Attempt to find the hidden symmetry in the asymmetric quantum Rabi model

Abstract

It has been observed that the asymmetric quantum Rabi model (QRM), which does not possess any obvious symmetry, exhibits energy level crossings, which are often associated with symmetries. This observation suggests that there is in fact a symmetry in the asymmetric QRM, even though simple inspection of the model and its Hamiltonian does not reveal the nature of this symmetry. Here we present the results of numerical calculations on the energy eigenstates of the asymmetric QRM in an attempt to elucidate the nature of the symmetry. In particular, we note that the distribution of states in the Hilbert space among different symmetry classes is normally independent of system parameters and test whether this property holds for the asymmetric QRM. We find that it does not, which both helps explain why the symmetry is hidden and adds more intrigue as to what its nature might be.

5 pages (two-column) + 5 figures + 3 tables

References in corpus (7)

• Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
• Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime
• Generalized rotating-wave approximation for arbitrarily large coupling
• Interqubit coupling mediated by a high-excitation-energy quantum object
• Simulating Anisotropic quantum Rabi model via frequency modulation
• Asymptotic behavior of observables in the asymmetric quantum Rabi model
• An analytical variational method for the biased quantum Rabi model in the ultra-strong coupling regime

Cited by in corpus (21)

• The hidden symmetry of the asymmetric quantum Rabi model
• Hidden symmetry and tunnelling dynamics in asymmetric quantum Rabi models
• Error-Tolerant Amplification and Simulation of the Ultrastrong-Coupling Quantum Rabi Model
• Remarks on the hidden symmetry of the asymmetric quantum Rabi model
• Multiple ground-state instabilities in the anisotropic quantum Rabi model
• Entanglement resonance in the asymmetric quantum Rabi model
• Double degeneracy associated with hidden symmetries in the asymmetric two-photon Rabi model
• Generalized adiabatic approximation to the asymmetric quantum Rabi model: conical intersections and geometric phases
• Non-orthogonal qubit states expansion for the asymmetric quantum Rabi model
• Degeneracy and hidden symmetry -- an asymmetric quantum Rabi model with an integer bias
• Hidden symmetry operators for asymmetric generalised quantum Rabi models
• The heat kernel of the asymmetric quantum Rabi model
• Spectral continuum in the Rabi-Stark model
• General symmetry operators of the asymmetric quantum Rabi model
• Superradiant phase transition induced by the indirect Rabi interaction
• Floquet analysis of extended Rabi models based on high-frequency expansion
• Vacuum Rabi Splitting and Quantum Fisher Information of a Non-Hermitian Qubit in a Single-Mode Cavity
• Deterministic two-photon C-Z gate with the two-photon quantum Rabi model
• On the Origin of the Hidden Symmetry in the Asymmetric Quantum Rabi Model
• Symmetry operators of the asymmetric two-photon quantum Rabi model
• Hidden time-nonlocal Floquet symmetries