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Atomic and Molecular Physics|75 Article(s)
Potential-Assisted Target Atomic Ionization Excitation Radiation Near-Infrared Spectra
Ying Zhang, Zhongfeng Xu, Xing Wang, Jieru Ren, Yanning Zhang, Cexiang Mei, Xianming Zhou, Changhui Liang, Wei Wang, and Xiaoan Zhang
Objective129Xeq+(q=17, 20, 23, 25, 27) highly charged ions with a kinetic energy of 1360 keV are incident on the surface of metal Al and Ti solid targets respectively. The near-infrared spectral lines (800-1700 nm) of excited Xe atoms and low ionized Xe ions, and the spectral lines of excited target atoms and excited by ionization are measured during the interaction between the highly charged ions and the surface to achieve surface electron neutralization. The experimental results show that during the process of high charged ion incident on the metal surface, the potential energy carried by the ion instantly (in the femtosecond range) deposits on the target surface, ionizing and exciting the target atoms. Due to the strong Coulomb potential energy, the target atoms can form a highly ionized state and complex electronic configuration to de-excite the emission spectrum. As the charge state of the incident ion increases, the measured spectral line intensity rises, and the increasing trend is generally consistent with the growing trend of the potential energy of the incident ion, which indicates that the classical over-the-barrier model is valid in the near Bohr velocity energy region. We also hope that our experimental data can provide basic support for related research and provide new methods for spectral measurement.MethodsThe experiment is performed at the Heavy Ion Research Facility in Lanzhou (HIRFL) and the experimental platform is shown in Fig. 1. Gaseous 129Xe atoms repeatedly collide with electrons in an 18 GHz microwave field in the ECR, gradually peeling off to form highly charged 129Xeq+ ions. They are introduced at the required voltage for the experiment, and the required projectile ions are selected by analytical magnets based on the charge-to-mass ratio. The beam spot is controlled to be less than 5 mm using a beam splitter, quadrupole lens, and aperture, and the beam intensity is recorded via a Faraday tube. The beam enters a metal ultra-high vacuum chamber with magnetic shielding (vacuum degree maintained at 10-8 Pa). The chemical purity of sample Al or Ti is 99.99%, and the surface has been purified with a target area of 15 mm×15 mm and thickness of 0.1 mm. The infrared optical window and monochromator incident slit are perpendicular to the beam direction and form a 45° angle with the target surface. The experiment employs an infrared spectrometer SP-2357 produced by ARC (Action Reserve Corporation) in the United States, with a grating density of 600 g/mm and a flashing wavelength of 1.6 μm. The InGaA-C detector is selected with an effective range of 800-1700 nm and an integration time of 3000 ms. To improve the signal-to-noise ratio and measurement accuracy, we adopt a phase-locked amplifier (SR830) and a chopper (SR540). Additionally, we have to operate in the darkroom or the dark cover screening to eliminate or reduce the background of spectral measurement.Results and DiscussionsThe near-infrared spectral lines (800-1700 nm) emitted from the interaction between high charge state 129Xeq+ (q=17-27) and metal solid targets are measured (Table 1). These spectral lines can be adopted in the research on the damage of space-charged particles to aerospace devices, high-precision optical clocks, and in the infrared background radiation of the universe in laboratory astrophysics. Xe ion emission near-infrared is an important basis for manipulating Hall thrusters, with space stations performing attitude calibration and other actions in space.Under the action of highly charged ions, it is possible to ionize and excite transitions between complex configurations of target atoms, and electric dipole forbidden transitions (magnetic dipole and electric quadrupole transitions). Additionally, we measure spectral lines of 842.42 nm and 1525.03 nm for helium like (Al XII) Al ions (i.e. Al11+) radiation, and 1251.08 nm for lithium like (Al XI) Al (Al10+) ions, which belong to electric dipole transition radiation. The 989.01 nm spectral line for Ti XVIII (i.e. Ti17+) de-excitation radiation belongs to magnetic dipole transition radiation. To our knowledge, these spectral lines are predicted by theoretical predictions from 1987 and 2013, and there have been no reports of experimental data so far.The classical over-the-barrier model for the interaction between highly charged ions and metal solid targets in the Bohr velocity energy region has been validated. The trend of single particle fluorescence yield increasing with the potential energy of the incident ion is measured, which is roughly the same as the charge state trend of the incident ion rising with the potential energy (Fig. 3). The classical over-the-barrier model suggests that the charge state of the incident ion plays an important role in the ionization excitation of the target atom and the neutralization process of the target electron captured by the incident ion.ConclusionsHighly charged ions are incident on a metal solid target surface and deposit the carried energy in the nano-space of the target surface within the femtosecond time scale, which ionizes and excites the target atoms and results in the emission of spectral lines. Some of the spectral lines are transitions between complex electronic configurations, leading to strong electric dipole forbidden transitions. There have been no experimental data reports on the 842.42 nm and 1525.03 nm spectral lines emitted by helium-like Al ions, as well as the 1251.08 nm spectral lines emitted by lithium-like Al ions, and the 989.01 nm spectral lines of Ti XVIII (i.e. Ti17+) ion de-excitation radiation since the theoretical calculation results were published in 1987. The relative intensity of the spectral lines (single ion fluorescence production) we measure increases with the growing charge state of the incident ion, and the increasing trend is generally consistent with the potential energy trend of the incident ion increasing with the charge state. This indicates that the classical over-the-barrier model holds true in the energy region of the incident ion's kinetic energy near the Bohr velocity. The research methods for elastic and inelastic scattering caused by collisions between ions and gas target atoms are different. Due to many novel phenomena generated by highly charged ions incident on solid surfaces, such as the controversy over Auger and ICD processes, the energy shift caused by multiple ionization of target atoms, and the dissipation channels of total energy and gain energy of incident ions, a large quantity of work should be done. Meanwhile, we sincerely hope that our study can provide basic data and support for related research, and propose new methods for spectral measurement. Objective129Xeq+(q=17, 20, 23, 25, 27) highly charged ions with a kinetic energy of 1360 keV are incident on the surface of metal Al and Ti solid targets respectively. The near-infrared spectral lines (800-1700 nm) of excited Xe atoms and low ionized Xe ions, and the spectral lines of excited target atoms and excited by ionization are measured during the interaction between the highly charged ions and the surface to achieve surface electron neutralization. The experimental results show that during the process of high charged ion incident on the metal surface, the potential energy carried by the ion instantly (in the femtosecond range) deposits on the target surface, ionizing and exciting the target atoms. Due to the strong Coulomb potential energy, the target atoms can form a highly ionized state and complex electronic configuration to de-excite the emission spectrum. As the charge state of the incident ion increases, the measured spectral line intensity rises, and the increasing trend is generally consistent with the growing trend of the potential energy of the incident ion, which indicates that the classical over-the-barrier model is valid in the near Bohr velocity energy region. We also hope that our experimental data can provide basic support for related research and provide new methods for spectral measurement.MethodsThe experiment is performed at the Heavy Ion Research Facility in Lanzhou (HIRFL) and the experimental platform is shown in Fig. 1. Gaseous 129Xe atoms repeatedly collide with electrons in an 18 GHz microwave field in the ECR, gradually peeling off to form highly charged 129Xeq+ ions. They are introduced at the required voltage for the experiment, and the required projectile ions are selected by analytical magnets based on the charge-to-mass ratio. The