Continued Fractions and the Rabi Model

Abstract

Techniques based on continued fractions to compute numerically the spectrum of the quantum Rabi model are reviewed. They are of two essentially different types. In the first case, the spectral condition is implemented using a representation in the infinite-dimensional Bargmann space of analytic functions. This approach is shown to approximate the correct spectrum of the full model if the continued fraction is truncated at sufficiently high order. In the second case, one considers the limit of a sequence of models defined in finite-dimensional state spaces. Contrary to the first, the second approach is ambiguous and can be justified only through recourse to the analyticity argument from the first method.

published version

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• Exceptional solutions in two-mode quantum Rabi models
• Beyond adiabatic elimination: Effective Hamiltonians and singular perturbation
• Cross-cavity quantum Rabi model
• Quantum Simulation of Spin Chains Coupled to Bosonic Modes with Superconducting Circuits
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• A continued fraction based approach for the Two-photon Quantum Rabi Model
• Spectral determinant of the two-photon quantum Rabi model
• Algebraic structure of the two-qubit quantum Rabi model and its solvability using Bogoliubov operators
• The asymmetric quantum Rabi model in the polaron picture
• Physical background for parameters of the quantum Rabi model
• The Quantization of the Rabi Hamiltonian
• Entanglement generation in the ultra-strongly coupled Rabi model
• Continued-fraction representation of the Kraus map for non-Markovian reservoir damping
• Comment on `Parameter-dependent unitary transformation approach for quantum Rabi model'