Connecting nth order generalised quantum Rabi models: Emergence of nonlinear spin-boson coupling via spin rotations

Abstract

We establish an approximate equivalence between a generalised quantum Rabi model and its nth order counterparts where spin-boson interactions are nonlinear as they comprise a simultaneous exchange of $n$ bosonic excitations. Although there exists no unitary transformation between these models, we demonstrate their equivalence to a good approximation in a wide range of parameters. This shows that nonlinear spin-boson couplings, i.e. nth order quantum Rabi models, are accessible to quantum systems with only linear coupling between boson and spin modes by simply adding spin rotations and after an appropriate transformation. Furthermore, our result prompts novel approximate analytical solutions to the dynamics of the quantum Rabi model in the ultrastrong coupling regime improving previous approaches.

9 pages, 3 figures plus Supplemental Information

References in corpus (15)

• Quantum computing with trapped ions
• Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime
• Deep Strong Coupling Regime of the Jaynes-Cummings model
• Manipulation and Detection of a Trapped Yb+ Ion Hyperfine Qubit
• Generalized rotating-wave approximation for arbitrarily large coupling
• Two-photon quantum Rabi model with superconducting circuits
• Probing the Dynamics of Superradiant Quantum Phase Transition in a Single Trapped-Ion
• Spectral Classification of Coupling Regimes in the Quantum Rabi Model
• Protected ultrastrong coupling regime of the two-photon quantum Rabi model with trapped ions
• Integrability vs exact solvability in the quantum Rabi and Dicke models
• Excited-state quantum phase transition in the Rabi model
• Spin-Mechanical Scheme with Color Centers in Hexagonal Boron Nitride Membranes
• Cold-atom based implementation of the quantum Rabi model
• A robust scheme for the implementation of the quantum Rabi model in trapped ions
• Pulsed Dynamical Decoupling for Fast and Robust Two-Qubit Gates on Trapped Ions

Cited by in corpus (29)

• Polaron picture of the two-photon quantum Rabi model
• Unified Superradiant phase transitions
• Selective Interactions in the Quantum Rabi Model
• Switchable Superradiant Phase Transition with Kerr Magnons
• Symmetry breaking patterns, tricriticalities and quadruple points in quantum Rabi model with bias and nonlinear interaction
• Waveguide quantum optomechanics: parity-time phase transitions in ultrastrong coupling regime
• Waveguide QED with Quadratic Light-Matter Interactions
• Quantum simulation of multiphoton and nonlinear dissipative spin-boson models
• Hidden Single-Qubit Topological Phase Transition without Gap Closing in Anisotropic Light-Matter Interactions
• Two-photon-interaction effects in the bad-cavity limit
• The mixed quantum Rabi model
• Spin-boson model as a simulator of non-Markovian multiphoton Jaynes-Cummings models
• Invariant approach to the Driven Jaynes-Cummings model
• Two-photon Rabi-Stark model
• Nodes and Spin Windings for Topological Transitions in Light-Matter Interactions: \\ Anisotropic Quantum Rabi Model as a Born Abstract Artist
• Robust topological feature against non-Hermiticity in Jaynes-Cummings Model
• Universal quantum Fisher information and simultaneous occurrence of Landau-class and topological-class transitions in non-Hermitian Jaynes-Cummings models
• Heat kernel for the quantum Rabi model II: propagators and spectral determinants
• Spin Winding and Topological Nature of Transitions in Jaynes-Cummings Model with Stark Non-linear Coupling
• Bohm potential for the time dependent harmonic oscillator
• Quantum Fisher information and polaron picture for identification of transition coupling in quantum Rabi model
• Combining Squeezing and Transition Sensitivity Resources for Quantum Metrology by Asymmetric Non-Linear Rabi model
• Effective and efficient resonant transitions in periodically modulated quantum systems
• Ion-laser-like interaction in optomechanical systems with Kerr nonlinearities
• Statistical properties of London modified coherent states
• Localized vibrational modes in waveguide quantum optomechanics with spontaneously broken PT symmetry
• Generation of quasi-rectangle-states of the vibrational motion of an ion
• Engineering nonlinear boson-boson interactions using mediating spin systems
• Anomalous quantum correlations in the motion of a trapped ion