Analytical Study of the Non-Hermitian Semiclassical Rabi Model
arXiv:2412.02918 · doi:10.1103/PhysRevResearch.7.023004
Abstract
The symmetric semiclassical Rabi model explores the fundamental interaction between a two-level atom and a classical field, revealing novel phenomena in open systems through the inclusion of non-Hermitian terms. We propose a single similarity transformation that yields an effective Hamiltonian in rotating-wave approximation, enabling an analytical solution. The phase boundary of the -broken phase, derived from the analytical eigenvalues, closely matches the numerical exact one over a wide range of atomic frequencies, demonstrating the effectiveness of the analytical approach, especially at the main resonance. The Floquet parity operator is also introduced, providing a deeper physical understanding of the emergence of the -broken phase. Furthermore, by analyzing the dynamics of excited-state population, we observe several stable oscillations in the Fourier spectrum, demonstrating the applicability of the analytical method beyond the single-photon resonance region. The Bloch-Siegert shift is also discussed and, surprisingly, resembles its Hermitian counterpart, except for the higher-order terms in the coupling strength. The present analytical treatment provides a concise and accurate description of the main physics of this non-Hermitian atom-field interaction system.
11 pages, 7 figures
References in corpus (36)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Non-Hermitian Physics
- Symmetry and Topology in Non-Hermitian Physics
- Nonlinear waves in -symmetric systems
- Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
- Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
- Topological phase transition in non-Hermitian quasicrystals
- Metrology with -symmetric cavities: Enhanced sensitivity near the -phase transition
- Observation of PT phase transition in a simple mechanical system
- Dynamically encircling exceptional points: Exact evolution and polarization state conversion
- Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
- Semi-classical and quantum Rabi models: in celebration of 80 years
- Pseudo Parity-Time Symmetry in Optical Systems
- -symmetric circuit-QED
- Parametric amplification and bidirectional invisibility in PT-symmetric time-Floquet systems
- The dissipative two-level system under strong ac-driving: a combination of Floquet and Van Vleck perturbation theory
- Exceptional points in topological edge spectrum of PT symmetric domain walls
- Non-Hermitian fractional quantum Hall states
- Observation of a non-Hermitian phase transition in an optical quantum gas
- Non-Hermitian dynamics and nonreciprocity of optically coupled nanoparticles
- PT spectroscopy of the Rabi problem
- Stabilizing Non-Hermitian Systems by Periodic Driving
- PT-symmetric Rabi model: Perturbation theory
- Effects of counterrotating interaction on driven tunneling dynamics: coherent destruction of tunneling and Bloch-Siegert shift
- Bloch-Siegert shift of the Rabi model
- Exact analytical solutions for time-dependent Hermitian Hamiltonian systems from static unobservable non-Hermitian Hamiltonians
- Time-dependent -symmetric quantum mechanics in generic non-Hermitian systems
- Observation of non-Hermitian topology in a multi-terminal quantum Hall device
- Universal Critical Behaviors in Non-Hermitian Phase Transitions
- Defining the semiclassical limit of the quantum Rabi Hamiltonian
- Non-reciprocal dynamics and the non-Hermitian skin effect of repulsively bound pairs
- Controlling decoherence via -symmetric non-Hermitian open quantum systems
- Non-Hermitian non-Abelian topological insulators with symmetry
- PT-symmetric quantum Rabi model
- Non-Hermitian Hamiltonians in decoherence and equilibrium theory
- Floquet dynamics of Rabi model beyond the counterrotating hybridized rotating wave method