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The mixed quantum Rabi model.

Liwei Duan1, You-Fei Xie1, Qing-Hu Chen2,3

  • 1Department of Physics and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, 310027, China.

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This summary is machine-generated.

Researchers found exact solutions for the mixed quantum Rabi model (QRM) using Bogoliubov operators. This work offers new insights into quantum systems and potential pathways to strong coupling regimes.

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Area of Science:

  • Quantum optics
  • Quantum mechanics
  • Many-body physics

Background:

  • The quantum Rabi model (QRM) describes light-matter interactions.
  • Investigating the mixed QRM with one- and two-photon terms is crucial for understanding complex quantum phenomena.
  • Previous studies often focused on unmixed or simplified versions of the QRM.

Purpose of the Study:

  • To derive analytical exact solutions for the mixed quantum Rabi model (QRM) incorporating both one- and two-photon interactions.
  • To analyze the spectral properties and energy level behavior, including collapse points and avoided crossings.
  • To explore the relationship between the mixed QRM and the one-photon QRM in different coupling regimes.

Main Methods:

  • Utilizing Bogoliubov operators to find exact solutions.
  • Deriving transcendental functions (G-functions) based on 4x4 determinants.
  • Analyzing the pole structures and zeros of G-functions to determine spectral properties.
  • Investigating energy limits and level crossings/avoided crossings.

Main Results:

  • Exact solutions obtained via G-functions, reducible to those of unmixed QRMs.
  • Regular spectra reproduced by G-function zeros; exceptional eigenvalues found via another transcendental function.
  • Energy levels collapse to a single lower level diverging negatively at the two-photon coupling collapse point.
  • Level crossings in unmixed QRMs become avoided crossings in the mixed QRM due to broken parity symmetry.

Conclusions:

  • The derived G-functions provide a unified framework for solving mixed QRMs.
  • The study reveals unique spectral behaviors, including negative energy divergence and avoided crossings.
  • In the weak two-photon coupling regime, the mixed QRM effectively mimics a one-photon QRM, suggesting a route to deep-strong coupling.