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arXiv · 2501.03760

Dissipative evolution of a two-level system through a geometry-based classical mapping

Daniel Martínez Gil·Pedro Bargueño·Salvador Miret-Artés
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Abstract

In this manuscript, we introduce a geometry-based formalism to obtain a Meyer-Miller-Stock-Thoss mapping in order to study the dynamics of both isolated and interacting two-level systems. After showing the description of the isolated case using canonically conjugate variables, we implement an interaction model by bilinearly coupling the corresponding population differences {\it à la} Caldeira-Leggett, showing that the dynamics behave as a Gross-Pitaevskii-like one. We also find a transition between oscillatory and tunneling-suppressed dynamics that can be observed by varying the coupling constant. After extending our model to the {\it system plus environment} case, where the environment is considered as a collection of two-level systems, we show tunneling-suppressed dynamics in the strong coupling limit and the usual damping effect similar to that of a harmonic oscillator bath in the weak coupling one. Finally, we observe that our interacting model turns an isolated symmetric two-level system into an environment-assisted asymmetric one.

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Daniel Martínez Gil, Pedro Bargueño, Salvador Miret-Artés. 2025-01-07. Dissipative evolution of a two-level system through a geometry-based classical mapping. https://doi.org/10.1088/1367-2630%2Fae2989

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