Symmetry operators of the asymmetric two-photon quantum Rabi model

Abstract

The true level crossings in a subspace of the asymmetric two-photon quantum Rabi model (tpQRM) have been observed when the bias parameter of qubit is an even multiple of the renormalized cavity frequency. Generally, such level crossings imply the existence of the hidden symmetry because the bias term breaks the obvious symmetry exactly. In this work, we propose a Bogoliubov operator approach (BOA) for the asymmetric tpQRM to derive the symmetry operators associated with the hidden symmetry hierarchically. The explicit symmetry operators consisting of Lie algebra at low biases can be easily obtained in our general scheme. We believe the present approach can be extended for other asymmetric Rabi models to find the relevant hidden symmetry.

arXiv comment13 pages,1 figure

References in corpus (36)

• Circuit Quantum Electrodynamics
• Quantum nature of a strongly-coupled single quantum dot-cavity system
• Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
• Ultrastrong coupling regimes of light-matter interaction
• On the Integrability of the Rabi Model
• Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime
• Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime
• Ultrastrong coupling of a single artificial atom to an electromagnetic continuum in the nonperturbative regime
• Dephasing of a superconducting qubit induced by photon noise
• 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
• Semi-classical and quantum Rabi models: in celebration of 80 years
• Spectral collapse via two-phonon interactions in trapped ions
• Two-photon Rabi model: Analytic solutions and spectral collapse
• Theoretical methods for ultrastrong light-matter interactions
• Protected ultrastrong coupling regime of the two-photon quantum Rabi model with trapped ions
• Polaron picture of the two-photon quantum Rabi model
• Analytical method of spectra calculations in the Bargmann representation
• Cold-atom based implementation of the quantum Rabi model
• Symmetry of asymmetric quantum Rabi models
• The hidden symmetry of the asymmetric quantum Rabi model
• Hidden symmetry and tunnelling dynamics in asymmetric quantum Rabi models
• Asymmetry and decoherence in a double-layer persistent-current qubit
• Analytical energy spectrum for hybrid mechanical systems
• Attempt to find the hidden symmetry in the asymmetric quantum Rabi model
• Remarks on the hidden symmetry of the asymmetric quantum Rabi model
• Determinant expressions of constraint polynomials and the spectrum of the asymmetric quantum Rabi model
• Energy landscape and conical intersection points of the driven 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
• Addendum to `Algebraic equations for the exceptional eigenspectrum of the generalized Rabi model'
• Bound states of two-photon Rabi model at the collapse point
• Hidden symmetry in the biased Dicke model
• Hidden symmetry operators for asymmetric generalised quantum Rabi models
• General symmetry operators of the asymmetric quantum Rabi model