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 (24)

• Introducing Quantum Discord
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor
• On the Integrability of the Rabi Model
• Coherent quantum state storage and transfer between two phase qubits via a resonant cavity
• Towards fault-tolerant quantum computing with trapped ions
• Generation of Three-Qubit Entangled States using Superconducting Phase Qubits
• Quantum Discord and Maxwell's Demons
• Exact solvability of the quantum Rabi models within Bogoliubov operators
• Process verification of two-qubit quantum gates by randomized benchmarking
• Accurate numerical solution to the finite-size Dicke model
• Analytical eigenstates for the quantum Rabi model
• Exact Solvability of the two-photon Rabi Hamiltonian
• Randomized benchmarking of single and multi-qubit control in liquid-state NMR quantum information processing
• Tavis-Cummings model beyond the rotating wave approximation: Quasi-degenerate qubits
• Large-N scaling behavior of the ground-state energy and fidelity in the Dicke Model
• Analytical method of spectra calculations in the Bargmann representation
• Toolbox of resonant quantum gates in Circuit QED
• Generalized rotating-wave approximation to the two-qubit and cavity coupling system
• On the spectrum of a class of quantum models
• Solutions to the quantum Rabi model with two equivalent qubits
• Creation of quantum correlations between two atoms in a dissipative environment from an initial vacuum state
• Searching for structure beyond parity in the two-qubit Dicke model
• New symmetry in the Rabi model

Cited by in corpus (15)

• The quantum Rabi model: solution and dynamics
• Delocalization and quantum chaos in atom-field systems
• Solution of the two-mode quantum Rabi model using extended squeezed states
• Quantum phase transitions for an integrable quantum Rabi-like model with two interacting qubits
• Approximated integrability of the Dicke model
• Dark-like states for the multi-qubit and multi-photon Rabi models
• Adiabatic invariants for the regular region of the Dicke model
• Cross-cavity quantum Rabi 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
• Entanglement dynamics of the ultra-strong coupling three-qubit Dicke model
• Application of polaron picture in the two-qubit quantum Rabi model
• Quantum coherence, correlations and nonclassical states in the two-qubit Rabi model with parametric oscillator
• Quantum Features of the Thermal Two-Qubit Quantum Rabi Model in Ultra- and Deep-Strong Regimes
• Tripartite quantum Rabi model with trapped Rydberg ions