Generalized adiabatic approximation to the quantum Rabi model

Abstract

The quantum Rabi model (QRM) describes the interaction between a two-level system (qubit) and a quantum harmonic oscillator. In the limit where the qubit frequency is smaller than the harmonic frequency, the QRM can be well approximated by the adiabatic approximation (AA). The AA is widely used due to its simplicity and explicit physical interpretation. However, the level crossings in the spectrum of the QRM predicted by the AA are determined by the zeros of Laguerre polynomials, which deviate from the exact points. We propose a new approximation to the QRM that predicts the level crossings correctly. This is done by exploiting a surprising connection between isolated exact solutions to the QRM and the Laguerre polynomials in the AA. We thus refer to this approach as the generalized adiabatic approximation (GAA). By construction, the GAA always predicts the exact exceptional spectrum and approximates the regular spectrum remarkably well in a much larger parameter regime than the AA. This generalized approach offers a framework to deal with the family of Rabi-type light-matter interaction models in a simple but accurate manner.

arXiv commentAccepted version, to appear in PRA

References in corpus (32)

• Circuit Quantum Electrodynamics
• Ultrastrong coupling between light and matter
• 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
• Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime
• Generalized rotating-wave approximation for arbitrarily large coupling
• Exact solvability of the quantum Rabi models within Bogoliubov operators
• Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator
• The quantum Rabi model: solution and dynamics
• Accurate numerical solution to the finite-size Dicke model
• Analytical eigenstates for the quantum Rabi model
• Inversion of Qubit Energy Levels in Qubit-Oscillator Circuits in the Deep-Strong-Coupling Regime
• Spectral Classification of Coupling Regimes in the Quantum Rabi Model
• Theoretical methods for ultrastrong light-matter interactions
• Full spectrum of the Rabi model
• Integrability vs exact solvability in the quantum Rabi and Dicke models
• On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations
• Generalized coherent states
• Exceptional and regular spectra of a generalized Rabi model
• Hidden symmetry and tunnelling dynamics in asymmetric quantum Rabi models
• Oscillator tunneling dynamics in the Rabi model
• Analytical energy spectrum for hybrid mechanical systems
• Generalized rotating-wave approximation to biased qubit-oscillator systems
• 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
• Multiple ground-state instabilities in the anisotropic quantum Rabi model
• Addendum to `Algebraic equations for the exceptional eigenspectrum of the generalized Rabi model'
• Simple variational ground state and pure cat state generation in the quantum Rabi model
• Non-orthogonal qubit states expansion for the asymmetric quantum Rabi model
• The asymmetric quantum Rabi model and generalised Pöschl-Teller potentials
• A unified treatment of polynomial sectors and constraint polynomials of the Rabi models

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• Steady state in ultrastrong coupling regime: perturbative expansion and first orders
• Characterizing Superradiant Phase of the Quantum Rabi Model
• 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
• Anisotropic Rabi model with two-photon relaxation
• Eigenstates of two-level systems in a single-mode quantum field: from quantum Rabi model to $N$-atom Dicke model
• Enhanced charging in open Rabi and Dicke quantum batteries
• Topological enhancement of a PT-symmetric Su-Schrieffer-Heeger quantum battery