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Dynamics of atoms and molecules at extremes

      极端条件原子分子动力学涉及的强激光场、强电磁场和高温高压高密环境广泛地存在于核爆炸、聚变科学和天体物理等领域研究中, 由于涉及多通道、强关联、非微扰以及多体相互作用等难题, 如何建立极端条件下原子分子动力学先进的实验方法和准确的理论模型、获得高精度的结构和动力学过程数据, 是当前原子分子物理及其相关领域面临的巨大挑战. 超快超强激光和离子加速器等实验技术的发展, 极大地推动了极端条件原子分子动力学研究的开拓和深入. 开展极端条件原子分子动力学研究, 能够深入认识极端环境下原子分子过程的反应机制和动力学演化规律, 提升极端条件原子分子数据的精密研究能力, 这对于天体物理、等离子体物理、磁约束和惯性约束核聚变等多个领域以及超快物理等科学前沿, 具有重要的应用价值. 

       受《物理学报》编辑部委托, 我们策划组织了“极端条件原子分子动力学”专题, 邀请本领域中青年科学家撰稿, 涵盖双电子俘获过程, 离子的低能电子弹性散射, 强激光场下的 Rydberg态激发,超快强场调控分子电离、解离和准直, 等离子体动力学演化, 原子物理中的辐射过程, 电子碰撞激发过程, 高温非平衡气体分子态-态碰撞, 光场加速稠密物质中离子电荷转移等主题的多篇最新研究成果, 同时就强激光场中可能产生独特的光-核相互作用的前沿研究进行了展望, 综述了基于原子内壳层跃迁的 X射线腔量子光学、超快和高压结合的综合极端条件下分子动力学过程的研究进展等. 希望本专题能够为相关领域学者提供参考, 吸引更多青年学者进入本领域开展研究, 推动极端条件原子分子动力学领域的蓬勃发展.

客座编辑:吴勇 北京应用物理与计算数学研究所; 丁大军 吉林大学
Acta Physica Sinica. 2024, 73(24).
From “strong-field atomic physics” to “strong-field nuclear physics”
Wang Xu
2024, 73 (24): 244202. doi: 10.7498/aps.73.20241456
Abstract +
In the mid-1980s, chirped pulse amplification (Nobel Prize in Physics 2018) broke through previous limits to laser intensity, allowing intensities to exceed the atomic unit threshold (1 atomic unit of laser intensity corresponds to a power density of 3.5×1016 W/cm2). These strong laser fields can cause high-order nonlinear responses in atoms and molecules, resulting in a series of novel phenomena, among which high-order harmonic generation and attosecond pulse generation (Nobel Prize in Physics 2023) are particularly important. With the development of high-power laser technology, laser intensity has now reached the order of 1023 W/cm2 and is constantly increasing. Now, a fundamental question has been raised: can such a powerful laser field induce similar high-order nonlinear responses in atomic nuclei, potentially transitioning “strong-field atomic physics” into “strong-field nuclear physics”?To explore this, we investigate a dimensionless parameter that estimates the strength of light-matter interaction: $ \eta = D{E_0}/{{\Delta }}E $, where D is the transition moment (between two representative levels of the system), E0 is the laser field amplitude, DE0 quantifies the laser-matter interaction energy, and ΔE is the transition energy. If $ \eta \ll 1 $, the interaction is within the linear, perturbative regime. However, when $ \eta \sim 1 $, highly nonlinear responses are anticipated. For laser-atom interactions, D ~ 1 a.u. and ΔE = 1 a.u., so if E0 ~ 1 a.u., then $ \eta \sim 1 $ and highly nonlinear responses are initiated, leading to the above-mentioned strong-field phenomena.In the case of light-nucleus interaction, it is typical that $ \eta \ll 1 $. When considering nuclei instead of atoms, D becomes several (~5 to 7) orders of magnitude smaller, while ΔE becomes several (~5) orders of magnitude larger. Consequently, the laser field amplitude E0 will need to be 10 orders of magnitude higher, or the laser intensity needs to be 20 orders of magnitude higher (~ 1036 W/cm2), which is beyond existing technological limit and even exceeds the Schwinger limit, where vacuum breakdown occurs.However, there exist special nuclei with exceptional properties. For instance, the 229Th nucleus has a uniquely low-lying excited state with an energy value of only 8.4 eV, or 0.3 a.u. This unusually low transition energy significantly increases η. This transition has also been proposed for building nuclear clocks, which have potential advantages over existing atomic clocks.Another key factor is nuclear hyperfine mixing (NHM). An electron, particularly the one in an inner orbital, can generate a strong electromagnetic field at the position of the nucleus, leading to the mixing of nuclear eigenstates. For 229Th, this NHM effect is especially pronounced: the lifetime of the 8.4-eV nuclear isomeric state in a bare 229Th nucleus (229Th90+) is on the order of 103 s, while in the hydrogenlike ionic state (229Th89+) it decreases by five orders of magnitude to 10–2 s. This 1s electron greatly affects the properties of the 229Th nucleus, effectively changing the nuclear transition moment from D for the bare nucleus to $ D' = D + b{\mu _{\text{e}}} $ for the hydrogenlike ion, where D ~ 10–7 a.u., $ b \approx 0.03 $ is the mixing coefficient, $ {\mu _{\text{e}}} $ is the magnetic moment of the electron, and $ D'\approx b\mu_{\text{e}}\sim10^{-4}\ \text{a}\text{.u}. $ That is to say, the existence of the 1s electron