Lindblad Master Equations for Quantum Systems Coupled to Dissipative Bosonic Modes

Simon B. Jäger, Tom Schmit, Giovanna Morigi, Murray J. Holland, and Ralf Betzholz
Phys. Rev. Lett. 129, 063601 – Published 2 August 2022
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Abstract

We present a general approach to derive Lindblad master equations for a subsystem whose dynamics is coupled to dissipative bosonic modes. The derivation relies on a Schrieffer-Wolff transformation which allows us to eliminate the bosonic degrees of freedom after self-consistently determining their state as a function of the coupled quantum system. We apply this formalism to the dissipative Dicke model and derive a Lindblad master equation for the atomic spins, which includes the coherent and dissipative interactions mediated by the bosonic mode. This master equation accurately predicts the Dicke phase transition and gives the correct steady state. In addition, we compare the dynamics using exact diagonalization and numerical integration of the master equation with the predictions of semiclassical trajectories. We finally test the performance of our formalism by studying the relaxation of a NOON state and show that the dynamics captures quantum metastability.

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  • Received 7 March 2022
  • Accepted 11 July 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.063601

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Simon B. Jäger1,2, Tom Schmit3, Giovanna Morigi3, Murray J. Holland2, and Ralf Betzholz4,5,*

  • 1Physics Department and Research Center OPTIMAS, Technische Universität Kaiserslautern, D-67663, Kaiserslautern, Germany
  • 2JILA and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
  • 3Theoretical Physics, Department of Physics, Saarland University, 66123 Saarbrücken, Germany
  • 4School of Physics, International Joint Laboratory on Quantum Sensing and Quantum Metrology, Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
  • 5Hubei Key Laboratory of Gravitation and Quantum Physics, Huazhong University of Science and Technology, Wuhan 430074, China

  • *ralf_betzholz@hust.edu.cn

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Issue

Vol. 129, Iss. 6 — 5 August 2022

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