence-preserving effect of the far environment.

Analytical solutions cover from weak to strong coupling regimes.

Abstract

We consider a particularly simple exactly solvable model for a qubit coupled to sequentially nested environments. The purpose is to exemplify the coherence conserving effect of a central system, that has been reported as a result of increasing the coupling between near and far environment. The paradigmatic example is the Jaynes-Cummings Hamiltonian, which we introduce into a Kossakowski-Lindblad master equation using alternatively the lowering operator of the oscillator or its number operator as Lindblad operators. The harmonic oscillator is regarded as the near environment of the qubit, while effects of a far environment are accounted for by the two options for the dissipative part of the master equation. The exact solution allows us to cover the entire range of coupling strength from the perturbative regime to strong coupling analytically. The coherence conserving effect of the coupling to the far environment is confirmed throughout.