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考虑原子质心量子运动的Jaynes-Cummings模型的Stationary states：驻波和反向传播波情形的直接比较

Stationary states of Jaynes-Cummings model with atomic center-of-mass quantum motion: direct comparison of standing-wave and counterpropagating-waves cases

A. Zh. Muradyan, G. A. Muradyan

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13 pages, 9 Postscript figures, zipped
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摘要：

本文讨论了在包含质心动能算符的完全哈密顿量基础上的Jaynes-Cummings模型的本征态问题。计算了驻波和反向传播波的能谱和波函数，并进行了比较。结果表明，在共面波导情形下，原子动量分布是不对称的，一般情况下会变窄;准动量的概念不适用，而普通动量的概念则与问题有关;原子和光子态分布是自洽的，因此，反向传播的行波中的平均光子数与平均原子动量相匹配.在Tavis-Cummings型近似[Phys.Rev.170，379（1968）]中找到了能量本征值和本征函数的显式解析表达式，并指出它只意味着原子质心运动的类束缚态。如果考虑反冲能的影响，则Doppleron共振分裂为两个分支，其中一个分支在高阶范围内发散为类布拉格共振。

英文摘要：

The eigenstate problem of the Jaynes-Cummings model on the basis of complete Hamiltonian, including the center-of -mass kinetic energy operator, is treated. The energy spectrum and wave functions in standing-wave (SW)- and counterpropagating waves (CPW)- cases are calculated and compared with each other. It is shown that in CPW-case i) the atomic momentum distribution is asymmetric and somewhat narrower in general; ii) the concept of quasimomentum is not applicable and instead the ordinary momentum concerns the problem; iii) atomic and photonic state distributions are self-consistent, and, in consequence iiii) mean number of photons in the counterpropagating traveling waves and mean atomic momentum match. Explicit analytic expressions for energy eigenvalues and eigenfunctions are found in Tavis -Cummings-type approximation [Phys. Rev. 170, 379(1968)] and is pointed, that it implies only the bounded-like states for atomic center-of-mass motion. It is also shown that if the recoil energy is taken into account, the Doppleron resonance is split into two branches, one of which diverges to Bragg-like resonance in the high-order range.

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