Concise analytic solutions to the quantum Rabi model with two arbitrary qubits

Abstract

Using extended coherent states, an analytical exact study has been carried out for the quantum Rabi model (QRM) with two arbitrary qubits in a very concise way. The $G$-functions with $2\times 2$ determinants are generally derived. For the same coupling constants, the simplest $G$-function, resembling that in the one-qubit QRM, can be obtained. Zeros of the $G$-function yield the whole regular spectrum. The exceptional eigenvalues, which do not belong to the zeros of the $G$ function, are obtained in the closed form. The Dark states in the case of the same coupling can be detected clearly in a continued-fraction technique. The present concise solution is conceptually clear and practically feasible to the general two-qubit QRM and therefore has many applications.

13 pages, 3 figures

References in corpus (9)

• Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor
• Coherent quantum state storage and transfer between two phase qubits via a resonant cavity
• Towards fault-tolerant quantum computing with trapped ions
• Process verification of two-qubit quantum gates by randomized benchmarking
• Accurate numerical solution to the finite-size Dicke model
• Randomized benchmarking of single and multi-qubit control in liquid-state NMR quantum information processing
• Analytical method of spectra calculations in the Bargmann representation
• Generalized rotating-wave approximation to the two-qubit and cavity coupling system
• On the spectrum of a class of quantum models

Cited by in corpus (4)

• The quantum Rabi model: solution and dynamics
• Approximated integrability of the Dicke model
• Algebraic structure of the two-qubit quantum Rabi model and its solvability using Bogoliubov operators
• Exact solvability, non-integrability, and genuine multipartite entanglement dynamics of the Dicke model