beam spot is controlled to be less than 5 mm using a beam splitter, quadrupole lens, and aperture, and the beam intensity is recorded via a Faraday tube. The beam enters a metal ultra-high vacuum chamber with magnetic shielding (vacuum degree maintained at 10-8 Pa). The chemical purity of sample Al or Ti is 99.99%, and the surface has been purified with a target area of 15 mm×15 mm and thickness of 0.1 mm. The infrared optical window and monochromator incident slit are perpendicular to the beam direction and form a 45° angle with the target surface. The experiment employs an infrared spectrometer SP-2357 produced by ARC (Action Reserve Corporation) in the United States, with a grating density of 600 g/mm and a flashing wavelength of 1.6 μm. The InGaA-C detector is selected with an effective range of 800-1700 nm and an integration time of 3000 ms. To improve the signal-to-noise ratio and measurement accuracy, we adopt a phase-locked amplifier (SR830) and a chopper (SR540). Additionally, we have to operate in the darkroom or the dark cover screening to eliminate or reduce the background of spectral measurement.Results and DiscussionsThe near-infrared spectral lines (800-1700 nm) emitted from the interaction between high charge state 129Xeq+ (q=17-27) and metal solid targets are measured (Table 1). These spectral lines can be adopted in the research on the damage of space-charged particles to aerospace devices, high-precision optical clocks, and in the infrared background radiation of the universe in laboratory astrophysics. Xe ion emission near-infrared is an important basis for manipulating Hall thrusters, with space stations performing attitude calibration and other actions in space.Under the action of highly charged ions, it is possible to ionize and excite transitions between complex configurations of target atoms, and electric dipole forbidden transitions (magnetic dipole and electric quadrupole transitions). Additionally, we measure spectral lines of 842.42 nm and 1525.03 nm for helium like (Al XII) Al ions (i.e. Al11+) radiation, and 1251.08 nm for lithium like (Al XI) Al (Al10+) ions, which belong to electric dipole transition radiation. The 989.01 nm spectral line for Ti XVIII (i.e. Ti17+) de-excitation radiation belongs to magnetic dipole transition radiation. To our knowledge, these spectral lines are predicted by theoretical predictions from 1987 and 2013, and there have been no reports of experimental data so far.The classical over-the-barrier model for the interaction between highly charged ions and metal solid targets in the Bohr velocity energy region has been validated. The trend of single particle fluorescence yield increasing with the potential energy of the incident ion is measured, which is roughly the same as the charge state trend of the incident ion rising with the potential energy (Fig. 3). The classical over-the-barrier model suggests that the charge state of the incident ion plays an important role in the ionization excitation of the target atom and the neutralization process of the target electron captured by the incident ion.ConclusionsHighly charged ions are incident on a metal solid target surface and deposit the carried energy in the nano-space of the target surface within the femtosecond time scale, which ionizes and excites the target atoms and results in the emission of spectral lines. Some of the spectral lines are transitions between complex electronic configurations, leading to strong electric dipole forbidden transitions. There have been no experimental data reports on the 842.42 nm and 1525.03 nm spectral lines emitted by helium-like Al ions, as well as the 1251.08 nm spectral lines emitted by lithium-like Al ions, and the 989.01 nm spectral lines of Ti XVIII (i.e. Ti17+) ion de-excitation radiation since the theoretical calculation results were published in 1987. The relative intensity of the spectral lines (single ion fluorescence production) we measure increases with the growing charge state of the incident ion, and the increasing trend is generally consistent with the potential energy trend of the incident ion increasing with the charge state. This indicates that the classical over-the-barrier model holds true in the energy region of the incident ion's kinetic energy near the Bohr velocity. The research methods for elastic and inelastic scattering caused by collisions between ions and gas target atoms are different. Due to many novel phenomena generated by highly charged ions incident on solid surfaces, such as the controversy over Auger and ICD processes, the energy shift caused by multiple ionization of target atoms, and the dissipation channels of total energy and gain energy of incident ions, a large quantity of work should be done. Meanwhile, we sincerely hope that our study can provide basic data and support for related research, and propose new methods for spectral measurement.
Acta Optica Sinica
- Publication Date: Apr. 10, 2024
- Vol. 44, Issue 7, 0702001 (2024)
Stability Improvement of Optical Lattice Clocks by Reducing Collision-Induced Decoherence and Broadening Spectrum Line
Chihua Zhou, Xiaotong Lu, Feng Guo, Yebing Wang, Ting Liang, and Hong Chang
ObjectiveSystem stability and uncertainty are the two most important indicators of a clock, which represent the fluctuation of the clock output frequency in the time domain and the possible deviation between the clock output frequency and the absolute frequency, respectively. Stability improvement can reduce the measurement error of system frequency shifts and thus decrease systematic uncertainty. At present, the factors that limit the stability of an optical lattice clock mainly include quantum projection noise and Dick noise. By extending the optical probing time (τp), the effective operating rate of the clock can be improved, and the quantum projection noise and Dick noise can be reduced at the same time. However, compared with those of a case having smaller τp (such as 100 ms), the collisional frequency shifts are in the same order of magnitude as the Rabi frequency, and the loss of particles in the excited state due to inelastic scattering is enhanced when both τp and the number of atoms are large (e.g., τp=500 ms, N=6000). At the same time, the difference in Rabi frequency between the atoms in different external states and different lattice sites also rises (inhomogeneous excitation induced by atomic temperature, atomic interactions, clock laser frequency noise, and the detuning angle between the clock laser and the lattice light). All these factors make the excitation fraction of the clock transition spectrum line decrease and the linewidth widen when τp is large and eventually lead to the stability of the clock below the corresponding Dick limit.MethodsIn this paper, based on the prototype of the 87Sr one-dimensional space optical lattice clock, we experimentally observe the influence of atomic interactions on spectral linewidth and excitation fraction and even the corresponding influence on system stability. In the experiment, we measure the Rabi spectrum of clock transition at 6000 and 2000 atoms. In the measurements, the atomic temperature is kept at 3 μK (for T is constant, the number of atoms is proportional to the atomic density). The detuning angle between the clock laser and the lattice light is 13 mrad, and the optical probing time is set as 500 ms. Additionally, the stability of the optical lattice clock at two different atomic densities (for 6000 and 2000 atoms, respectively) is measured by the interleaved self-comparison method.Results and DiscussionsThe research results of the dramatic effect of atomic interactions on the Rabi spectrum (Fig. 4) are shown. The Rabi spectrum of clock transition at the high atomic density (6000 atoms) is achieved experimentally, which has a maximum excitation fraction of 0.49 and a full width at half maximum (FWHM) of 4 Hz [Fig. 4(a)]. On the contrary, the maximum excitation fraction is 0.68, and the FWHM is 1.9 Hz under the condition of the low atomic density (2000 atoms) [Fig. 4(c)]. The results clearly demonstrate that the suppression of the excitation fraction and the broadening of the spectrum are caused by atomic interactions [Fig. 4(a) and (c)], which is coincident with the theoretical expectation. Moreover, when the clock laser resonates with the clock transition, the atoms trapped in the lattice are decreased distinctly [Fig. 4(b)]. This indicates that inelastic collisions between excited particles make a part of atoms escape from the trapping of the lattice. When the total number of atoms is reduced, the atomic loss caused by inelastic collisions is nearly not observed [Fig. 4(d)] in the experimental setup. This result also conforms to the two-body interaction theory. We also present the experimental results of