Theory of Quantum Super Impulses
Theory of Quantum Super Impulses
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DOI：
10.1103/prxquantum.5.010322
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发表时间：
2023-12
期刊：
影响因子：
9.7
通讯作者：
Christopher Jarzynski
中科院分区：
文献类型：
--
作者：
Christopher Jarzynski
量子脉冲是一种短暂但强烈的微扰，它会产生波函数$\psi（x）$的突然变化。我们发展了量子脉冲理论，区分普通脉冲和超级脉冲。一个普通的脉冲在$\psi$上画出一个相位，而一个超级脉冲--这篇文章的主要焦点--在一个可逆映射下使波函数变形，$\mu：x -> x '$。借用工具，从最佳质量输运理论和捷径绝热，我们展示了如何设计一个超级脉冲，变形波函数下所需的地图$\mu$，我们用可解的例子来说明我们的结果。我们指出量子和经典的超脉冲之间的强有力的连接，表示在量子力学的路径积分公式。我们简要地讨论混合脉冲，其中普通和超级脉冲同时应用。虽然我们的中心结果是针对随时间变化的薛定谔方程下的演化推导出来的，但它们同样适用于随时间变化的Gross-Pitaevskii方程，因此可能与玻色-爱因斯坦凝聚的操纵有关。
A quantum impulse is a brief but strong perturbation that produces a sudden change in a wavefunction $\psi(x)$. We develop a theory of quantum impulses, distinguishing between ordinary and super impulses. An ordinary impulse paints a phase onto $\psi$, while a super impulse -- the main focus of this paper -- deforms the wavefunction under an invertible map, $\mu: x ->x'$. Borrowing tools from optimal mass transport theory and shortcuts to adiabaticity, we show how to design a super impulse that deforms a wavefunction under a desired map $\mu$, and we illustrate our results using solvable examples. We point out a strong connection between quantum and classical super impulses, expressed in terms of the path integral formulation of quantum mechanics. We briefly discuss hybrid impulses, in which ordinary and super impulses are applied simultaneously. While our central results are derived for evolution under the time-dependent Schrodinger equation, they apply equally well to the time-dependent Gross-Pitaevskii equation, and thus may be relevant for the manipulation of Bose-Einstein condensates.