Hidden symmetry and tunnelling dynamics in asymmetric quantum Rabi models

Abstract

The asymmetric quantum Rabi model (AQRM) has a broken ${\mathbb{Z}}_2$ symmetry, with generally a non-degenerate eigenvalue spectrum. In some special cases where the asymmetric parameter is a multiple of the cavity frequency, stable level crossings typical of the ${\mathbb{Z}}_2$-symmetric quantum Rabi model are recovered, however, without any obvious parity-like symmetry. This unknown "symmetry" has thus been referred to as hidden symmetry in the literature. Here we show that this hidden symmetry is not limited to the AQRM, but exists in various related light-matter interaction models with an asymmetric qubit bias term. Conditions under which the hidden symmetry exists in these models are determined and discussed. By investigating tunnelling dynamics in the displaced oscillator basis, a strong connection is found between the hidden symmetry and selective tunnelling.

9 pages, 6 figures

References in corpus (8)

• Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime
• The quantum Rabi model: solution and dynamics
• Analytical method of spectra calculations in the Bargmann representation
• Generalized rotating-wave approximation to the two-qubit and cavity coupling system
• Attempt to find the hidden symmetry in the asymmetric quantum Rabi model
• Non-orthogonal qubit states expansion for the asymmetric quantum Rabi model
• The asymmetric quantum Rabi model in the polaron picture
• An analytical variational method for the biased quantum Rabi model in the ultra-strong coupling regime

Cited by in corpus (28)

• The hidden symmetry of the asymmetric quantum Rabi model
• Error-Tolerant Amplification and Simulation of the Ultrastrong-Coupling Quantum Rabi Model
• Entanglement resonance in the asymmetric quantum Rabi model
• Double degeneracy associated with hidden symmetries in the asymmetric two-photon Rabi model
• Hidden Single-Qubit Topological Phase Transition without Gap Closing in Anisotropic Light-Matter Interactions
• Generalized adiabatic approximation to the quantum Rabi model
• PT-symmetric quantum Rabi 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
• Spin Winding and Topological Nature of Transitions in Jaynes-Cummings Model with Stark Non-linear Coupling
• Hidden symmetry in the biased Dicke model
• Degeneracy and hidden symmetry -- an asymmetric quantum Rabi model with an integer bias
• Hidden symmetry operators for asymmetric generalised quantum Rabi models
• Spectral continuum in the Rabi-Stark model
• 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
• General symmetry operators of the asymmetric quantum Rabi model
• Spectral response of a nonlinear Jaynes-Cummings model
• A supersymmetry journey from the Jaynes-Cummings to the anisotropic Rabi model
• Deterministic single-photon source in the ultrastrong coupling regime
• Vacuum Rabi Splitting and Quantum Fisher Information of a Non-Hermitian Qubit in a Single-Mode Cavity
• Upgrading Quantum Metrology by Combined Sensitivity Resources in Mixed Linear-Nonlinear Light-Matter Interactions with Bias Field
• Symmetry operators of the asymmetric two-photon quantum Rabi model
• On the Origin of the Hidden Symmetry in the Asymmetric Quantum Rabi Model
• Anisotropic Rabi model with two-photon relaxation
• Quantum Multicritical Behavior for Coupled Optical Cavities with Driven Laser Fields
• Topological enhancement of a PT-symmetric Su-Schrieffer-Heeger quantum battery