increases the light-nucleus coupling matrix element by approximately three orders of magnitude, leading to the five-orders-of-magnitude reduction in the isomeric lifetime.With the minimized transition energy ΔE and the NHM-enhanced transition moment D', it is found that $ \eta \sim 1 $ for currently achievable laser intensities. Highly nonlinear responses are expected in the 229Th nucleus. This is confirmed by our numerical results. Highly efficient nuclear isomeric excitation can be achieved: an excitation probability of over 10% is achieved per nucleus per femtosecond laser pulse at a laser intensity of 1021 W/cm2. Correspondingly, the intense laser-driven 229Th89+ system emits secondary light in the form of high harmonics, which share similarities with those from laser-driven atoms but also have different features.In conclusion, it appears feasible to extend “strong-field atomic physics” to “strong-field nuclear physics”, at least in the case of 229Th. “Strong-field nuclear physics” is emerging as a new frontier in light-matter interaction and nuclear physics, providing opportunities for precisely exciting and controlling atomic nuclei with intense lasers and new avenues for coherent light emission based on nuclear transitions.
X-ray cavity quantum optics of inner-shell transitions
Wang Shu-Xing, Li Tian-Jun, Huang Xin-Chao, Zhu Lin-Fan
2024, 73 (24): 246101. doi: 10.7498/aps.73.20241218
Abstract +
Over the past decade, X-ray quantum optics has emerged as a dynamic research field, driven by significant advancements in X-ray sources such as next-generation synchrotron radiation facilities and X-ray free-electron lasers, as well as improvements in X-ray methodologies and sample fabrication techniques. One of the most successful platforms in this field is the X-ray planar thin-film cavity, also known as the X-ray cavity QED setup. To date, most studies in X-ray cavity quantum optics have focused on Mössbauer nuclear resonances. However, this approach is constrained by the limited availability of suitable nuclear isotopes and the lack of universal applicability. Recently, experimental realizations of X-ray cavity quantum control in atomic inner-shell transitions have demonstrated that cavity effects can simultaneously modify transition energies and core-hole lifetimes. These pioneering studies suggest that X-ray cavity quantum optics based on inner-shell transitions will become a promising new platform. Notably, the core-hole state is a fundamental concept in various modern X-ray spectroscopic techniques. Therefore, integrating X-ray quantum optics with X-ray spectroscopy holds the potential to open new frontiers in the field of core-level spectroscopy.In this review, we introduce the experimental systems used in X-ray cavity quantum optics with inner-shell transitions, covering cavity structures, sample fabrications, and experimental methodologies. We explain that X-ray thin-film cavity experiments require high flux, high energy resolution, minimal beam divergence, and precise angular control, necessitating the use of synchrotron radiations. Grazing reflectivity and fluorescence measurements are described in detail, along with a brief introduction to resonant inelastic X-ray scattering techniques. The review also outlines simulation tools, including the classical Parratt algorithm, semi-classical matrix formalism, quantum optical theory based on the Jaynes-Cummings model, and the quantum Green’s function method. We discuss the similarities and unique features of electronic inner-shell transitions and highlight recent advancements, focusing on cavity-induced phenomena such as collective Lamb shift, Fano interference, core-hole lifetime control, etc. Observables such as reflectivity and fluorescence spectra play a central role in these studies. Finally, we review and discuss potential future directions for the field. Designing novel cavities is crucial for addressing current debates regarding cavity effects in inner-shell transitions and uncovering new quantum optical phenomena. Integrating modern X-ray spectroscopies with X-ray cavity quantum optics represents a promising research frontier with significant application potential. Furthermore, X-ray free-electron lasers, with much higher pulse intensity and shorter pulse duration, are expected to propel X-ray cavity quantum optics into the nonlinear and multiphoton regimes, opening new avenues for exploration.
