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Effective Hamiltonian of the Jaynes–Cummings model beyond rotating-wave approximation

Chinese Physics B 2021年第6期30卷 300-305页

作者： Yi-Fan Wang Hong-Hao Yin Ming-Yue Yang An-Chun Ji Qing Sun Department of Physics Capital Normal UniversityBeijing 100048China

The Jaynes–Cummings model with or without rotating-wave approximation plays a major role to study the interaction between atom and light. We investigate the Jaynes–Cummings model beyond the rotating-wave approximation. Treating the counter-rotating terms as periodic drivings, we solve the model in the extended Floquet space. It is found that the full energy spectrum folded in the quasi-energy bands can be described by an effective Hamiltonian derived in the highfrequency regime. In contrast to the Z_(2) symmetry of the original model, the effective Hamiltonian bears an enlarged U(1)symmetry with a unique photon-dependent atom-light detuning and coupling strength. We further analyze the energy spectrum, eigenstate fidelity and mean photon number of the resultant polaritons, which are shown to be in accordance with the numerical simulations in the extended Floquet space up to an ultra-strong coupling regime and are not altered significantly for a finite atom-light detuning. Our results suggest that the effective model provides a good starting point to investigate the rich physics brought by counter-rotating terms in the frame of Floquet theory.

关键词： Jaynes–Cummings model Floquet theory high-frequency approximation

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SOLVING THE PROPAGATION OF ELECTROMAGNETIC WAVE IN A SIMPLE TWO-DIMENSIONALINHOMOGENEOUS MEDIUM BASED ON SYMPLECTIC GEOMETRICAL THEORY

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Journal of Electronics(China) 2002年第3期19卷 265-269页

作者： Zhao Jin Wu Xianliang Fu Biao(Dept. of Electric Eng. and Info. Science, Anhui University, Hefei 230039)Li Shixiong(Dept. of Mathematics, Anhui University, Hefei 230039) Dept. of Electric Eng. and Info. Science Anhui University Hefei 230039 Dept. of Mathematics Anhui University Hefei 230039

A new symplectic geometrical high-frequency approximation method for solving the propagation of electromagnetic wave in the two-dimensional inhomogeneous medium is used in this paper. The propagating caustic problem of electromagnetic wave is translated into non-caustic problem by the coordinate transform on the symplectic space. The high-frequency approximation solution that includes the caustic region is obtained with the method combining with the geometrical optics. The drawback that the solution in the caustic region can not be obtained with geometrical optics is overcome by this method. The results coincide well with that of finite element method.

关键词： Symplectic geometrical theory high-frequency approximation Caustics Two-dimensional inhomogeneous medium

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