双色场驱动下高次谐波的径向量子轨道干涉

研究了双色场驱动下的高次谐波量子轨道的相位匹配特性. 通过调整激光束腰优化双色场空间分布, 可以有效地增加长轨道的径向相位匹配区域, 使得长轨道和短轨道在近轴处和离轴处都同时相位匹配.通过选取合适的近场空间过滤片, 可以获得清晰的径向干涉条纹. 这些结果在分辨不同的干涉现象以及更高精度的观察高阶轨道方面有很大的潜在应用价值. 关键词： 高次谐波 量子轨道 干涉     

Minimum structure of high-harmonic spectrafrom aligned O2 and N2 molecules

We experimentally investigated the high-order harmonic generation (HHG) from aligned O₂ and N₂ molecules in a linearly polarized laser field, and presented the dependence of the harmonic spectrum on the driving laser intensity and molecular alignment angle. The minimum position of HHG of O₂ varies with changing the laser intensity, which is caused by multi-orbital interference. However, the location of the observed minimum structure in N₂ harmonic spectrum remained unchanged upon changing the laser intensity. The mechanism of the spectral minimum for N₂ case is regarded as a Cooper-like minimum in HHG associated with the molecular electronic structure. This work indicates that harmonic spectroscopy can effectively uncover information about molecular structure and electron dynamics.     

激光强度依赖的阈下谐波产生机制

利用广义伪谱方法精确数值求解了氢原子在强激光场中的三维含时薛定谔方程,获得了强激光中氢原子的含时波函数,利用时间依赖的偶极矩的傅里叶变换得到了高次谐波谱,研究了氢原子在强激光场中发射低于电离阈值的谐波谱对激光强度的依赖性.研究发现,激光强度在低于电离阈值的谐波产生的通道选择的过程中扮演着重要角色,主要有两种量子通道对阈下谐波的产生有贡献,即广义的短轨道和长轨道,其中长轨道对激光场强度比较敏感.结合小波时频变换、经典轨道分析、以及强度依赖的量子通道选择分析,本文阐明了其背后的物理机制.     

Bohmian mechanics to high-order harmonic generation

This paper introduces Bohmian mechanics (BM) into the intense laser-atom physics to study high-order harmonic generation. In BM, the trajectories of atomic electron in an intense laser field can be obtained with the Bohm--Newton equation. The power spectrum with the trajectory of an atomic electron is calculated, which is found to be irregular. Next, the power spectrum associated with an atom ensemble from BM is considered, where the power spectrum becomes regular and consistent with that from quantum mechanics. Finally, the reason of the generation of the irregular spectrum is discussed.     

Atomic even-harmonic generation due to symmetry-breaking effects induced by spatially inhomogeneous field

We ab initio investigate the interaction between the hydrogen atom and the inhomogeneous field which is induced by resonant plasmons within a metal nanostructure.Same as normal laser pulse(homogeneous field), only odd-harmonic generation occurs when the bow-tie nanostructure is utilized.For the single nanotip case, the even-harmonic generation can be distinctly found in the harmonic emission spectrum.By investigating the symmetry and trajectories of different inhomogeneous fields, we demonstrate that the breaking symmetry of system can enable even high harmonic generations.     

Controlling continuum wavepacket interference by two-color laser field in over-the-barrier ionization regime

Continuum wavepacket interference is investigated by numerically solving the time-dependent Schröodinger equation for the interaction of hydrogen atoms with laser fields. The obtained wavepacket evolution indicates that, in the over-the-barrier ionization regime (10¹⁶ W/cm²), the continuum–continuum (CC) interference of ionizing electrons becomes the main process in highorder harmonics generation (HHG), compared with continuum-bound (CB) transition, as reported by Kohler et al. [Phys. Rev. Lett. 105(20), 203902 (2010)].We propose a two-color laser field scheme for controlling the quantum trajectories of ionizing electrons and for extending the CC harmonic energy. As a result, a high energy platform occurs in the HHG spectrum, which entirely originates from the CC harmonics, with a cutoff adjustable by the relative phase of the two-color fields. This provides further understanding of the dynamic feature of atoms and molecules in super intense laser fields and provides an opportunity to image the atomic or molecular potential.     

Accurate prediction of interference minima in linear molecular harmonic spectra by a modified two-center model

We demonstrate that the interference minima in the linear molecular harmonic spectra can be accurately predicted by a modified two-center model. Based on systematically investigating the interference minima in the linear molecular harmonic spectra by the strong-field approximation(SFA), it is found that the locations of the harmonic minima are related not only to the nuclear distance between the two main atoms contributing to the harmonic generation, but also to the symmetry of the molecular orbital. Therefore, we modify the initial phase difference between the double wave sources in the two-center model, and predict the harmonic minimum positions consistent with those simulated by SFA.     