Experimental measurement of state selective double electron capture in collision between 1.4–20 keV/u Ar8+ with He
Wu Yi-Jiao, Meng Tian-Ming, Zhang Xian-Wen, Tan Xu, Ma Pu-Fang, Yin Hao, Ren Bai-Hui, Tu Bing-Sheng, Zhang Rui-Tian, Xiao Jun, Ma Xin-Wen, Zou Ya-Ming, Wei Bao-Ren
2024, 73 (24): 240701. doi: 10.7498/aps.73.20241290
Abstract +
Electron capture in the collision of highly charged ions with atoms and molecules is a fundamental process related to the electron transition between bound states belonging to two atomic-centers. The X-ray emission after electron capture is important for X-ray astrophysical modeling, fusion plasma diagnostics, and ion irradiated biophysics. In the past few decades, momentum-imaging cold-target recoil ion momentum spectroscopy has been a significantly developed technique and widely used to measure the quantum state-selective population in electron capture processes. Based on the cold target recoil ion momentum spectroscopy installed on the 150 kV highly charged ion platform in Fudan University, Shanghai City, China, the state-selectivity of double electron capture in the bombardment of 1.4–20 keV/u Ar8+ on He is measured, and the relative cross sections of the 3l 3l' to 3l 7l' double excited states are obtained. It is found that with the increase of collision energy, more quantum state-selectivity channels are open in the double electron capture of Ar8+-He collision. It is also found that the relative cross section of the quantum state population is strongly dependent on the collision energy of the projectile ion. The present measurements not only enrich the state-selective cross-sectional library and collision dynamics of highly charged ion charge exchange processes, but also provide experimental benchmarks for existing theoretical calculations.
Laser envelope control of strong field excited Rydberg states
Zhao Ling-Yi, Liu Jin-Lei, Jiang Tao, Lang Yue, Zhao Zeng-Xiu
2024, 73 (24): 243201. doi: 10.7498/aps.73.20241222
Abstract +
Rydberg atoms are important building blocks for quantum technologies, and because of their unique tunable quantum properties, they possess new applications in quantum computing, quantum communication, and quantum sensing. Besides the widely-used few-photon resonant excitation for the specific Rydberg state, multiple Rydberg states can be populated coherently and efficiently through the frustrated tunneling ionization or the Coulomb potential recapture effect in a strong laser field. The excitation of Rydberg states in a strong field provides an opportunity for realizing the ultrafast quantum control on Rydberg atom and bridging the gap between strong field physics and quantum information technology. Using the classical trajectory Monte Carlo method and Qprop package to solve time-dependent Schrödinger equation, we calculate the population of Rydberg states. Our results show that the population increases with the increase of parameter of the asymmetric laser envelope. Based on the quantitative rescattering theory, the calculated time-dependent recapture rate is negatively related to the laser envelope and the residual laser interaction time, which is termed the envelope effect. Combined with the carrier-wave effect, an analytic formula can be used to calculate the Rydberg state population: $ Y(t) \propto $$ W_0\left(t\right) \dfrac{t-\tau+c}{f\left(t\right)} \cos \left(\omega t+\phi\right) . $ This result opens the way to enhancing the generation of Rydberg states by using the laser envelope control, which is beneficial to the future quantum technology based on the Rydberg states generated in the strong laser field.
