Master equation for dissipative interacting qubits in a common environment

J. P. Santos and F. L. Semião
Phys. Rev. A 89, 022128 – Published 28 February 2014

Abstract

In this paper, we derive a microscopic master equation for a pair of XY-coupled two-level systems interacting with the same memoryless reservoir. In particular, we apply this master equation to the case of a pair of two-level atoms in free space where we can clearly contrast the predictions made with the microscopic master equation obtained here and the phenomenological approaches where the atom-atom coupling is included just a posteriori, i.e., not taking into account in the derivation of the open system equation of motion. We show, for instance, that the phenomenological approach fails completely in the assessment of the role played by the symmetric and antisymmetric decay channels. As a consequence, the predictions related to collective effects such as superradiance, for instance, are misleading in the phenomenological approach. We also obtain the fluorescence spectrum using the microscopic model developed here.

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  • Received 6 November 2013

DOI:https://doi.org/10.1103/PhysRevA.89.022128

©2014 American Physical Society

Authors & Affiliations

J. P. Santos1,2 and F. L. Semião2

  • 1Centre for Theoretical Atomic, Molecular and Optical Physics, School of Mathematics and Physics, Queen's University Belfast, BT7 1NN, United Kingdom
  • 2Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Santo André, 09210-170 São Paulo, Brazil

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Vol. 89, Iss. 2 — February 2014

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