the self-comparison stability at high and low atomic densities (Fig. 5). The self-comparison stability under the high-density condition is 2.6×10-15 (τ/s)-0.5, while it is 1×10-15 (τ/s)-0.5 under the low-density condition. The stability of the system is improved to 2.6 times by reducing the number of atoms.ConclusionsIn summary, the suppression of the excitation fraction and the broadening of the clock transition spectrum induced by atomic interactions are observed experimentally on the prototype of the 87Sr one-dimensional space optical lattice clock, and the atomic loss due to inelastic collisions is also found. The Rabi spectra are measured experimentally in the conditions of 6000 and 2000 atoms in lattice. The excitation fraction and linewidth for the large number of atoms are 0.49 and 4 Hz, and those for the small number of atoms are 0.68 and 1.9 Hz, respectively. At the same time, the atomic loss caused by inelastic collisions is also observed when the number of atoms is large. In the experiment, by measuring self-comparison stability at different atomic densities, we confirm that reducing the number of atoms to 1/3 can improve the system stability by 1.6 times. Finally, a spectrum with a linewidth of 1.9 Hz is achieved, and the self-comparison stability of the prototype of the space optical lattice clock is improved to 1×10-15 (τ/s)-0.5. The experimental results in this paper are significant for the study of the influence of many-body interactions in optical lattices on the clock transition spectrum. The measurement results of stability show that the best stability can be obtained by optimizing the atomic density of the optical lattice atomic clock. ObjectiveSystem stability and uncertainty are the two most important indicators of a clock, which represent the fluctuation of the clock output frequency in the time domain and the possible deviation between the clock output frequency and the absolute frequency, respectively. Stability improvement can reduce the measurement error of system frequency shifts and thus decrease systematic uncertainty. At present, the factors that limit the stability of an optical lattice clock mainly include quantum projection noise and Dick noise. By extending the optical probing time (τp), the effective operating rate of the clock can be improved, and the quantum projection noise and Dick noise can be reduced at the same time. However, compared with those of a case having smaller τp (such as 100 ms), the collisional frequency shifts are in the same order of magnitude as the Rabi frequency, and the loss of particles in the excited state due to inelastic scattering is enhanced when both τp and the number of atoms are large (e.g., τp=500 ms, N=6000). At the same time, the difference in Rabi frequency between the atoms in different external states and different lattice sites also rises (inhomogeneous excitation induced by atomic temperature, atomic interactions, clock laser frequency noise, and the detuning angle between the clock laser and the lattice light). All these factors make the excitation fraction of the clock transition spectrum line decrease and the linewidth widen when τp is large and eventually lead to the stability of the clock below the corresponding Dick limit.MethodsIn this paper, based on the prototype of the 87Sr one-dimensional space optical lattice clock, we experimentally observe the influence of atomic interactions on spectral linewidth and excitation fraction and even the corresponding influence on system stability. In the experiment, we measure the Rabi spectrum of clock transition at 6000 and 2000 atoms. In the measurements, the atomic temperature is kept at 3 μK (for T is constant, the number of atoms is proportional to the atomic density). The detuning angle between the clock laser and the lattice light is 13 mrad, and the optical probing time is set as 500 ms. Additionally, the stability of the optical lattice clock at two different atomic densities (for 6000 and 2000 atoms, respectively) is measured by the interleaved self-comparison method.Results and DiscussionsThe research results of the dramatic effect of atomic interactions on the Rabi spectrum (Fig. 4) are shown. The Rabi spectrum of clock transition at the high atomic density (6000 atoms) is achieved experimentally, which has a maximum excitation fraction of 0.49 and a full width at half maximum (FWHM) of 4 Hz [Fig. 4(a)]. On the contrary, the maximum excitation fraction is 0.68, and the FWHM is 1.9 Hz under the condition of the low atomic density (2000 atoms) [Fig. 4(c)]. The results clearly demonstrate that the suppression of the excitation fraction and the broadening of the spectrum are caused by atomic interactions [Fig. 4(a) and (c)], which is coincident with the theoretical expectation. Moreover, when the clock laser resonates with the clock transition, the atoms trapped in the lattice are decreased distinctly [Fig. 4(b)]. This indicates that inelastic collisions between excited particles make a part of atoms escape from the trapping of the lattice. When the total number of atoms is reduced, the atomic loss caused by inelastic collisions is nearly not observed [Fig. 4(d)] in the experimental setup. This result also conforms to the two-body interaction theory. We also present the experimental results of the self-comparison stability at high and low atomic densities (Fig. 5). The self-comparison stability under the high-density condition is 2.6×10-15 (τ/s)-0.5, while it is 1×10-15 (τ/s)-0.5 under the low-density condition. The stability of the system is improved to 2.6 times by reducing the number of atoms.ConclusionsIn summary, the suppression of the excitation fraction and the broadening of the clock transition spectrum induced by atomic interactions are observed experimentally on the prototype of the 87Sr one-dimensional space optical lattice clock, and the atomic loss due to inelastic collisions is also found. The Rabi spectra are measured experimentally in the conditions of 6000 and 2000 atoms in lattice. The excitation fraction and linewidth for the large number of atoms are 0.49 and 4 Hz, and those for the small number of atoms are 0.68 and 1.9 Hz, respectively. At the same time, the atomic loss caused by inelastic collisions is also observed when the number of atoms is large. In the experiment, by measuring self-comparison stability at different atomic densities, we confirm that reducing the number of atoms to 1/3 can improve the system stability by 1.6 times. Finally, a spectrum with a linewidth of 1.9 Hz is achieved, and the self-comparison stability of the prototype of the space optical lattice clock is improved to 1×10-15 (τ/s)-0.5. The experimental results in this paper are significant for the study of the influence of many-body interactions in optical lattices on the clock transition spectrum. The measurement results of stability show that the best stability can be obtained by optimizing the atomic density of the optical lattice atomic clock.
Acta Optica Sinica
- Publication Date: May. 10, 2023
- Vol. 43, Issue 9, 0902001 (2023)
Linear Operation Point in Demodulating Microwave Amplitude Modulation Signals Based on Rydberg Atom System
Yuankai Jin, Ruijian Rao, Jinyun Wu, and Yinfa Zhang
Without complicated processes, in direct demodulation, it is simply to detect the variance of probe laser transmission intensity using photodetector while the Rydberg atom system is at the zero-detune. The photo-generated current is approximately the baseband signal. However, due to the nonlinear relationship between the transmissivity of the Rydberg atom cell and microwave E-field strength, the direct demodulation method will result in nonlinear distortion. The optimum linear operation point of the Rydberg atom system should be studied to decrease the distortion.As far as we know, until now, there is no theoretical analysis about the optimal linear operation point of the Rydberg atom system, and the relationship between the baseband signal amplitude and nonlinear distortion in the AM microwave demodulation. We focus on the optimal linear operation point and nonlinear distortion in the Rydberg atom system.Firstly, we analyze the AM microwave direct demodulation model of the Rydberg atom system. In this model, we explain the nonlinear relationship between probe laser transmissivity and microwave E-field strength.Secondly, we calculate the first and second derivatives of probe laser transmissivity concerning microwave Rabi frequency and analyze the relationship between the first/second derivatives and optimal linear operation point.Thirdly, we adopt total harmonic distortion (THD) to explore the relationship among the Rydberg atom cell operation point, the baseband signal amplitude, and the nonlinear distortion.When THD is introduced to describe the degree