库仑势对阿秒钟实验方案的影响

量子隧穿是量子力学中的基本课题之一。尽管教科书中对隧穿问题已有详细讨论,但是到目前为止,关于电子穿过势垒成为自由电子是否需要有限的时间这一问题尚未达成共识。解决此问题的关键是要充分理解隧穿过程本身。阿秒钟技术(Attoclock)是一个非常有吸引力的实验方案,其具有阿秒(10-18 s)尺度的时间分辨率,可用于测量隧穿时间。具体来说,原子在椭圆偏振激光场作用下,电子发生隧穿的时刻将会映射到末态电子在偏振面上的动量角分布中,该角分布可以在实验中直观测量。阿秒钟方案最突出的优点是不需要使用阿秒脉冲即可达到阿秒量级的时间分辨,这在很大程度上降低了实验的技术要求,增强了实验的可行性。

尽管如此,阿秒钟实验方案仍存在一些问题,导致目前已经报道的隧穿延时的测量无法达成一致。其中一个非常重要的问题就是如何精确测定库仑势的影响。实际上,在阿秒钟实验中存在一个库仑势引起的等效时间偏移(TOCP),其对实验结果的影响无法与隧穿延迟分开。尽管TOCP通常会大于隧穿延时,但是要精确地计算或测量TOCP是非常困难的。受这些因素的影响,阿秒钟实验的可靠性和时间分辨率很难达到让人满意的程度,并使得人们很难对隧穿延时进行精确地研究。基于半经典计算,中国科学院武汉物理与数学研究所的研究人员提出了一种有效提取TOCP的方案,这对于解决隧穿延时问题将具有非常重要的意义。相关研究成果发表于Chinese Optics Letters 2020年第18卷第1期中(Zhilei Xiao, Wei Quan, Songpo Xu, Shaogang Yu, Yanlan Wang, Meng Zhao, Mingzheng Wei, Yu Zhou, Xuanyang Lai, Jing Chen, Xiaojun Liu. Coulomb potential influence in the attoclock experimental scheme[J]. Chinese Optics Letters, 2020, 18(1): 010201)。

为了探索库仑势对阿秒钟实验的影响,此项工作研究了激光强度保持恒定时椭偏激光场下原子的超快电离动力学的波长依赖性。为了计算隧穿延迟,在数值模拟中令电子在人为给定的延时结束之前都停留在初始位置。通过比较有延时和无延时模拟结果之间的差异,就可以提取出隧穿延时的影响。进一步地,此项工作在半经典模型中引入了库仑势,研究了库仑势效应的影响,并系统地研究了H原子和几个稀有气体原子(Ne、Ar和Kr)的超快电离动力学过程。数值模拟结果显示,当忽略隧穿延时的影响时,稀有气体原子的TOCP与H的TOCP之比将近似满足函数(2Ip )-3⁄2,其中Ip为目标原子的电离势。需要指出的是,H原子的Ip为Ip_H =0.5 a.u,所以该比值满足(Ip/ Ip_H )-3⁄2的函数关系。也就是说,尽管原子的TOCP随波长的增加显示出下降特征的曲线,但是目标原子与H原子TOCP的比值对波长并不敏感,可以利用此规律来有效地提取TOCP。

此项工作提出了一种有效提取库仑势影响的方法,对解决隧穿延时问题具有非常重要的意义。

工作中采用的数值计算方法为Simpleman模型和半经典方法,这些方法均忽略原子的一些物理效应,比如非绝热效应、多电子效应等。因此,下一步将会围绕这些物理效应对阿秒钟实验测量的影响开展系统的研究。其次,基于第一步的结果,此项工作提到的方案将应用在原子钟实验中,通过提取稀有气体原子在阿秒钟实验中的TOCP,从而实现隧穿延时的精确测量。最后,该方案将进一步拓展到双原子分子体系(如H2,N2,O2)。