Dissociation of chlorobromomethane molecules coherently controlled by ultrafast strong field
Jing Wen-Quan, Jia Li-Juan, Sun Zhao-Peng, Zhao Song-Feng, Shu Chuan-Cun
2024, 73 (24): 243301. doi: 10.7498/aps.73.20241401
Abstract +
Coherent control of molecular dissociation in ultrafast strong fields has received considerable attention in various scientific disciplines, such as atomic and molecular physics, physical chemistry, and quantum control. Many fundamental issues still exist regarding the understanding of phenomena, exploration of mechanisms, and development of control strategies. Recent progress has shown that manipulating the spectral phase distribution of a single ultrafast strong ultraviolet laser pulse while maintaining the same spectral amplitude distribution can effectively control the total dissociation probability and branching ratio of molecules initially in the ground state. In this work, the spectral phase control of the photodissociation reaction of chlorobromomethane (CH2BrCl) is studied in depth by using a time-dependent quantum wave packet method, focusing on the influence of the initial vibrational state on the dissociation reaction. The results show that modifying the spectral phase of a single ultrafast pulse does not influence the total dissociation probability or branching ratio in the weak field limit. However, these factors exhibit significant dependence on the spectral phase of the single ultrafast pulse in the strong field limit. By analyzing the population distribution of vibrational states in the ground electronic state, we observe that chirped pulses can effectively control the resonance Raman scattering (RRS) phenomenon induced in strong fields, thereby selectively affecting the dissociation probability and branching ratio based on initial vibrational states. Furthermore, we demonstrate that by selecting an appropriate initial vibration state and controlling both the value and sign of the chirp rate, it is possible to achieve preferential cleavage of Cl+CH2Br bonds. This study provides new insights into understanding of ultrafast coherent control of photodissociation reactions in polyatomic molecules.
Low-energy electron elastic scattering of $ {\mathbf{C}}_{4}^{-} $ anions: Resonance states and conformers
Li Jiong-Yuan, Meng Ju, Wang Ke-Dong
2024, 73 (24): 243401. doi: 10.7498/aps.73.20241377
Abstract +
This paper reports low-energy electron scattering with $ {{\mathrm{C}}}_{4}^{-} $ anions by using the ab initio R -matrix method in the single state close-coupling (CC) model and the fixed-nuclei approximation. We predict the elastic integral scattering cross sections (ICSs) of four conformers of $ {{\mathrm{C}}}_{4}^{-} $ ions in an energy range of 0 < E ≤12 eV and discuss the effects of configuration changes on resonance position and width. Additionally, the theoretical results and experimental data are compared and analyzed. The results indicate that the 8.8 eV resonance peak observed in experiment is mainly derived from the $ {{{\Sigma }}}_{{\mathrm{u}}}^{+} $ and $ {{{\Sigma }}}_{{\mathrm{u}}}^{-} $ resonances of the conformer A and the A2 resonance of the conformer C. The scattering cross-section reveals that the conformer A has five resonant states, and the conformer B has three resonances, while C and D each have four resonances. Finally, we use the Boltzmann distribution to calculate the populations of different conformers at different temperatures, and simulate the low-energy electron elastic integrated scattering cross-section at room temperature, which is in good agreement with available experimental results. We also find a shape resonance with a width of 0.20 eV at 3.3 eV in our total cross sections, which is not detected in the existing experimental results. This provides new opportunities for measurement.
Theoretical study on photo-ionization of helium atoms by Bessel vortex light
Zhao Ting, Gong Mao-Mao, Zhang Song-Bin
2024, 73 (24): 244201. doi: 10.7498/aps.73.20241378
Abstract +
Owing to vortex light possessing the additional orbital angular momentum, its interaction with atoms and molecules can reveal in more depth insights into dynamics than the plane wave light. This paper aims to establish a theoretical framework for the photoionization of atoms and molecules by Bessel vortex light. In the case of macroscopic gas target, helium atoms are randomly dispersed around the entire region of the Bessel vortex beam. The final photoionization cross-section is not dependent on the angular momentum of the vortex light, but depends on the opening angle of the Bessel vortex light. This paper systematically computes the variation of photoionization cross-section with photon energy and the angular distributions of photoelectrons under different geometric conditions. The computation results demonstrate that there is a significant difference in the photo-ionization cross-section between vortex light and plane wave light. In order to further investigate the characteristics of the phase singularity of the vortex light (when the light intensity reaches zero), this paper further calculates the photo-ionization of the vortex light with opening angles of 5°, 30°, and 60° at the phase singularity, respectively. The results indicate that the angular distribution of photoelectrons at these three angles is significantly dependent on the orbital angular momentum and the opening angle of the vortex light, and the calculated absolute cross-section does not equate to zero. This represents an important distinguishing feature of the Bessel vortex light when interacting with atoms, distinguishing it from the plane wave. This work lays the foundation for further studying vortex light photo-ionization and their applications.