of demodulation nonlinear distortion, we find two parameters that will affect the THD value. One is the operation point of the Rydberg atom system, and the other is the Rabi frequency of the microwave baseband signal.The simulation shows that by adjusting the operation point, THD will reach a minimum value, which is consistent with the value that we obtain theoretically from the transmissivity second derivative of zero.Fig. 4(b) shows that when the system is at the optimum linear operation point, the nonlinear distortion of the system declines with the decreasing baseband signal amplitude. Meanwhile, by comparing the THD at three different coupling laser Rabi frequencies, we find that the demodulation nonlinear distortion can be reduced by increasing the coupling laser Rabi frequency.ObjectiveRydberg atom system can strongly respond to weak microwave signals on the electromagnetically induced transparency (EIT) effect and Aulter-Townes (AT) effect. Therefore, people want to utilize this system to detect and demodulate microwaves instead of the traditional mode. At present, there are two methods to demodulate amplitude modulation (AM) microwave signals using the Rydberg atom system, including indirect demodulation and direct demodulation. In the indirect method, the first step is to scan the probe or coupling laser frequency near the zero-detune point, and the second step is to measure the splitting peak-to-peak frequency separation in the probe transmission spectrum. The third step is to calculate the microwave electric field (E-field) strength because the above frequency separation is proportion to the microwave E-field strength.MethodsWe build a simplified Rydberg atom system model (Fig. 1) and numerically simulate the probe laser transmissivity in the Rydberg atom system when 133Cs (energy levels of 6S1/2, 6P3/2, 47D5/2, and 48P3/2) is chosen as Rydberg atom. Our simulation assumes the coupling laser Rabi frequencies separately are 2π×2.7 MHz, 2π×3.2 MHz, and 2π×3.7 MHz. Additionally, our simulation is kept under the frequency-zero-detune, which means probe and coupling laser frequencies are both locked to the energy transition frequency of the Rydberg atom. In these conditions, we conduct the following research.Results and DiscussionsBy mathematical analysis we obtain the optimal linear operation point of the Rydberg atom system from the second derivative of zero (Fig. 3). When the system is operating at that point, the nonlinear distortion of AM microwave demodulation is minimum.ConclusionsWe study the relationship between the nonlinear distortion and the operation point in the Rydberg atom system demodulating the AM microwave signals by the direct method. First, we analyze the demodulation model of the Rydberg atom system in the frequency-zero-detune condition. Second, we calculate the first and second derivatives of the probe laser transmissivity for the microwave Rabi frequency. Utilizing the second derivatives of zero, we find the optimal linear operation point of the Rydberg atom cell in which the nonlinear distortion is the minimum in demodulating AM microwave. Third, the THD is adopted to explore the relationship between the operation point of the Rydberg atom cell, the baseband signal amplitude, and the nonlinear distortion. The simulation shows that the THD of the demodulation system with the Rydberg atom 133Cs (energy levels of 6S1/2, 6P3/2, 47D5/2, and 48P3/2) can reach -95.4984 dB, when the Rydberg atom cell is near the optimum operation point, at 2π×2.7 MHz (coupling laser Rabi frequency) and 1 mV/m (baseband signal electrical field amplitude). Without complicated processes, in direct demodulation, it is simply to detect the variance of probe laser transmission intensity using photodetector while the Rydberg atom system is at the zero-detune. The photo-generated current is approximately the baseband signal. However, due to the nonlinear relationship between the transmissivity of the Rydberg atom cell and microwave E-field strength, the direct demodulation method will result in nonlinear distortion. The optimum linear operation point of the Rydberg atom system should be studied to decrease the distortion.As far as we know, until now, there is no theoretical analysis about the optimal linear operation point of the Rydberg atom system, and the relationship between the baseband signal amplitude and nonlinear distortion in the AM microwave demodulation. We focus on the optimal linear operation point and nonlinear distortion in the Rydberg atom system.Firstly, we analyze the AM microwave direct demodulation model of the Rydberg atom system. In this model, we explain the nonlinear relationship between probe laser transmissivity and microwave E-field strength.Secondly, we calculate the first and second derivatives of probe laser transmissivity concerning microwave Rabi frequency and analyze the relationship between the first/second derivatives and optimal linear operation point.Thirdly, we adopt total harmonic distortion (THD) to explore the relationship among the Rydberg atom cell operation point, the baseband signal amplitude, and the nonlinear distortion.When THD is introduced to describe the degree of demodulation nonlinear distortion, we find two parameters that will affect the THD value. One is the operation point of the Rydberg atom system, and the other is the Rabi frequency of the microwave baseband signal.The simulation shows that by adjusting the operation point, THD will reach a minimum value, which is consistent with the value that we obtain theoretically from the transmissivity second derivative of zero.Fig. 4(b) shows that when the system is at the optimum linear operation point, the nonlinear distortion of the system declines with the decreasing baseband signal amplitude. Meanwhile, by comparing the THD at three different coupling laser Rabi frequencies, we find that the demodulation nonlinear distortion can be reduced by increasing the coupling laser Rabi frequency.ObjectiveRydberg atom system can strongly respond to weak microwave signals on the electromagnetically induced transparency (EIT) effect and Aulter-Townes (AT) effect. Therefore, people want to utilize this system to detect and demodulate microwaves instead of the traditional mode. At present, there are two methods to demodulate amplitude modulation (AM) microwave signals using the Rydberg atom system, including indirect demodulation and direct demodulation. In the indirect method, the first step is to scan the probe or coupling laser frequency near the zero-detune point, and the second step is to measure the splitting peak-to-peak frequency separation in the probe transmission spectrum. The third step is to calculate the microwave electric field (E-field) strength because the above frequency separation is proportion to the microwave E-field strength.MethodsWe build a simplified Rydberg atom system model (Fig. 1) and numerically simulate the probe laser transmissivity in the Rydberg atom system when 133Cs (energy levels of 6S1/2, 6P3/2, 47D5/2, and 48P3/2) is chosen as Rydberg atom. Our simulation assumes the coupling laser Rabi frequencies separately are 2π×2.7 MHz, 2π×3.2 MHz, and 2π×3.7 MHz. Additionally, our simulation is kept under the frequency-zero-detune, which means probe and coupling laser frequencies are both locked to the energy transition frequency of the Rydberg atom. In these conditions, we conduct the following research.Results and DiscussionsBy mathematical analysis we obtain the optimal linear operation point of the Rydberg atom system from the second derivative of zero (Fig. 3). When the system is operating at that point, the nonlinear distortion of AM microwave demodulation is minimum.ConclusionsWe study the relationship between the nonlinear distortion and the operation point in the Rydberg atom system demodulating the AM microwave signals by the direct method. First, we analyze the demodulation model of the Rydberg atom system in the frequency-zero-detune condition. Second, we calculate the first and second derivatives of the probe laser transmissivity for the microwave Rabi frequency. Utilizing the second derivatives of zero, we find the optimal linear operation point of the Rydberg atom cell in which the nonlinear distortion is the minimum in demodulating AM microwave. Third, the THD is adopted to explore the relationship between the operation point of the Rydberg atom cell, the baseband signal amplitude, and the nonlinear distortion. The simulation shows that the THD of the demodulation system with the Rydberg atom 133Cs (energy levels of 6S1/2, 6P3/2, 47D5/2, and 48P3/2) can reach -95.4984 dB, when the Rydberg atom cell is near the optimum operation point, at 2π×2.7 MHz (coupling laser Rabi frequency) and 1 mV/m (baseband signal electrical field amplitude).
