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自旋相干态变换和自旋-玻色模型的基于变分法的基态解析解*
Spin coherent-state transformation and analytical solutions of ground-state based on variational-method for spin-Bose models*
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摘要: 提出一种基于自旋相干态变换求解自旋-玻色模型基态的变分法,并将其用于单原子模型,得到旋波近似和非旋波近似情形下的解析基态能量和波函数,特别是在光场与原子的弱、强耦合区域都与数值对角化结果符合得很好.另外,该方法也可以直接用于求解任意原子数的Dicke模型基态和相应的量子相变研究,而通常基于Holstein-Primakoff变换的变分法,原则上只适用于原子数趋于无穷的热力学极限情形.Abstract: We present a variational method for the ground-state solutions of the spin-Bose models by means of the spin coherent-state transformation. For the Jaynes-Cummings (J-C) models with and without the rotating-wave approximation, the ground-state energies obtained by this method are in perfect agreement with the results from numerical diagonalization in the whole region of the coupling between a light field and an atom. The present variational-method can be directly used to solve the ground-state energies of the Dicke models with arbitrary atom-numbers and furoher study the quantum phase transition;while the variational-method based on the Holstein-Primakoff transformation is only valid in principle for the thermodynamic limit with the atom-number tending to infinity.
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