近日，越南孙德胜大学的Cam-Tu Le与越南胡志明市科技大学的Van-Hoang Le等人合作并取得一项新进展。他们从波姆轨迹观点对电子动力学相位差和高次谐波频移进行了研究。相关研究成果已于2024年12月18日在国际知名学术期刊《物理评论A》上发表。

最近，该研究团队从玻姆力学的角度直观地阐明了少周期激光脉冲作用下，不对称一氧化碳分子高次谐波过程的动力学特性，并发现只有初始位置靠近碳原子的一个中心轨迹（BT(P)）对谐波谱的高能部分有主要贡献。而另一个起始于氧原子附近的中心轨迹（BT(N)）的作用仍是一个值得探讨的问题。

本研究表明，在使用FC碰碰胡老虎机法典-提高赢钱机率的下注技巧光学周期的激光脉冲时，BT(N)对高次谐波谱中频率偏移的贡献不可忽视。实际上，当分子取向与激光电场极化方向反平行时，通过分析加速度分布和谐波谱可以发现，尽管BT(N)对谐波强度的贡献较小，但它在再现谐波谱结构方面，特别是在截止能量区域，具有显著作用。

BT(N)的贡献在发射时刻调制了动力学相位，从而改变了连续两次发射脉冲之间的动力学相位差。这种调制导致与没有BT(N)贡献的情况相比，截止区域的谐波阶数出现蓝移，使得由BT(P)和BT(N)组合得到的谐波谱更接近直接求解含时薛定谔方程的结果。这一发现从玻姆力学的角度证实了量子过程的非局域性，即中心轨迹包含了高次谐波产生所需的所有基本动力学信息。

附：英文原文

Title: Electron dynamical phase difference and high-order harmonic frequency shift: A Bohmian-trajectory perspective

Author: Cam-Tu Le^1,2,*, Ngoc-Loan Phan³, and Van-Hoang Le^3,†

Issue&Volume: 2024-12-18

Abstract: Recently, we have visually elucidated the dynamics of the high-order harmonic process of an asymmetric CO molecule with a few-cycle laser pulse using the Bohmian perspective and found that only one central trajectory, BT(P), whose initial start is near the C atom, principally contributes to the high-energy part of the harmonic spectrum. The role of the other central trajectory originating near the O atom, BT(N), remains a question of interest. The present study shows the non-negligible contribution of the BT(N) to cause a frequency shift in the high harmonic spectrum when using a laser pulse with more optical cycles. Indeed, when the molecule is oriented antiparallel to the laser's electric polarization, analyzing the acceleration profiles and harmonic spectra reveals that despite smaller weight contributing to the harmonic intensity, BT(N) is significant in reproducing the harmonic spectrum structure, especially in the cutoff-energy region. The BT(N) contribution modulates the dynamical phase at the emission time, altering the dynamical phase difference between two consecutive emission bursts. This modification leads to a blueshift of harmonic orders in the cutoff region compared to the scenarios without BT(N) contribution, bringing the harmonic spectrum from the combination BTs(P +N) closer to the result of directly solving the time-dependent Schrdinger equation. This finding confirms the nonlocality of the quantum process via the Bohmian perspective that central trajectories contain all the essential dynamic information of high-order harmonic generation.

DOI: 10.1103/PhysRevA.110.063115

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.063115