Acta Optica Sinica
- Publication Date: Nov. 25, 2023
- Vol. 43, Issue 22, 2202001 (2023)
Spin-Orbit-Coupling-Induced Modulation Instability
Yunjia Zhai, Yuanyuan Chen, and Yongping Zhang
ObjectiveModulation instability is a crucial phenomenon in the study of nonlinear dynamics, where an unstable system results in the destruction of its original states, accompanied by the rapid growth of small perturbation instabilities. The Bose-Einstein condensate serves as an ideal platform for exploring modulation instability due to its precise experimental control over the system's nonlinear dynamics. Therefore, studying modulation instabilities holds profound significance in comprehending the nature of Bose-Einstein condensate systems. In this paper, we reveal that spin-orbit coupling can always introduce modulation instability into a kind of specific state. We call it spin-orbit-coupling-induced modulation instability. The states are specific as they are zero-quasimomentum states. We find that there exist four different zero-quasimomentum states, and we classify them as no-current-carrying states and current-carrying states according to whether the states carry current or not. In literature, modulation instability of the no-current-carrying states has been investigated. The current-carrying states are unique due to their current originating from spin-orbit coupling, and their existence is unstable due to nonlinearity. We find that all these zero-quasimomentum states are modulationally unstable in all parameter regimes. The consequence of such modulation instability is the formation of complex wave structures.MethodsThe properties of modulation instability and the corresponding nonlinear dynamic images are primarily investigated using Bogoliubov de Gennes (BdG) instability analysis and the split step Fourier method. BdG instability analysis is a widely employed technique for analyzing instability in the study of superfluidity and Bose-Einstein condensates. It primarily examines the system's stability and its response to perturbations by solving nonlinear eigenvalue equations. By diagonalizing the BdG Hamiltonian matrix, the eigenvalues can be obtained. The eigenvalues of the matrix may be complex due to the non-Hermitian nature of the BdG Hamiltonian. If one or more complex numbers exist in the eigenvalues, the state becomes unstable. Consequently, any imposed disturbance experiences exponential growth, leading to the instability of the state. In addition, the split step Fourier method is commonly used for handling time evolution. The underlying principle of this method is to separate the terms of the system Hamiltonian and process them individually. The key step involves employing distinct treatments for the nonlinear and linear terms of the equation to be solved.Results and DiscussionsInitially, we investigate the case of g>g12 and observe that the system exhibits a four-band modulation instability image in Fig. 1. Among these bands, the two branches positioned near the lower quasi-momentum region are referred to as the primary modulation instability band, while the two branches near the higher quasi-momentum region are known as the secondary modulation instability band. Notably, it is determined that identical chemical potentials of the two current-carrying states yield the same modulation instability image. Furthermore, we perform calculations to ascertain the nonlinear dynamic images (Figs. 2 and 3). The investigation reveals that the density evolution of the two components follows similar ways, exhibiting trends of movement in both positive and negative directions along the x-axis. As time progresses, both components undergo chaotic oscillations. In the quasi-momentum space, distinct motion trends and reversal symmetry are observed between the two components. After a certain period of evolution, significant separation occurs. This phenomenon arises from the modulation instability being predominantly influenced by different modulation instability bands at various stages. Initially, the primary modulation instability band dominates, while in later stages, the secondary modulation instability band takes control. Ultimately, the system tends to approach the quasi-momentum space of the secondary modulation instability band, leading to chaotic propagation. Simultaneously, we also examine the scenario where g<g12 and observe that the system's modulation instability image consists of only two bands (Fig. 4): the primary modulation instability band. This disappearance of the secondary modulation instability band occurs as the repulsive interaction between the components intensifies, causing the two unstable branches to merge. Following a nonlinear dynamic analysis (Figs. 5 and 6), we observe that the motion trends become less pronounced due to the absence of the secondary modulation instability band. Nevertheless, in this case, the two components still exhibit distinct motion patterns and maintain reverse symmetry. The reason behind this phenomenon remains consistent with the previous situation. However, since there are only two branches of modulation instability, the system consistently resides near the quasi-momentum space of the main modulation instability band once the wave function enters chaotic oscillation.ConclusionsWe delve into the examination of modulation instability and its consequential dynamic patterns in one-dimensional two-component Bose-Einstein condensates with spin-orbit coupling. The study reveals the existence of four distinct zero momentum states within the system, where two of them carry currents while the remaining two do not under specific conditions. It should be noted that the generation of these four states is not solely determined by spin-orbit coupling; however, the presence of spin-orbit coupling does impact the modulation instability of the system. Previous research predominantly focuses on the zero quasi-momentum state without current carrying, neglecting the investigation of the zero quasi-momentum state with current carrying. We specifically explore the modulation instability of current-carrying zero momentum states. The findings indicate that in the presence of Rabi coupling, when the intra-component interaction surpasses the inter-component interaction, the modulation instability image manifests four branches, consisting of two main modulation instability bands and two secondary modulation instability bands. Conversely, when the intra-component interaction is lower than the inter-component interaction, the modulation instability image presents only two branches. We also establish a correlation between modulation instability and the nonlinear dynamic evolution of the system. Additionally, the presence of modulation instability can trigger the emergence of intricate patterns. ObjectiveModulation instability is a crucial phenomenon in the study of nonlinear dynamics, where an unstable system results in the destruction of its original states, accompanied by the rapid growth of small perturbation instabilities. The Bose-Einstein condensate serves as an ideal platform for exploring modulation instability due to its precise experimental control over the system's nonlinear dynamics. Therefore, studying modulation instabilities holds profound significance in comprehending the nature of Bose-Einstein condensate systems. In this paper, we reveal that spin-orbit coupling can always introduce modulation instability into a kind of specific state. We call it spin-orbit-coupling-induced modulation instability. The states are specific as they are zero-quasimomentum states. We find that there exist four different zero-quasimomentum states, and we classify them as no-current-carrying states and current-carrying states according to whether the states carry current or not. In literature, modulation instability of the no-current-carrying states has been investigated. The current-carrying states are unique due to their current originating from spin-orbit coupling, and their existence is unstable due to nonlinearity. We find that all these zero-quasimomentum states are modulationally unstable in all parameter regimes. The consequence of such modulation instability is the formation of complex wave structures.MethodsThe properties of modulation instability and the corresponding nonlinear dynamic images are primarily investigated using Bogoliubov de Gennes (BdG) instability analysis and the split step Fourier method. BdG instability analysis is a widely employed technique for analyzing instability in the study of superfluidity and Bose-Einstein condensates. It primarily examines the system's stability and its response to perturbations by solving nonlinear eigenvalue equations. By diagonalizing the BdG Hamiltonian matrix, the eigenvalues can be obtained. The eigenvalues of the matrix may be complex due to the non-Hermitian nature of the BdG Hamiltonian. If one or more complex numbers exist in the eigenvalues, the state becomes unstable. Consequently, any imposed disturbance experiences exponential growth, leading to the instability of the state. In addition, the split step Fourier method is commonly used for handling time evolution. The underlying principle of this method is to separate the terms of the system Hamiltonian and process them individually. The key step involves employing distinct treatments for the nonlinear and linear terms of the equation to be solved.Results and DiscussionsInitially, we investigate the case of g>g12 and observe that the system exhibits a four-band modulation instability image in Fig. 1. Among these bands, the two branches positioned near the lower quasi-momentum region are referred to as the primary modulation instability band, while the two branches near the higher quasi-momentum region are known as the secondary modulation instability band. Notably, it is determined that identical chemical potentials of the two current-carrying states yield the same modulation instability image. Furthermore, we perform calculations to ascertain the nonlinear dynamic images (Figs. 2 and 3). The investigation reveals that the density evolution of the two components follows similar ways, exhibiting trends of movement in both positive and negative directions along the x-axis. As time progresses, both components undergo chaotic oscillations. In the quasi-momentum space, distinct motion trends and reversal symmetry are observed between the two components. After a certain period of evolution, significant separation occurs. This phenomenon arises from the modulation instability being predominantly influenced by different modulation instability bands at various stages. Initially, the primary modulation instability band dominates, while in later stages, the secondary modulation instability band takes control. Ultimately, the system tends to approach the quasi-momentum space of the secondary modulation instability band, leading to chaotic propagation. Simultaneously, we also examine the scenario where g<g12 and observe that the system's modulation instability image consists of only two bands (Fig. 4): the primary modulation instability band. This disappearance of the secondary modulation instability band occurs as the repulsive interaction between the components intensifies, causing the two unstable branches to merge. Following a nonlinear dynamic analysis (Figs. 5 and 6), we observe that the motion trends become less pronounced due to the absence of the secondary modulation instability band. Nevertheless, in this case, the two components still exhibit distinct motion patterns and maintain reverse symmetry. The reason behind this phenomenon remains consistent with the previous situation. However, since there are only two branches of modulation instability, the system consistently resides near the quasi-momentum space of the main modulation instability band once the wave function enters chaotic oscillation.ConclusionsWe delve into the examination of modulation instability and its consequential dynamic patterns in one-dimensional two-component Bose-Einstein condensates with spin-orbit coupling. The study reveals the existence of four distinct zero momentum states within the system, where two of them carry currents while the remaining two do not under specific conditions. It should be noted that the generation of these four states is not solely determined by spin-orbit coupling; however, the presence of spin-orbit coupling does impact the modulation instability of the system. Previous research predominantly focuses on the zero quasi-momentum state without current carrying, neglecting the investigation of the zero quasi-momentum state with current carrying. We specifically explore the modulation instability of current-carrying zero momentum states. The findings indicate that in the presence of Rabi coupling, when the intra-component interaction surpasses the inter-component interaction, the modulation instability image manifests four branches, consisting of two main modulation instability bands and two secondary modulation instability bands. Conversely, when the intra-component interaction is lower than the inter-component interaction, the modulation instability image presents only two branches. We also establish a correlation between modulation instability and the nonlinear dynamic evolution of the system. Additionally, the presence of modulation instability can trigger the emergence of intricate patterns.