利用半周期激光场调控H_2~+谐波辐射过程

采用数值求解核与电子耦合的薛定谔方程,对H_2~+分子谐波辐射调控进行了研究.计算结果表明,激光场正向时,谐波能量主要来源于负向H核贡献;激光场负向时,谐波能量主要来源于正向H核.随后,通过适当引入半周期激光场,可以有效调节正负H核辐射谐波的强度.最后,适当叠加谐波谱上的谐波,可获得一个46 as的脉冲.该研究对调控分子谐波的辐射过程及阿秒脉冲的输出是有帮助的.     

Multi-photon resonance enhanced super high-order harmonic generation

This paper proposes highly charged ions pumped by intense laser to produce very high order harmonics.Numerical simulations and full quantum theory of Ne 9+ ions driven by laser pulses at 1064 nm in the power range of 10 9 W/cm 2 ～ 10 15 W/cm 2 show that the emission spectrum corresponds to the electronic transitions from the excited states to the ground state,which is very different from the spectrum of general high-order harmonic generation.In such situation,harmonic order as high as 1000 can be obtained without producing lower order harmonics and the energy conversion efficiency is close to general high order harmonic generation of hydrogen atom in the same laser field.     

理论研究激光强度对H2+分子高次谐波产生的影响

本文通过求解非波恩-奥本海默近似条件下的一维含时薛定谔方程来研究脉冲强度对H₂⁺分子高次谐波的影响.由于干涉相消,在啁啾激光场的条件下在谐波谱中出现了干涉最小值.我们用全量子方法计算的时频分布图分析了分子高次谐波产生中的微观机制.此外,数值计算结果显示随着脉冲强度的增加电子的有质动力势随之增加,同时干涉最小值的位置移向谐波的高阶部分.     

Quantum interference of multi-orbital effects in high-harmonic spectra from aligned carbon dioxide and nitrous oxide

We investigate experimentally multi-orbital effects in high-order harmonic generation(HHG) from aligned CO_2 and N_2O molecules by intense femtosecond laser fields with linear and elliptical polarizations.For either of the aligned molecules, a minimum in the harmonic spectrum is observed, the position of which shifts to lower-order harmonics when decreasing the intensity or increasing the ellipticity of the driving laser.This indicates that the minimum originates from the dynamic interference of different channels, of which the tunneling ionization and recombination are contributed via different molecular orbitals.The results show that both the highest occupied molecular orbital(HOMO) and low-lying HOMO-2 in CO_2(or HOMO-1 in N_2O) contribute to the molecular HHG in both linearly and elliptically polarized strong laser fields.Our study would pave a way for understanding multi-electron dynamics from polyatomic molecules irradiated by strong laser fields.     

利用双色激光场下阈上电离谱鉴别H3^2+两种不同分子构型

我们最近证明,利用红外和深紫外双色激光场,SF6分子的结构信息可以通过其电离谱上的相干条纹获得[arXiv,1912.08499(2019)].在本文中,我们利用该方法考察了两种不同几何结构的分子离子H32+ 在激光场中的直接阈上电离(ATI)过程.通过与单色激光场中电离谱的比较发现,双色激光场的电离谱可以分辨分子的不同几何结构.由相干条件导出的公式可以很好地解释直接ATI动能谱和动量谱中的干涉条纹.此外,还发现通过改变分子核间距或改变激光强度可以改变电离谱的形状.由此可以推断,双色激光场诱导的ATI谱具有鉴别分子不同构型的能力,对复杂分子的几何结构成像具有一定的参考意义.     

非均匀激光场中氢分子离子高次谐波的增强

通过数值求解非波恩-奥本海默近似下的一维含时薛定谔方程,研究了蝴蝶结型纳米结构基元中氢分子离子高次谐波的产生.研究表明,在蝴蝶结型纳米结构基元内部产生的非均匀场的空间位置对高次谐波的发射有较大影响.当非均匀场的空间位置从30 a.u.平移到-30 a.u.时,高次谐波的截止位置被延展且形成光滑的超连续的谐波谱,并应用时频分析方法、经典三步模型以及电离概率等解释了高次谐波发射的物理机理.研究了高次谐波谱对非均匀场空间位置的依赖性与载波包络值的关系,发现随着载波包络值的变化,非均匀场在不同空间位置处的高次谐波谱变化趋势相同.     

相干叠加态高次谐波发射的时间行为分析

本文研究了一维模型分子离子(初态为基态和一个激发束缚态叠加的相干态)在超强超短激光脉冲作用下的谐波发射谱.我们发现在高次谐波谱平台区域出现了周期性的结构变化.我们利用小波变换对谐波谱进行了暂态时间频率分析,结果表明该谐波结构产生的原因是由电离电子返回母离子时与不同束缚态复合而产生的谐波光脉冲之间相干叠加.同时采用半经典计算,对所得到的计算结果进行了分析,验证了我们的结论.     