阿秒钟实验方案原理图

The Coulomb potential influence in the attoclock experimental scheme

Tunneling is one of the fundamental topics of quantum mechanics. Although the issue of tunneling has already been discussed in detail in text books, the consensus on whether tunneling of a particle through a barrier takes a finite time has not been achieved so far. The resolution of this problem is paramount to fully comprehend the tunneling process itself. Attoclock is an intriguing experimental procedure with temporal resolution in the scale of attoseconds to measure the tunneling delay. Specifically, for atoms subject to the elliptically polarized (EP) laser field, the instant when the electron appears in the continuum is mapped to the final angle of the momentum vector in the polarization plane, which can be measured experimentally. As well accepted, the most crucial advantage of the attoclock scheme is that, to achieve temporal resolution in the scale of attoseconds, the attosecond pulse is not necessary any longer, which lowers the technical demand to a great extent and makes this experimental procedure attractive.

Nevertheless, the experimental method of attoclock suffers from some problems, which gives rise to inconsistent conclusion of tunneling delay measurements. One of the most important problems is how to determine the Coulomb potential influence. In fact, during the attoclock experiments, there is an equivalent temporal offset solely induced by the Coulomb potential (TOCP), which cannot be easily separated from the tunneling delay. Usually, TOCP could be larger than tunneling delay. However, it is very difficult to accurately calculate or measure the TOCP. Therefore, as one may expect, the reliability and temporal resolution of attoclock is limited, which may hinder the investigation of the issue of tunneling delay. Based on the semiclassical calculations, the research group from Wuhan Institute of Physics and Mathematics (WIPM) proposes a procedure to extract the TOCP effectively, which might be significant to solve the tunneling delay problem. The research results are published in Chinese Optics Letters, Vol. 18, Issue 1, 2020 (Zhilei Xiao, Wei Quan, Songpo Xu, Shaogang Yu, Yanlan Wang, Meng Zhao, Mingzheng Wei, Yu Zhou, Xuanyang Lai, Jing Chen, Xiaojun Liu. Coulomb potential influence in the attoclock experimental scheme[J]. Chinese Optics Letters, 2020, 18(1): 010201).

To explore the Coulomb potential effect on the attoclock experiments, wavelength dependence of ultrafast dynamics of atoms subject to strong EP laser field has been investigated when the laser intensity is kept constant. To simulate the tunneling delay, numerically, the electron will stay in the origin until the artificial time delay elapses. The influence of the tunneling delay can be extracted by comparing the calculations with and without the time delay. The Coulomb potential has been further introduced in the semiclassical model, where its influence has been investigated. During the calculation, the ultrafast ionization dynamics of several noble atoms, such as H, Ne, Ar, and Kr, have been studied. It has been numerically shown that, when the tunneling delay has been ignored, the ratio of TOCP of the target atom to that of H follows closely to the function of (2Ip)-3⁄2, where Ip is the ionization potential of the system in question. Note that the Ip of H atom is Ip_H =0.5 a.u. Thus the ratio is linearly proportional to the function of (Ip/Ip_H)-3⁄2. That is to say, although the wavelength dependence of TOCP shows a curve with peculiar declining feature, the ratio of the TOCP of the atom in question to that of H becomes insensitive to the wavelength, which can be employed to extract TOCP effectively.

This work has proposed a procedure to extract the TOCP in attoclock scheme, which could be significant to improve the resolution of attoclock and meaningful to solve the problem of tunneling delay.

The research group gave their research plan in the near future. Firstly, the numerical procedures employed in this work are simpleman model and semiclassical method, where some physical effects, such as nonadiabatic tunneling effect, multi-electron influence etc., have been ignored. Hence, further systematical investigations of the influences of the relevant physical effects on their results will be performed soon. Secondly, based on the results of the 1st step, their procedure will be applied to experimentally extract the TOCP in the attoclock experiments for noble gas atoms subject to intense laser fields and, in turn, achieve the tunneling delay precisely. Finally, their procedure will be extended to molecules (e.g., H2, N2, O2).

The schematic of the attoclock procedure.