Entanglement of a qubit with a single oscillator mode

TL;DR

This paper analyzes a model where a qubit is strongly coupled to an environmental oscillator, revealing an entangled state and a localization transition with unique spectral and coherence properties.

Contribution

It provides an exact solution for the qubit-oscillator model, deriving an effective action and revealing the coexistence of coherence and localization unlike traditional models.

Findings

Emergence of an entangled state as an instanton

Spectral weight shifts to low energies below transition

Coexistence of coherence and localization phenomena

Abstract

We solve a model of a qubit strongly coupled to a massive environmental oscillator mode where the qubit backaction is treated exactly. Using a Ginzburg-Landau formalism, we derive an effective action for this well known localization transition. An entangled state emerges as an instanton in the collective qubit-environment degree of freedom and the resulting model is shown to be formally equivalent to a Fluctuating Gap Model (FGM) of a disordered Peierls chain. Below the transition, spectral weight is transferred to an exponentially small energy scale leaving the qubit coherent but damped. Unlike the spin-boson model, coherent and effectively localized behaviors may coexist.