冷分子形成的非线性Demkov-Kunike问题的一个分析
An ansatz for the nonlinear Demkov-Kunike problem for cold molecule formation
摘要：
我们研究了超冷分子形成的非线性平均场动力学的情况下，外场配置的水平交叉Demkov-Kunike模型，其特征在于钟形耦合和失谐的有限变化的定义。分析快速扫描速率制度的强相互作用限制，它模拟的情况下，耦合的峰值是足够大的，共振交叉是足够快的，我们构建了一个高精度的分析来描述的时间动力学的分子形成在上述相互作用制度。对于最终跃迁概率，构造的近似值的绝对误差小于3*10^-6，而在某些时间点，它可能会增加到10^-3。研究了不同项在所构造近似中的作用，我们证明了在强相互作用极限的快速扫描速率区域中，原子-分子转换的时间动力学有效地包括由非线性方程支配的共振交叉过程，随后是基本上由线性问题的解描述的原子-分子相干振荡，与所考虑的非线性相关。
英文摘要：
We study nonlinear mean-field dynamics of ultracold molecule formation in the case when the external field configuration is defined by the level-crossing Demkov-Kunike model, characterized by a bell-shaped coupling and finite variation of the detuning. Analyzing the fast sweep rate regime of the strong interaction limit, which models a situation when the peak value of the coupling is large enough and the resonance crossing is sufficiently fast, we construct a highly accurate ansatz to describe the temporal dynamics of the molecule formation in the mentioned interaction regime. The absolute error of the constructed approximation is less than 3*10^-6 for the final transition probability while at certain time points it might increase up to 10^-3. Examining the role of the different terms in the constructed approximation, we prove that in the fast sweep rate regime of the strong interaction limit the temporal dynamics of the atom-molecule conversion effectively consists of the process of resonance crossing, which is governed by a nonlinear equation, followed by atom-molecular coherent oscillations which are basically described by a solution of the linear problem, associated with the considered nonlinear one.
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