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arXiv quant-ph/0411112quant-ph
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大转移时间量子系统中的最优种群转移

Optimal population transfers in a quantum system for large transfer time

Symeon Grivopoulos, Bassam Bamieh

摘要:

将量子系统的态转移到给定的布居分布是量子化学和原子物理学中的一个重要应用问题。在这项工作中,我们考虑精确的人口转移,使控制的L^2范数最小化,控制的L^2范数通常是电磁场的振幅。这个问题在分析上和数值上都具有挑战性。除了极少数完全可解的情况外,对最优控制和轨迹的性质还没有普遍的理解。我们发现,通过检查大的传输时间的限制,我们可以发现这样的一般性质。特别地,对于相对于量子系统的自由动力学的时间尺度大的转移时间,最优控制是分量的总和,每个分量是由慢振幅调制的玻尔频率正弦曲线,即仅在转移时间尺度上显著变化的轮廓。此外,我们表明,最佳的轨迹遵循“平均”的演变调制的快速自由动力学的系统。“平均”的最佳轨迹和缓慢的控制剖面的计算是通过一个“平均”的两点边值问题,我们得到的,这是更容易解决比一个表达的必要条件,为最优的原始最优传输问题。

英文摘要:

Transferring the state of a quantum system to a given distribution of populations is an important problem with applications to Quantum Chemistry and Atomic Physics. In this work we consider exact population transfers that minimize the L^2 norm of the control which is typically the amplitude of an electromagnetic field. This problem is analytically and numerically challenging. Except for few exactly solvable cases, there is no general understanding of the nature of optimal controls and trajectories. We find that by examining the limit of large transfer times, we can uncover such general properties. In particular, for transfer times large with respect to the time scale of the free dynamics of the quantum system, the optimal control is a sum of components, each being a Bohr frequency sinusoid modulated by a slow amplitude, i.e. a profile that changes considerably only on the scale of the transfer time. Moreover, we show that the optimal trajectory follows a "mean'' evolution modulated by the fast free dynamics of the system. The calculation of the "mean'' optimal trajectory and the slow control profiles is done via an "averaged'' two-point boundary value problem which we derive and which is much easier to solve than the one expressing the necessary conditions for optimality of the original optimal transfer problem.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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