Analytical method of spectra calculations in the Bargmann representation
arXiv:1410.8610 · doi:10.1016/j.physleta.2014.10.001
Abstract
We formulate a universal method for solving an arbitrary quantum system which, in the Bargmann representation, is described by a system of linear equations with one independent variable, such as one- and multi-photon Rabi models, or level systems interacting with a single mode of the electromagnetic field and their various generalizations. We explain three types of conditions that determine the spectrum and show their usage for two deformations of the Rabi model. We prove that the spectra of both models are just zeros of transcendental functions, which in one case are given explicitly in terms of confluent Heun functions.
9 pages, 5 figures
References in corpus (8)
- 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
- Deep Strong Coupling Regime of the Jaynes-Cummings model
- An exactly solvable system from quantum optics
- Note on the Analytical Solution of the Rabi Model
- Continued Fractions and the Rabi Model
- On the spectrum of a class of quantum models
- How to calculate spectra of Rabi and related models
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- An exactly solvable system from quantum optics
- Concise analytic solutions to the quantum Rabi model with two arbitrary qubits
- Analytical Solution for the Anisotropic Rabi Model: Effects of Counter-Rotating Terms
- A novel approach to the spectral problem in the two photon Rabi model
- Robust topological feature against non-Hermiticity in Jaynes-Cummings Model