Attenuation of excitation decay rate due to collective effect

TL;DR

This paper investigates how collective effects in a chain of coupled oscillators reduce excitation decay rates, leading to prolonged relaxation times compared to individual oscillators, with implications for quantum coherence.

Contribution

It demonstrates that collective coupling in oscillator chains can attenuate decay rates, extending excitation lifetimes through a transformed Hamiltonian approach.

Findings

Decay constant is proportional to individual oscillator dephasing rate.

Collective effects prolong excitation relaxation lifetime.

System behaves like a two-level system with metastable states.

Abstract

We study a series of $N$ oscillators each coupled to its nearest neighbours, and linearly to a phonon field through the oscillator's number operator. We show that the Hamiltonian of a pair of adjacent oscillators, or a dimer, within the series of oscillators can be transformed to a form in which they are collectively coupled to the phonon field as a composite unit. In the weak coupling and rotating-wave approximation, the system behaves effectively like the trilinear boson model in the one excitation subspace of the dimer subsystem. The reduced dynamics of the one excitation subspace of the dimer subsystem coupled weakly to a phonon bath is similar to that of a two-level system, with a metastable state against the vacuum. The decay constant of the subsystem is proportional to the dephasing rate of the individual oscillator in a phonon bath, attenuated by a factor that depends on site asymmetry, intersite coupling and the resonance frequency between the transformed oscillator modes, or excitons. As a result of the collective effect, the excitation relaxation lifetime is prolonged over the dephasing lifetime of an individual oscillator coupled to the same bath.