Exact Solvability of the two-photon Rabi Hamiltonian

Abstract

Exact spectrum of the two-photon Rabi Hamiltonian is found, proceeding in full analogy with the solution of standard (one-photon) Rabi Hamiltonian, published by Braak in Phys. Rev. Lett. 107, 100401 (2011). The Hamiltonian is rewritten as a set of two differential equations. Symmetries that get hidden after further treatment are found. One can plainly see, how the Hilbert space splits into four disjunct subspaces, categorized by four values of the symmetry parameter $c=\pm 1,\pm i$. There were only two values $\pm 1$ for the standard Rabi model. Four analytic functions are introduced by a recurrence scheme for the coefficients of their series expansion. All their roots yield the complete spectrum of the Hamiltonian. Eigenstates in Bargmann space are also at disposal.

References in corpus (4)

• On the Integrability of the Rabi Model
• Symmetric Rotating Wave Approximation for the Generalized Single-Mode Spin-Boson System
• Quadratic Lie algebras and quasi-exact solvability of the two-photon Rabi Hamiltonian
• Optimized t-expansion method for the Rabi Hamiltonian

Cited by in corpus (64)

• Exact solvability of the quantum Rabi models within Bogoliubov operators
• The quantum Rabi model: solution and dynamics
• Two-photon quantum Rabi model with superconducting circuits
• Spectral collapse via two-phonon interactions in trapped ions
• Analytical eigenstates for the quantum Rabi model
• Two-photon Rabi model: Analytic solutions and spectral collapse
• Theoretical methods for ultrastrong light-matter interactions
• Multiphoton blockade in the two-photon Jaynes-Cummings model
• Superradiant phase transition in the ultrastrong coupling regime of the two-photon Dicke model
• Ultrastrong coupling regime of non-dipolar light-matter interactions
• Polaron picture of the two-photon quantum Rabi model
• Analytical method of spectra calculations in the Bargmann representation
• Unified Superradiant phase transitions
• On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations
• Connecting nth order generalised quantum Rabi models: Emergence of nonlinear spin-boson coupling via spin rotations
• Selective Interactions in the Quantum Rabi Model
• Continued Fractions and the Rabi Model
• Quantum Rabi-Stark model: Solutions and exotic energy spectra
• Solution of the two-mode quantum Rabi model using extended squeezed states
• Quantum Rabi model in the Brillouin zone with ultracold atoms
• Analytical energy spectrum for hybrid mechanical systems
• Comment on "Solvability of the two-photon Rabi Hamiltonian"
• Generalized quantum Rabi model with both one- and two-photon terms: A concise analytical study
• Symmetry breaking patterns, tricriticalities and quadruple points in quantum Rabi model with bias and nonlinear interaction
• Finite-size scaling analysis in the two-photon Dicke model
• Solutions to the quantum Rabi model with two equivalent qubits
• Waveguide QED with Quadratic Light-Matter Interactions
• Concise analytic solutions to the quantum Rabi model with two arbitrary qubits
• Dark-like states for the multi-qubit and multi-photon Rabi models
• Quantum simulation of multiphoton and nonlinear dissipative spin-boson models
• Double degeneracy associated with hidden symmetries in the asymmetric two-photon Rabi model
• Two-photon-interaction effects in the bad-cavity limit
• Analytical solutions of basic models in quantum optics
• Beyond adiabatic elimination: Effective Hamiltonians and singular perturbation
• Spectral determinant of the two-photon quantum Rabi model
• Quantum Simulation of Spin Chains Coupled to Bosonic Modes with Superconducting Circuits
• A continued fraction based approach for the Two-photon Quantum Rabi Model
• The mixed quantum Rabi model
• Hybrid quantum-classical dynamics of pure-dephasing systems
• Solving two-mode squeezed harmonic oscillator and $k$th-order harmonic generation in Bargmann-Hilbert spaces
• A novel approach to the spectral problem in the two photon Rabi model
• Two-photon Rabi-Stark model
• Nonlinear dynamics of the dissipative anisotropic two-photon Dicke model
• Nonlinear two-photon Rabi-Hubbard model: superradiance and photon/photon-pair Bose-Einstein condensate
• Algebraic structure of the two-qubit quantum Rabi model and its solvability using Bogoliubov operators
• Two-photon Rabi-Hubbard and Jaynes-Cummings-Hubbard models: photon pair superradiance, Mott insulator and normal phases
• Squeezed displaced entangled states in the quantum Rabi model
• Bound states of two-photon Rabi model at the collapse point
• Physical background for parameters of the quantum Rabi model
• Critical quantum metrology in a stabilized two-photon Rabi model
• Critical spectrum of the anisotropic two-photon quantum Rabi model
• Enhanced Photon Squeezing in Two-Photon Dicke Model
• Stark-induced tunable phase transition in the two-photon Dicke-Stark model
• Approximating the two-mode two-photon Rabi model
• Deterministic two-photon C-Z gate with the two-photon quantum Rabi model
• Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model
• Tripartite quantum Rabi model with trapped Rydberg ions
• On analytic solutions of the driven, 2-photon and two-mode quantum Rabi models
• Dispersive regime of multiphoton qubit-oscillator interactions
• Superradiant Phase Transition and Statistical Properties in the Dicke-Stark Model
• Loss of integrability in a system with two-photon interactions
• Phase Transitions in Light-Matter Systems for Quantum Sensing
• Purified pseudomode model for nonlinear system-bath interactions
• Observing the Spectral Collapse of Two-Photon Interaction Models