Quantum system dynamics with a weakly nonlinear Josephson junction bath

Yang, Jing; Jussiau, Étienne; Elouard, Cyril; Le Hur, Karyn; Jordan, Andrew N.

doi:10.1103/physrevb.103.085402

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Quantum system dynamics with a weakly nonlinear Josephson junction bath

Yang, Jing·Jussiau, Étienne·Elouard, Cyril·Le Hur, Karyn·Jordan, Andrew N.

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Abstract

Here, we investigate the influence of a weakly nonlinear Josephson bath consisting of a chain of Josephson junctions on the dynamics of a small quantum system (LC oscillator). Focusing on the regime where the charging energy is the largest energy scale, we perturbatively calculate the correlation function of the Josephson bath to the leading order in the Josephson energy divided by the charging energy while keeping the cosine potential exactly. When the variation of the charging energy along the chain ensures fast decay of the bath correlation function, the dynamics of the LC oscillator that is weakly and capacitively coupled to the Josephson bath can be solved through the Markovian master equation. We establish a duality relation for the Josephson bath between the regimes of large charging and Josephson energies, respectively. The results can be applied to cases where the charging energy either is nonuniformly engineered or disordered in the chain. Furthermore, we find that the Josephson bath may become non-Markovian when the temperature is increased beyond the zero-temperature limit in that the bath correlation function gets shifted by a constant and does not decay with time.

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1-dimensional systems 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY Brownian dynamics Markovian processes dissipative particle dynamics electrical properties master equation materials science non-Markovian processes optical & microwave phenomena physics

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Yang, Jing, Jussiau, Étienne, Elouard, Cyril, Le Hur, Karyn, Jordan, Andrew N.. 2021-02-01. Quantum system dynamics with a weakly nonlinear Josephson junction bath. https://doi.org/10.1103/physrevb.103.085402

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