Acta Optica Sinica
- Publication Date: Nov. 10, 2023
- Vol. 43, Issue 21, 2102001 (2023)
Yield of Non-Sequential Double Ionization of CO2 Molecules Driven by Intense Laser Fields
Keying Liu, Lihua Bai, Zhen Guo, and Zhenjie Ge
ObjectiveThe interaction of atoms, molecules, and laser fields can generate many interesting nonlinear phenomena in the research on strong field physics. Among them, non-sequential double ionization (NSDI) has become a research hotspot. In the past, people mainly studied phenomena related to NSDI in the monochromatic laser field. With the continuous development of laser technology, a combined electric field has been applied to the study of NSDI for atoms and molecules. The electric field is composed of two circularly polarized (CP) laser fields with fixed frequency and is also called two-color CP laser field. At present, the counter-rotating two-color circularly polarized (CRTC) laser field is widely applied in research on enhancing the NSDI yield due to its special electric field structure. In recent years, studies have shown that the CRTC laser field is beneficial to increase the NSDI yield for O2. However, for triatomic molecules with more nuclei, whether the CRTC laser field can still increase the NSDI yield is an unexplored question. The dynamics of linear triatomic molecules (CO2) in the linearly polarized (LP) laser field and CP laser field have been studied, but there are few studies on the CO2 dynamics in CRTC laser fields. Therefore, we compare and analyze the NSDI yield for CO2 driven by intense laser fields, and further complement the research on the electron dynamics process in NSDI of linear triatomic molecules.MethodsThe method we adopt is based on the classical ensemble method for solving the time-dependent Newton equation. This method has been widely employed in the study of strong laser fields and atomic-molecular interactions. The NSDI electron dynamics of atomic molecules are simulated through the classical ensemble method in the following three steps. First, a stable initial ensemble is obtained. Second, the laser field components are added to the time-dependent Newton equation, and the initial ensemble is substituted to obtain the final coordinates and momentum distribution of the electrons. Third, the data with double ionization is screened. The initial ensemble is mainly obtained by the following ways. At first, the spatial positions of two electrons are given by the Gaussian random matrix, the total potential energy of two electrons is calculated, and the coordinates of the potential energy less than the total energy are filtered. Then the total kinetic energy is obtained by subtracting the total potential energy from the total energy, and the total kinetic energy is randomly assigned to the electrons to obtain their momentum and coordinates. Finally, the coordinates and momentum of two electrons are substituted into the time-dependent Newton equation without the laser field for a period of time, and then a stable initial system synthesis is obtained. The LP laser field we leverage has a wavelength of 1200 nm, the CP laser field has a wavelength of 1200 nm, and the CRTC laser field is a combination of two circularly polarized laser beams with wavelengths of 1200 nm and 600 nm.Results and DiscussionsFirst, we calculate the NSDI yield for CO2 in LP, CP, and CRTC laser fields for various laser field intensities (Fig. 1). The results show that the yield of CO2 molecules under the CRTC laser field is higher than that under the LP laser field when the laser field is higher. However, the opposite results are obtained when the laser field intensity is lower. Since the knee structure doesn't occur in the yield curve under the action of the CP laser field, it is not discussed in our paper. Then, we calculate the electron return energy diagram based on the main time distribution of the recollision (Fig. 3). The return energy diagram can help us derive the reason for the intersection of the CO2 yield curves. Second, we investigate the factors affecting the CO2 NSDI under the action of intense laser fields. By comparing the single ionization rate and double ionization rate of CO2 in the LP laser field and CRTC laser field (Fig. 4), we can conclude that the main factors affecting the CO2 NSDI are the laser intensity and laser field type. Third, we explore the electron dynamics process for CO2NSDI in the areas with lower laser intensity and higher laser intensity respectively. The results show that under lower laser intensity, the NSDI yield driven by the LP laser field is higher than that driven by the CRTC laser field because of the lower suppression barrier (Fig. 5). However, when the laser intensity is higher, the suppression barrier will be distorted and then the main factor affecting the NSDI yield is the structure of the laser field in this case. As the CRTC has a three-lobed structure (Fig. 7) which helps to increase the number of electrons undergoing recollision, the NSDI yield in the CRTC laser field is higher than that in the LP laser field.ConclusionsOur paper investigates the NSDI yield for linear triatomic molecular (CO2) driven by LP, CP, and CRTC laser fields. The results indicate that the NSDI yield in the CRTC laser field is lower than that in the LP laser field under lower laser intensity. This is because the interaction between the laser field and the molecular coulomb potential forms a suppression barrier, and the suppression potential in the CRTC laser field is higher than that in the LP laser field. As a result, the ionization of the second electron in the CRTC laser field is limited. However, when the laser intensity is higher, the yield in the CRTC laser field is higher than that in the LP laser field. This is because with the increasing laser intensity, the molecular coulomb potential is distorted, and then the molecular structure almost no longer exerts an effect on the ionization rate, which is largely influenced by the laser field structure. The CRTC laser field is characterized by a special three-lobed structure, and it can help to increase the number of returning electrons and the electron recollision possibility. Therefore, the CO2 yield is higher under the action of the CRTC laser field. We further complement the study of the NSDI electron dynamics process of linear triatomic molecules driven by intense laser fields, and our results also provide references to improve the NSDI yield of molecules in experiments. ObjectiveThe interaction of atoms, molecules, and laser fields can generate many interesting nonlinear phenomena in the research on strong field physics. Among them, non-sequential double ionization (NSDI) has become a research hotspot. In the past, people mainly studied phenomena related to NSDI in the monochromatic laser field. With the continuous development of laser technology, a combined electric field has been applied to the study of NSDI for atoms and molecules. The electric field is composed of two circularly polarized (CP) laser fields with fixed frequency and is also called two-color CP laser field. At present, the counter-rotating two-color circularly polarized (CRTC) laser field is widely applied in research on enhancing the NSDI yield due to its special electric field structure. In recent years, studies have shown that the CRTC laser field is beneficial to increase the NSDI yield for O2. However, for triatomic molecules with more nuclei, whether the CRTC laser field can still increase the NSDI yield is an unexplored question. The dynamics of linear triatomic molecules (CO2) in the linearly polarized (LP) laser field and CP laser field have been studied, but there are few studies on the CO2 dynamics in CRTC laser fields. Therefore, we compare and analyze the NSDI yield for CO2 driven by intense laser fields, and further complement the research on the electron dynamics process in NSDI of linear triatomic molecules.MethodsThe method we adopt is based on the classical ensemble method for solving the time-dependent Newton equation. This method has been widely employed in the study of strong laser fields and atomic-molecular interactions. The NSDI electron dynamics of atomic molecules are simulated through the classical ensemble method in the following three steps. First, a stable initial ensemble is obtained. Second, the laser field components are added to the time-dependent Newton equation, and the initial ensemble is substituted to obtain the final coordinates and momentum distribution of the electrons. Third, the data with double ionization is screened. The initial ensemble is mainly obtained by the following ways. At first, the spatial positions of two electrons are given by the Gaussian random matrix, the total potential energy of two electrons is calculated, and the coordinates of the potential energy less than the total energy are filtered. Then the total kinetic energy is obtained by subtracting the total potential energy from the total energy, and the