Dissociation dynamic study of $\text{H}_2^+$ in time-delayed two-color femtosecond lasers
Wang Jing-Zhe, Dong Fu-Long, Liu Jie
2024, 73 (24): 248201. doi: 10.7498/aps.73.20241283
Abstract +
In recent years, the rapid development of ultrashort pulse laser technology has made it possible to regulate the ionization and dissociation dynamics of atoms and molecules. Among them, the microscopic dynamics of molecular dissociation have always been a hot topic. The phenomenon of molecular dissociation, which is caused by the interaction between femtosecond intense laser fields and $\text{H}_2^+$ molecules, has attracted widespread attention. Previous theoretical studies on the dissociation of $\text{H}_2^+$ molecules mainly focused on studying its dissociation dynamics through numerical calculations, with relatively few theoretical models. This paper aims to establish a simple classical model to describe the dissociation dynamics. Firstly, this paper calculates the joint distribution of nuclear energy and electronic energy in the dissociation process of $\text{H}_2^+$ molecules under the action of pump lasers by numerically solving the Schrödinger equation. The results prove that $\text{H}_2^+$ molecules initially in the ground state are dissociated into ${\rm H}^+ + {\rm H}^*$ after absorbing a pump photon in the pump light field. Next, this paper studies the dissociation dynamics of $\text{H}_2^+$ molecules in time-delayed two-color femtosecond lasers. We find that it greatly depends on the specific forms of the pump light and the probe light. By utilizing the dependence of the dissociation kinetic energy release (KER) spectrum on the time delay of the two-color femtosecond lasers, we retrieve the sub-attosecond microscopic dynamic behaviors of electrons and atomic nuclei in the dissociation process. Furthermore, we establish a classical model based on the conservation of energy and momentum to describe the dissociation dynamics. This model can qualitatively predict the ion dissociation KER spectrum depending on the time delay of the two-color femtosecond lasers. The electronic resonant transition between the molecular ground state and the first excited state caused by the probe light will affect the ion kinetic energy spectrum in the dissociation process. Namely, the ion kinetic energy spectrum is dependent on the frequency of the probe laser. By taking advantage of this characteristic, we propose a scheme to reconstruct the evolution of the internuclear distance with time. Our reconstruction results can qualitatively predict the trend of the numerical simulation results, and this scheme may provide some theoretical guidance for experiments.
