Adiabatic elimination and subspace evolution of open quantum systems

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TitreAdiabatic elimination and subspace evolution of open quantum systems
Type de publicationJournal Article
Year of Publication2020
AuteursFinkelstein-Shapiro D, Viennot D, Saideh I, Hansen T, Pullerits T, Keller A
JournalPHYSICAL REVIEW A
Volume101
Pagination042102
Date PublishedAPR 1
Type of ArticleArticle
ISSN2469-9926
Résumé

Efficient descriptions of open quantum systems can be obtained by performing an adiabatic elimination of the fast degrees of freedom and formulating effective operators for the slow degrees of freedom in reduced dimensions. Here, we perform the construction of effective operators in frequency space, and using the final value theorem or alternatively the Keldysh theorem, we provide a correction for the trace of the density matrix which takes into account the non-trace-preserving character of the evolution. We illustrate our results with two different systems, one where the eliminated fast subspace is constituted by a continuous set of states and ones with discrete states. Furthermore, we show that the two models converge for very large dissipation and at coherent population trapping points. Our results also provide an intuitive picture of the correction to the trace of the density matrix as a detailed balance equation.

DOI10.1103/PhysRevA.101.042102