Assessment of weak-coupling approximations on a driven two-level system under dissipation

W. S. Teixeira (Corresponding Author), F. L. Semião, J. Tuorila, Mikko Möttönen

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5 Citations (Scopus)


The standard weak-coupling approximations associated to open quantum systems have been extensively used in the description of a two-level quantum system, qubit, subjected to relatively weak dissipation compared with the qubit frequency. However, recent progress in the experimental implementations of controlled quantum systems with increased levels of on-demand engineered dissipation has motivated precision studies in parameter regimes that question the validity of the approximations, especially in the presence of time-dependent drive fields. In this paper, we address the precision of weak-coupling approximations by studying a driven qubit through the numerically exact and non-perturbative method known as the stochastic Liouville-von Neumann equation with dissipation. By considering weak drive fields and a cold Ohmic environment with a high cutoff frequency, we use the Markovian Lindblad master equation as a point of comparison for the SLED method and study the influence of the bath-induced energy shift on the qubit dynamics. We also propose a metric that may be used in experiments to map the regime of validity of the Lindblad equation in predicting the steady state of the driven qubit. In addition, we study signatures of the well-known Mollow triplet and observe its meltdown owing to dissipation in an experimentally feasible parameter regime of circuit electrodynamics. Besides shedding light on the practical limitations of the Lindblad equation, we expect our results to inspire future experimental research on engineered open quantum systems, the accurate modeling of which may benefit from non-perturbative methods.

Original languageEnglish
Article number013005
JournalNew Journal of Physics
Issue number1
Publication statusPublished - Jan 2022
MoE publication typeA1 Journal article-refereed


We acknowledge Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) through Grants Nos. 2017/09058-2 and 2018/26726-1, the Brazilian National Institute of Science and Technology of Quantum Information (CNPq INCT-IQ 465469/2014-0), CNPq (Grant No. 305723/2020-0), CAPES/PrInt (88881.310346/2018-01), the Academy of Finland under its Centers of Excellence Program Grants Nos. 312300 and 336810, the European Research Council under Grants Nos. 681311 (QUESS) and 957440 (SCAR), the Jane and Aatos Erkko Foundation, and the Technology Industries of Finland Centennial Foundation for financial support.


  • bath-induced energy shift
  • circuit QED
  • driven open quantum systems
  • stochastic master equation


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