Fully relativistic distorted-wave method of studying electron-atom collision excitation process
LI Wenbo, LI Bingbing, CHEN Hao, XIE Luyou, WU Zhongwen, DING Xiaobin, ZHANG Denghong, JIANG Jun, DONG Chenzhong
2025, 74 (3): 033401. doi: 10.7498/aps.74.20241467
Abstract +
The electron-atom (ion) collision excitation process is one of the most common inelastic scattering processes. It is of great significance in the fields of astrophysics and laboratory plasma. The relativistic distorted-wave method is a widely used theoretical tool for studying electron-atom (ion) collisions, with the aim of obtaining scattering parameters, such as impact cross sections and rate coefficients.In recent years, we have developed a set of fully relativistic distorted-wave methods and programs of studying the electron-atom collision excitation processes. This method is based on the multi-configuration Dirac-Hartree-Fock (MCDHF) method, together with the corresponding packages GRASP 92/2K/2018 and RATIP. In the present work, continuum state wave functions, total and differential cross sections, state multipoles, integral and differential Stokes parameters of the radiation photon after the impact excitation processes of polarized electrons and atoms are calculated. The influences of electron correlation effects, Breit interaction, and plasma screening effects on the excitation cross sections are discussed. The present methods and programs possess several advantages below.1) In the calculations of the continuum electron wave functions, the direct interaction and exchange interaction between the bound electron and the continuum electron are both included. Then, the anti-symmetrized coupling wave function, which is composed of the continuum electron wave function and the continuum ion wave function, is utilized as the wave function of the system. This method is employed to study the low-energy electron scattering process and medium energy electron scattering process.2) In this method, the target state wave function is obtained form the MCDHF theory and the corresponding GRASP packages. The MCDHF method has the advantage of being able to consider the electron correlation effects, including valence-valence, core-valence, and core-core correlations, as well as the influence of Breit interaction and quantum electrodynamics effect on the target state wave function. Furthermore, the calculation of the collision excitation matrix elements also includes the contribution of the Breit interaction. Consequently, the present method integrates the advantages of both the MCDHF method and distorted-wave method, thus is made suitable for studying the scattering processes of highly charged ions. In addition, it facilitates the study of the influence of higher-order effects on the collision dynamics, thereby obtaining high-precision theoretical data.3) The current method and program can also be utilized to study the scattering cross section of electron-atom collision excitation processes, as well as the influence of plasma screening effects on collision excitation. Furthermore, the state multipoles, differential Stokes parameters, integral Stokes parameters, and orientation parameters of electron-complex atom collision excitation can be studied in detail by using the present method and program.
Analysis of dynamic response and screening effects on electron-ion energy relaxation in dense plasma
LIN Chengliang, HE Bin, WU Yong, WANG Jianguo
2025, 74 (3): 035101. doi: 10.7498/aps.74.20241588
Abstract +
Accurate knowledge of electron-ion energy relaxation plays a vital role in non-equilibrium dense plasmas with widespread applications such as in inertial confinement fusion, in laboratory plasmas, and in astrophysics. We present a theoretical model for the energy transfer rate of electron-ion energy relaxation in dense plasmas, where the electron-ion coupled mode effect is taken into account. Based on the proposed model, other simplified models are also derived in the approximations of decoupling between electrons and ions, static limit, and long-wavelength limit. The influences of dynamic response and screening effects on electron-ion energy relaxation are analyzed in detail. Based on the models developed in the present work, the energy transfer rates are calculated under different plasma conditions and compared with each other. It is found that the behavior of electron screening in the random phase approximation is significantly different from the one in the long-wave approximation. This difference results in an important influence on the electron-ion energy relaxation and temperature equilibration in plasmas with temperature $T_{\rm{e}} < T_{\rm{i}}$. The comparison of different models shows that the effects of dynamic response, such as dynamic screening and coupled-mode effect, have stronger influence on the electron-ion energy relaxation and temperature equilibration. In the case of strong degeneracy, the influence of dynamic response will result in an order of magnitude difference in the electron-ion energy transfer rate. In conclusion, it is crucial to properly consider the finite-wavelength screening of electrons and the coupling between electron and ion plasmonic excitations in order to determine the energy transfer rate of electron-ion energy relaxation in dense plasma.
Electronic screening effects during bremsstrahlung of carbon atoms and ions
YAN Tong, LIU Aihua, JIAO Liguang
2025, 74 (3): 033402. doi: 10.7498/aps.74.20241638
Abstract +
Bremsstrahlung, as an important radiation process in atomic physics, has significant applications in the fields of astrophysics, plasma physics, magnetic and inertial confinement fusion. In this work, the relativistic partial-wave expansion method is used to investigate the bremsstrahlung of neutral carbon atoms and different charged carbon ions scattered from intermediate- and high-energy relativistic electrons, with special attention paid to the electronic screening effect produced by the target electrons. The target wave function is obtained from the Dirac-Hartree-Fock self-consistent calculations, and the electron-atom scattering interaction potential is constructed in the central-field approximation. By solving the partial-wave Dirac equation, the continuum wave functions of the relativistic electron are obtained, from which the bremsstrahlung single and double differential cross sections can be calculated via the multipole free-free transitions between the incident and exit free electrons. The target electronic screening effects on the bremsstrahlung single and double differential cross sections are analyzed under a variety of conditions of incident electron energy and emitted photon energy. It is shown that the target electronic screening effect will significantly suppress the cross sections both at low incident energy and in the soft-photon region. Such a suppressing effect decreases with the incident electron energy and the emitted photon energy gradually increasing. Overall, the electronic screening effect has no significant influence on the shape function of bremsstrahlung.
