Defining the semiclassical limit of the quantum Rabi Hamiltonian

Abstract

The crossover from quantum to semiclassical behavior in the seminal Rabi model of light-matter interaction still, surprisingly, lacks a complete and rigorous understanding. A formalism for deriving the semiclassical model directly from the quantum Hamiltonian is developed here. Working in a displaced Fock-state basis $|\alpha ,n⟩$, the semiclassical limit is obtained by taking $|\alpha |\to \infty$ and the coupling to zero. This resolves the discrepancy between coherent-state dynamics and semiclassical Rabi oscillations in both standard and ultrastrong coupling/driving regimes. Furthermore, it provides a framework for studying the quantum-to-classical transition, with potential applications in quantum technologies.

7 pages, 1 figure; 7 pages Supplemental Material; v3: change of author name from E.K. Irish to E.K. Twyeffort Irish

References in corpus (8)

• Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
• Quantum technologies with hybrid systems
• Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime
• Generalized rotating-wave approximation for arbitrarily large coupling
• Two-level systems driven by large-amplitude fields
• Coherence times of dressed states of a superconducting qubit under extreme driving
• The quantum-classical crossover of a field mode
• Landau-Zener-Stueckelberg interferometry with driving fields in the quantum regime

Cited by in corpus (18)

• Switchable Superradiant Phase Transition with Kerr Magnons
• The classical-quantum limit
• Robust topological feature against non-Hermiticity in Jaynes-Cummings Model
• Nodes and Spin Windings for Topological Transitions in Light-Matter Interactions: \\ Anisotropic Quantum Rabi Model as a Born Abstract Artist
• Universal quantum Fisher information and simultaneous occurrence of Landau-class and topological-class transitions in non-Hermitian Jaynes-Cummings models
• Spin Winding and Topological Nature of Transitions in Jaynes-Cummings Model with Stark Non-linear Coupling
• 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
• Analytical Study of the Non-Hermitian Semiclassical Rabi Model
• Upgrading Quantum Metrology by Combined Sensitivity Resources in Mixed Linear-Nonlinear Light-Matter Interactions with Bias Field
• Quantum Signatures of Chaos in Anisotropic Quantum Rabi Model
• Mixed Quantum-Classical Dynamics Yields Anharmonic Rabi Oscillations
• Tripartite quantum Rabi model with trapped Rydberg ions
• Comparison of Quantum and Semiclassical Rabi models near multiphoton resonances in the presence of parametric modulation
• Multilevel Quantum Rabi Models
• Long-time signatures of chaos in large atom-light frequency ratios Rabi model
• Open Quantum Systems Driven by Chirped Pulses: Quantized versus Semiclassical Fields and the Validity of the Rotating-Wave Approximation
• Compact cavity-dressed Hamiltonian framework at arbitrarily strong light-matter coupling