We carry out optimal control theory calculations for isotope-selective pure rotational and vibrational-rotational excitations of diatomic molecules. The fifty-fifty mixture of diatomic isotopologues, ⁷Li³⁷Cl and ⁷Li³⁵Cl, is considered and the molecules are irradiated with a control pulse. In the wave packet propagation we employ the method quantum mechanically rigorous for the two-dimensional system including both the radial and angular motions. We investigate quantum controls of the isotope-selective pure rotational excitation for two total times 1280000 and 2560000 a.u. (31.0 and 61.9 ps) and the vibrational-rotational excitation for three total times, 640000, 1280000, and 2560000 a.u. (15.5, 31.0, and 61.9 ps) The initial state is set to that both the isotopologues are in the ground vibrational and rotational levels, v = 0 and J = 0. The target state for pure rotational excitation is set to ⁷Li³⁷Cl (v = 0, J = 1) and ⁷Li³⁵Cl (v = 0, J = 0); that for vibrational-rotational excitation is set to ⁷Li³⁷Cl (v = 1, J = 1) and ⁷Li³⁵Cl (v = 0, J = 0). The obtained final yields are quite high and those for the longest total time are calculated to be nearly 1.0. When total time is 1280000 a.u., the final yields for the pure rotational excitation are slightly smaller than those for the vibrational-rotational excitation. This is because the isotope shift (difference in transition energy between the two isotopologues) for the pure rotational transition between low-lying levels is much smaller than that for the vibrational-rotational transition. We thus theoretically succeed in controlling the isotope-selective excitations of diatomic molecules using the method including both radial and angular motions quantum mechanically.

中文翻译：

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双原子分子同位素选择性振动振动的量子最优控制

我们对双原子分子的同位素选择性纯旋转和振动-旋转激发进行了最优控制理论计算。五十五种双原子同位素分子混合物⁷ Li ³⁷ Cl和⁷ Li ³⁵考虑到Cl，并且用控制脉冲照射分子。在波包传播中，我们对二维系统（包括径向运动和角运动）采用严格的量子力学方法。我们研究了同位素选择性纯旋转激发的两个总时间1280000和2560000 au（31.0和61.9 ps）的量子控制以及振动旋转激发总共三个的总时间640000、1280000和2560000 au（15.5、31.0和61.9 ps）初始状态设置为两个同位素都处于地面振动和旋转能级，即v = 0和J =0。纯旋转激发的目标状态设置为⁷ Li ³⁷ Cl（v = 0，J = 1）和⁷ Li ³⁵ Cl（v = 0，J = 0）; 振动-旋转激励的值设置为⁷ Li ³⁷ Cl（v = 1，J = 1）和⁷ Li ³⁵ Cl（v = 0，J= 0）。所获得的最终产量很高，总时间最长的最终产量据计算接近1.0。当总时间为1280000 au时，纯旋转激励的最终屈服比振动-旋转激励的最终屈服略小。这是因为低空能级之间的纯旋转跃迁的同位素位移（两个同位素之间的跃迁能量差）比振动-旋转跃迁的同位素位移小得多。因此，我们在理论上成功地使用了包括机械地径向和角向运动的方法来控制双原子分子的同位素选择性激发。