Measurement analysis of coherence in femtosecond laser-induced molecular alignment
LIAN Zhenzhong, HONG Qianqian, JIA Lijuan, MENG Jianqiao, SHU Chuancun
2025, 74 (3): 033301. doi: 10.7498/aps.74.20241400
Abstract +
Femtosecond laser-induced excitation of molecular rotational states can lead to phenomena such as alignment and orientation, which fundamentally stem from the coherence between the induced rotational states. In recent years, the quantitative study of coherence in the field of quantum information has received widespread attention. Different kinds of coherence measures have been proposed and investigated. In this work, the quantitative correlation is investigated in detail between the intrinsic coherence measurement and the degree of molecular alignment induced by femtosecond laser pulses at finite temperatures. By examining the molecular alignment induced by ultrafast non-resonant laser pulses, a quantitative relationship is established between the $l_1$ norm coherence measure $C_{l_1}(\rho)$ and the alignment amplitude ${\cal{D}}\langle \cos^2 \theta \rangle$. Here, $C_{l_1}(\rho)$ represents the sum of the absolute values of all off-diagonal elements of the density matrix ρ, ${\cal{D}}\langle \cos^2 \theta \rangle$ represents the difference between the maximum alignment and the minimum alignment. A quadratic relationship $ C_{l_1} = (a + b{\cal{E}}^2_0)\times $$ {\cal{D}}\langle \cos^2 \theta \rangle$ between the the $l_1$ norm coherence measure and ${\cal{D}}\langle \cos^2 \theta \rangle$ with respect to the electric field intensity ${\cal{E}}_0$ is obtained. This relationship is validated through numerical simulations of the CO molecule, and the ratio coefficients a and b for different temperatures are obtained. Furthermore, a mapping relationship between this ratio and the pulse intensity area is established. The findings of this study provide an alternative method for experimentally detecting the coherence measure within femtosecond laser-excited rotational systems, thereby extending the potential applicability of molecular rotational states to the study of the coherence measure in the field of quantum resources. This will facilitate the interdisciplinary integration of ultrafast strong-field physics and quantum information.
Numerical simulation of state parameter distributions and extreme ultraviolet radiation in laser-produced tin plasma
MIN Qi, WANG Guodong, HE Chaowei, HE Siqi, LU Haidong, LIU Xingbang, WU Yanhong, SU Maogen, DONG Chenzhong
2025, 74 (3): 033201. doi: 10.7498/aps.74.20241321
Abstract +
The laser-produced Sn plasma light source is a critical component in advanced extreme ultraviolet (EUV) lithography. The power and stability of EUV radiation within a 2% bandwidth centered at 13.5 nm are key indicators that determine success of the entire lithography process .The plasma state parameter distributions and the EUV radiation spectrum for a laser-produced Sn plasma light source are numerically simulated in this work. The radiative opacity of Sn plasma within the 12–16 nm range is calculated using a detailed-level-accounting model in the local thermodynamic equilibrium approximation. Next, the temperature distribution and the electron density distribution of plasma generated by nanosecond laser pulses interacting with both a Sn planar solid target and a liquid droplet target are simulated using the radiation hydrodynamics code for laser-produced plasma, RHDLPP. By combining the radiative opacity data with the plasma state data, the spectral simulation subroutine SpeIma3D is employed to model the spatially resolved EUV spectra for the planar target plasma and the angle-resolved EUV spectra for the droplet target plasma at a 60-degree observation angle. The variation of in-band radiation intensity at 13.5 nm within the 2% bandwidth as a function of observation angle is also analyzed for the droplet-target plasma. The simulated plasma state parameter distributions and EUV spectral results closely match existing experimental data, demonstrating the ability of RHDLPP code to model laser-produced Sn plasma EUV light sources. These findings provide valuable support for the development of EUV lithography and EUV light sources.