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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.
Scientific Reports
|December 5, 2019
Summary
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.
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.
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