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Entanglement of a qubit with a single oscillator mode

G. C. Levine·V. N. Muthukumar
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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.

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G. C. Levine, V. N. Muthukumar. 2003-09-15. Entanglement of a qubit with a single oscillator mode. https://doi.org/10.1103/physrevb.69.113203

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