total kinetic energy is randomly assigned to the electrons to obtain their momentum and coordinates. Finally, the coordinates and momentum of two electrons are substituted into the time-dependent Newton equation without the laser field for a period of time, and then a stable initial system synthesis is obtained. The LP laser field we leverage has a wavelength of 1200 nm, the CP laser field has a wavelength of 1200 nm, and the CRTC laser field is a combination of two circularly polarized laser beams with wavelengths of 1200 nm and 600 nm.Results and DiscussionsFirst, we calculate the NSDI yield for CO2 in LP, CP, and CRTC laser fields for various laser field intensities (Fig. 1). The results show that the yield of CO2 molecules under the CRTC laser field is higher than that under the LP laser field when the laser field is higher. However, the opposite results are obtained when the laser field intensity is lower. Since the knee structure doesn't occur in the yield curve under the action of the CP laser field, it is not discussed in our paper. Then, we calculate the electron return energy diagram based on the main time distribution of the recollision (Fig. 3). The return energy diagram can help us derive the reason for the intersection of the CO2 yield curves. Second, we investigate the factors affecting the CO2 NSDI under the action of intense laser fields. By comparing the single ionization rate and double ionization rate of CO2 in the LP laser field and CRTC laser field (Fig. 4), we can conclude that the main factors affecting the CO2 NSDI are the laser intensity and laser field type. Third, we explore the electron dynamics process for CO2NSDI in the areas with lower laser intensity and higher laser intensity respectively. The results show that under lower laser intensity, the NSDI yield driven by the LP laser field is higher than that driven by the CRTC laser field because of the lower suppression barrier (Fig. 5). However, when the laser intensity is higher, the suppression barrier will be distorted and then the main factor affecting the NSDI yield is the structure of the laser field in this case. As the CRTC has a three-lobed structure (Fig. 7) which helps to increase the number of electrons undergoing recollision, the NSDI yield in the CRTC laser field is higher than that in the LP laser field.ConclusionsOur paper investigates the NSDI yield for linear triatomic molecular (CO2) driven by LP, CP, and CRTC laser fields. The results indicate that the NSDI yield in the CRTC laser field is lower than that in the LP laser field under lower laser intensity. This is because the interaction between the laser field and the molecular coulomb potential forms a suppression barrier, and the suppression potential in the CRTC laser field is higher than that in the LP laser field. As a result, the ionization of the second electron in the CRTC laser field is limited. However, when the laser intensity is higher, the yield in the CRTC laser field is higher than that in the LP laser field. This is because with the increasing laser intensity, the molecular coulomb potential is distorted, and then the molecular structure almost no longer exerts an effect on the ionization rate, which is largely influenced by the laser field structure. The CRTC laser field is characterized by a special three-lobed structure, and it can help to increase the number of returning electrons and the electron recollision possibility. Therefore, the CO2 yield is higher under the action of the CRTC laser field. We further complement the study of the NSDI electron dynamics process of linear triatomic molecules driven by intense laser fields, and our results also provide references to improve the NSDI yield of molecules in experiments.
Acta Optica Sinica
- Publication Date: Oct. 25, 2023
- Vol. 43, Issue 20, 2002001 (2023)
Effect of Exchange on XUV Absorption Spectrum of Atoms
Xi Liu, Ruizhi Zhang, and Guoguo Xin
The homogeneity principle requires that the electron wave function must satisfy the condition of exchange antisymmetry. In view of its influence on the transient absorption spectrum of multi-electron system, the helium atom wave function with identical anti-symmetry is obtained by Ritz variational method. On this basis, the transient absorption spectra of attosecond extreme ultraviolet (XUV) light of helium atoms are studied theoretically by solving the three energy level model and comparing with the old model without considering electron exchange. This study breaks through the traditional single-electron transition model and focuses on the effect of electron exchange on the transient absorption spectrum of XUV light. It is found that the exchange interaction has an important influence on the physical quantities, such as the intensity of the transient absorption spectrum and the position of the absorption peak. The results can provide a reference for using transient absorption spectrum to detect the ultrafast correlation dynamics of electrons in atoms. The homogeneity principle requires that the electron wave function must satisfy the condition of exchange antisymmetry. In view of its influence on the transient absorption spectrum of multi-electron system, the helium atom wave function with identical anti-symmetry is obtained by Ritz variational method. On this basis, the transient absorption spectra of attosecond extreme ultraviolet (XUV) light of helium atoms are studied theoretically by solving the three energy level model and comparing with the old model without considering electron exchange. This study breaks through the traditional single-electron transition model and focuses on the effect of electron exchange on the transient absorption spectrum of XUV light. It is found that the exchange interaction has an important influence on the physical quantities, such as the intensity of the transient absorption spectrum and the position of the absorption peak. The results can provide a reference for using transient absorption spectrum to detect the ultrafast correlation dynamics of electrons in atoms.
Acta Optica Sinica
- Publication Date: Mar. 06, 2022
- Vol. 42, Issue 5, 0502001 (2022)
Microscopic Mechanism of Hydrogen Adsorption on Rutile Titanium Dioxide Surface and Its Optical Properties
Yajie Huo, Lei Luo, Yuanxia Yue, and Hongqiang Zhu
This paper studies the microscopic mechanisms of H2 adsorption on the rutile TiO2 (110) surface by the first-principle plane-wave ultrasoft pseudopotential method based on density functional theory. The changes in the adsorption energy, density of states, distribution of charges, and optical properties on the TiO2 surface are calculated. The experimental results indicate that the rutile TiO2 (110) surfaces doped with C, Mo, and C-Mo separately can easily adsorb H2 in the way of chemical adsorption. After doping, the impurity level formed in the forbidden band can induce the separation of photogenerated electrons and holes. This provides a "step" for electron transitions in the forbidden band and improves the optical properties of the TiO2 surface. In the visible light range of 380-780 nm, the optical performance of C-Mo co-doping,Mo doping, and C doping materials decreases in turn. The absorption coefficient and reflectance peak of the TiO2 surface doped with C-Mo are increased by about 5 times and 6 times, respectively, compared with those of the undoped one. This study deepens the understanding of the microscopic mechanism of H2 adsorption on the TiO2 surface and improves the optical properties of the material by using the doping method, which provides theoretical support for the application of TiO2 in hydrogen sensors. This paper studies the microscopic mechanisms of H2 adsorption on the rutile TiO2 (110) surface by the first-principle plane-wave ultrasoft pseudopotential method based on density functional theory. The changes in the adsorption energy, density of states, distribution of charges, and optical properties on the TiO2 surface are calculated. The experimental results indicate that the rutile TiO2 (110) surfaces doped with C, Mo, and C-Mo separately can easily adsorb H2 in the way of chemical adsorption. After doping, the impurity level formed in the forbidden band can induce the separation of photogenerated electrons and holes. This provides a "step" for electron transitions in the forbidden band and improves the optical properties of the TiO2 surface. In the visible light range of 380-780 nm, the optical performance of C-Mo co-doping,Mo doping, and C doping materials decreases in turn. The absorption coefficient and reflectance peak of the TiO2 surface doped with C-Mo are increased by about 5 times and 6 times, respectively, compared with those of the undoped one. This study deepens the understanding of the microscopic mechanism of H2 adsorption on the TiO2 surface and improves the optical properties of the material by using the doping method, which provides theoretical support for the application of TiO2 in hydrogen sensors.
