非基态凝聚的产生与绝热佯谬
Generation of nonground-state condensates and adiabatic paradox
摘要：
讨论了非基态凝聚体的共振生成问题，旨在解决绝热表象中出现的看似矛盾的问题。在这幅图中，含时的Gross-Pitaevskii哈密顿量的本征值和本征函数也是时间的函数。由于能级能量随时间变化，因此不能引入确定的跃迁频率。因此，不能使具有固定频率的外部调制谐振。因此，绝热相干模的共振产生是不可能的。然而，这种悖论只发生在绝热图像的框架中。结果表明，在适当制定的非绝热表象不存在悖论。非绝热相干模的共振产生是一个定义明确的现象。作为一个例子，导出了描述俘获势和原子散射长度的共振调制产生非绝热相干模的方程。
英文摘要：
The problem of resonant generation of nonground-state condensates is addressed aiming at resolving the seeming paradox that arises when one resorts to the adiabatic representation. In this picture, the eigenvalues and eigenfunctions of a time-dependent Gross-Pitaevskii Hamiltonian are also functions of time. Since the level energies vary in time, no definite transition frequency can be introduced. Hence no external modulation with a fixed frequency can be made resonant. Thus, the resonant generation of adiabatic coherent modes is impossible. However, this paradox occurs only in the frame of the adiabatic picture. It is shown that no paradox exists in the properly formulated diabatic representation. The resonant generation of diabatic coherent modes is a well defined phenomenon. As an example, the equations are derived, describing the generation of diabatic coherent modes by the combined resonant modulation of the trapping potential and atomic scattering length.
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