Analytical energy spectrum for hybrid mechanical systems

@article{Zhong2014AnalyticalES,
  title={Analytical energy spectrum for hybrid mechanical systems},
  author={Honghua Zhong and Qiongtao Xie and Xi-Wen Guan and Murray T Batchelor and Ke-Lin Gao and Chaohong Lee},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2014},
  volume={47}
}
We investigate the energy spectrum for hybrid mechanical systems described by non-parity-symmetric quantum Rabi models. A set of analytical solutions in terms of the confluent Heun functions and their analytical energy spectrum is obtained. The analytical energy spectrum includes regular and exceptional parts, which are both confirmed by direct numerical simulation. The regular part is determined by the zeros of the Wronskian for a pair of analytical solutions. The exceptional part is relevant… 

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References

SHOWING 1-10 OF 53 REFERENCES
Analytical eigenstates for the quantum Rabi model
We develop a method to find analytical solutions for the eigenstates of the quantum Rabi model. These include symmetric, anti-symmetric and asymmetric analytic solutions given in terms of the
Exceptional and regular spectra of a generalized Rabi model
We study the spectrum of the generalized Rabi model in which co- and counter-rotating terms have different coupling strengths. It is also equivalent to the model of a two-dimensional electron gas in
Analytical solutions for the Rabi model
In this Brief Report, we present a perturbation theory that omits the weak multiphoton process to obtain analytical solutions for the Rabi model. Under this approximation, the Rabi model can be
Exact real-time dynamics of the quantum Rabi model
We use the analytical solution of the quantum Rabi model to obtain absolutely convergent series expressions of the exact eigenstates and their scalar products with Fock states. This enables us to
Analytical results for energy spectrum and eigenstates of a Bose-Einstein condensate in a Mott insulator state
We present a method to solve the model describing either a Bose-Einstein condensate (BEC) in a Mott-insulator state or a double-well BEC. We show that all the energy eigenvalues and eigenstates for
The quantum Rabi model for two qubits
We study a system composed of two nonidentical qubits coupled to a single-mode quantum field. We calculate the spectra of the system in the deep-strong-coupling regime via perturbation theory up to
On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations
We study the solvability of the time-independent matrix Schr\"odinger differential equations of the quantum Rabi model and its 2-photon and two-mode generalizations in Bargmann Hilbert spaces of
Quasi exact solution of the Rabi Hamiltonian
A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for
Solvability of the two-photon Rabi Hamiltonian
Exact spectrum of the two-photon Rabi Hamiltonian is found, proceeding in full analogy with the solution of standard (one-photon) Rabi Hamiltonian, published by Braak in Phys. Rev. Lett. 107, 100401
Exact isolated solutions for the class of quantum optical systems
The authors present a method of obtaining exact isolated solutions for the class of quantum optical systems without the use of a rotating wave approximation. The method generalises the results known
...
...