Acta Optica Sinica
- Publication Date: Nov. 25, 2022
- Vol. 42, Issue 22, 2202001 (2022)
Nonsequential Double Ionization of Molecules in Counter-Rotating Two-Color Circularly Polarized Laser Fields
Zhen Guo, Lihua Bai, Keying Liu, and Yanwen Shen
Nonsequential double ionization (NSDI) of N2 molecules in counter-rotating two-color circularly polarized few-cycle laser fields is investigated by the classical ensemble method. The results show that for the determined laser intensity, the yield of NSDI decreases significantly with the increasing laser wavelength, which is caused by the diffusion effects of electron wave packets. It is also found that the ionization mechanism of NSDI is affected by the laser wavelength. Collision excitation ionization becomes increasingly dominant with the rising laser wavelength, which is related to the return trajectory and return energy of the first electron. At the same time, the electron momentum distribution of NSDI is discussed in this paper. The electron momentum distribution varies significantly with the laser wavelength, and the longer laser wavelength leads to clearer "rotating three-lobed fan-like" structures. Nonsequential double ionization (NSDI) of N2 molecules in counter-rotating two-color circularly polarized few-cycle laser fields is investigated by the classical ensemble method. The results show that for the determined laser intensity, the yield of NSDI decreases significantly with the increasing laser wavelength, which is caused by the diffusion effects of electron wave packets. It is also found that the ionization mechanism of NSDI is affected by the laser wavelength. Collision excitation ionization becomes increasingly dominant with the rising laser wavelength, which is related to the return trajectory and return energy of the first electron. At the same time, the electron momentum distribution of NSDI is discussed in this paper. The electron momentum distribution varies significantly with the laser wavelength, and the longer laser wavelength leads to clearer "rotating three-lobed fan-like" structures.
Acta Optica Sinica
- Publication Date: Nov. 10, 2022
- Vol. 42, Issue 21, 2102002 (2022)
Coulomb Shifts in Spiderlike Photoelectron Momentum Distributions by Analytically-Coulomb-Corrected Semiclassical Rescattering Model
Guoyue Fu, Guizhong Zhang, Shenghua Zhang, Wei Shi, and Jianquan Yao
This paper presents numerical results on the spiderlike photoelectron momentum distributions (PMDs) induced by the ionization of hydrogen atoms by an intense laser pulse. In addition, although the standard semiclassical rescattering model (SRM) has simplified actions of electrons, it fails to take complex Coulomb interaction into account. Different from existing numerical correction, this paper carries out an analytical approximate treatment of Coulomb interaction during the ionization, introduces it into SRM, and successfully constructs an analytically-Coulomb-corrected SRM (AC-SRM). Based on AC-SRM, the systematic shifts of interference patterns caused by spiderlike PMDs and Coulomb interaction are simulated and calculated. Furthermore, through the classical phase, time-dependent Schr?dinger equation (TDSE), electron orbit, and other methods, this paper quantitatively analyzes the shifts and explores the corresponding mechanism. The results show that the proposed classical phase method is the most sensitive to the Coulomb interaction in the spiderlike PMDs, especially to the first interference minima, and the accurate TDSE values verify the correctness of simulated results obtained by AC-SRM. This paper presents numerical results on the spiderlike photoelectron momentum distributions (PMDs) induced by the ionization of hydrogen atoms by an intense laser pulse. In addition, although the standard semiclassical rescattering model (SRM) has simplified actions of electrons, it fails to take complex Coulomb interaction into account. Different from existing numerical correction, this paper carries out an analytical approximate treatment of Coulomb interaction during the ionization, introduces it into SRM, and successfully constructs an analytically-Coulomb-corrected SRM (AC-SRM). Based on AC-SRM, the systematic shifts of interference patterns caused by spiderlike PMDs and Coulomb interaction are simulated and calculated. Furthermore, through the classical phase, time-dependent Schr?dinger equation (TDSE), electron orbit, and other methods, this paper quantitatively analyzes the shifts and explores the corresponding mechanism. The results show that the proposed classical phase method is the most sensitive to the Coulomb interaction in the spiderlike PMDs, especially to the first interference minima, and the accurate TDSE values verify the correctness of simulated results obtained by AC-SRM.
Acta Optica Sinica
- Publication Date: Nov. 10, 2022
- Vol. 42, Issue 21, 2102001 (2022)
Wavelength-Dependent Non-Sequential Double Ionization of Diatomic Molecules N2 and O2 in Intense Femtosecond Laser Fields
Zhiyang Lin, and You Chen
Experiments are conducted to systematically study the single ionization and non-sequential double ionization (NSDI) of rare gas atoms (Xe and Ar) and diatomic molecules (O2 and N2 with different symmetry of molecular structure) in near-infrared intense femtosecond fields with various wavelengths of 800 nm, 1250 nm, and 1500 nm. It is found that,compared with Xe, Ar, and N2, O2 has a higher yield of NSDI as the slope of the flat region in the changing curve of light intensity increases. The wavelength scaling of the yield of NSDI in the flat region for all gases deviates from the prediction of the semiclassical "three-step" model of ionization. Furthermore, we find that the yield of NSDI of O2 is significantly suppressed compared with that of its companion atom Xe in all wavelengths, and the suppression becomes more pronounced as the wavelength increases. For the yield of NSDI of N2, however, it is almost the same as that of its companion atom Ar at a short wavelength of 800 nm, but it is also suppressed at long wavelengths. These experimental findings can be used to improve the wavelength scaling of molecular NSDI and identify the influence of molecular structure on NSDI of molecules, which indicates that the ultrafast control of molecular NSDI involving multi-electron correlation effects can be achieved by macroscopically tuning the wavelength. Experiments are conducted to systematically study the single ionization and non-sequential double ionization (NSDI) of rare gas atoms (Xe and Ar) and diatomic molecules (O2 and N2 with different symmetry of molecular structure) in near-infrared intense femtosecond fields with various wavelengths of 800 nm, 1250 nm, and 1500 nm. It is found that,compared with Xe, Ar, and N2, O2 has a higher yield of NSDI as the slope of the flat region in the changing curve of light intensity increases. The wavelength scaling of the yield of NSDI in the flat region for all gases deviates from the prediction of the semiclassical "three-step" model of ionization. Furthermore, we find that the yield of NSDI of O2 is significantly suppressed compared with that of its companion atom Xe in all wavelengths, and the suppression becomes more pronounced as the wavelength increases. For the yield of NSDI of N2, however, it is almost the same as that of its companion atom Ar at a short wavelength of 800 nm, but it is also suppressed at long wavelengths. These experimental findings can be used to improve the wavelength scaling of molecular NSDI and identify the influence of molecular structure on NSDI of molecules, which indicates that the ultrafast control of molecular NSDI involving multi-electron correlation effects can be achieved by macroscopically tuning the wavelength.
Acta Optica Sinica
- Publication Date: Jul. 10, 2022
- Vol. 42, Issue 13, 1302001 (2022)
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