Laser phase effect on asymmetric harmonic distribution in H_2~+

The laser phase effect on the spatial distribution of the molecular high-order harmonic generation(MHHG) spectrum from H_2~+ is theoretically investigated through solving the Non-Bohn-Oppenheimer(NBO) time-dependent Schrodinger equation(TDSE).The results are shown as follows,(i) The generated harmonics from the two nuclei each present an asymmetric distribution.Particularly,when the laser phases are chosen from 0.0π to 0.6π and from 1.7π to 2.0π,the contribution from the negative-H plays a main role in harmonic generation.When the laser phases are chosen from 0.7πto 1.6k,the contribution from the positive-H to the harmonic generation is remarkably enhanced and becomes greater than that from the negative-H.The electron localization,the time-frequency analyses of the harmonic spectrum and the time-dependent wave function are shown to explain the asymmetric harmonic distribution in H_2~+,which provides us with a method to control the electron motion in molecules,(ⅱ) As the pulse duration increases,the asymmetric distributions of the MHHG in two H nuclei decrease,(ⅲ) Isotope investigation shows that the asymmetric harmonic distribution can be reduced by introducing the heavy nucleus(i.e.,D_2~+).     

Spectral modulation of third-harmonic generation by molecular alignment and preformed plasma

We demonstrate spectral modulation of third-harmonic generation from molecular alignment effects. The third harmonic spectrum is broadened or narrowed under different influences of cross-phase modulations originating from various molecular alignment revivals. Furthermore, the spectrum and spatial distribution of the generated third harmonic pulse change dramatically in the presence of a preformed plasma. Under the influence of a preformed plasma, a narrower third harmonic spectrum is observed, and the conical third-harmonic pulse increases while the axial part decreases. The investigation provides an effective method to modulate the spectral characteristic and spatial distribution of third-harmonic generation from intense femtosecond filament.     

Measurement of the polarization of high-order harmonics from aligned N(2) molecules by spatial interferometry

The polarization of high-harmonics from aligned N(2) molecules was measured by observing the visibility of spatial interference between two high-harmonics generated separately. The minimum visibility was observed at an angle of 60 degrees between the polarization of the harmonic generation laser field and the molecular orientation. In this case, the angular shift of harmonic polarization is 15 degrees from the molecular orientation. Our measurement of the visibility variation matches the theoretical prediction based on the harmonic field calculation for aligned N(2) molecules.     

Frequency dependence of quantum path interference in non-collinear high-order harmonic generation

High-order harmonic generation(HHG) driven by two non-collinear beams including a fundamental and its weak second harmonic is numerically studied. The interference of harmonics from adjacent electron quantum paths is found to be dependent on the relative delay of the driving pulse, and the dependences are different for different harmonic orders.This frequency dependence of the interference is attributed to the spatial frequency chirp in the HHG beam resulting from the harmonic dipole phase, which in turn provides a potential way to gain an insight into the generation of high-order harmonics. As an example, the intensity dependent dipole phase coefficient α is retrieved from the interference fringe.     

Exact Timing of Returned Molecular Wavepacket

An ionizing wavepacket of electron will re-visit its parent molecular ion during photoionization by strong laser field. This scenario is associated with physical concepts such as molecular re-scattering/collision, interference, diffraction, molecular clock, and generation of XUV light via high-order harmonic generation. On the workbench of a reduced dimensionality model of molecular hydrogen ions irradiated by laser pulse of 0.01-10.0 a.u. intensities, one-cycle pulsewidth, and 800nm wavelength, by deploying a momentum operator on the time-dependent wavefunction of an ionizing wavepacket, we can determine, in a precise manner, the exact time instant for the re-visiting electron to come back to the cation position. The time value is 57.6% of an optical cycle of the exciting laser pulse. This result may be useful in attosecond pump-probe experiments or molecular clock applications.     

Generation of elliptical isolated attosecond pulse from oriented H2+ in a linearly polarized laser field

We investigate the ellipticity of the high-order harmonic generation from the oriented H₂⁺ exposed to a linearly polarized laser field by numerically solving the two-dimensional time-dependent Schrödinger equation (2D TDSE). Numerical simulations show that the harmonic ellipticity is remarkably sensitive to the alignment angle. The harmonic spectrum is highly elliptically polarized at a specific alignment angle θ=30°, which is insensitive to the variation of the laser parameters. The position of the harmonic intensity minima indicates the high ellipticity, which can be attributed to the two-center interference effect. The high ellipticity can be explained by the phase difference of the harmonics. This result facilitates the synthesis of a highly elliptical isolated attosecond pulse with duration down to 65 as, which can be served as a powerful tool to explore the ultrafast dynamics of molecules and study chiral light-matter interaction.