A method for detecting intramolecular electron transfer motion based on optoelectronic holographic interference

Abstract

The present application relates to attosecond strong field physics technical field, especially point to a kind of method based on photoelectron holographic interferometry detection intramolecular electron migration movement, including using mid-infrared or near-infrared femtosecond laser ionizes ground state electron wave packet in molecule, obtains first electron momentum distribution;Using far ultraviolet femtosecond laser acts on molecule ground state, obtains the superposition of ground state and excited state electron wave packet, using mid-infrared or near-infrared femtosecond laser ionizes intramolecular superposition state electron wave packet, obtains second electron momentum distribution;Obtain the momentum deviation of holographic interference in the first and second electron momentum distribution of both;Obtain the change of electron wave packet most probable density distribution with time at the exit of molecular tunneling ionization, and the proportion of excited state in superposition state electron wave packet.The present application realizes the detection of intramolecular electron migration movement, and the detection method is more efficient and direct, the result obtained is more accurate, the feasibility and applicability are stronger, and has practical value in the detection of ultrafast electron dynamics process.

Description

Technical Field

[0001] This invention relates to the field of attosecond strong field physics, and in particular to a method for detecting intramolecular electron migration based on photoelectron holographic interferometry. Background Technology

[0002] Detecting attosecond-scale electron motion within atoms and molecules using ultrafast, high-intensity laser fields is a hot topic in attosecond science. When a strong laser field interacts with atoms and molecules in matter, the atoms and molecules are ionized or excited by the laser field. The atomic and molecular systems that were originally in equilibrium generate superposition states of electron wave packets with evolution time periods ranging from a few femtoseconds to hundreds of attoseconds, a phenomenon known as "charge migration."

[0003] In 2011, Huisman et al. pointed out that under the influence of a strong laser field, atoms and molecules tunnel ionize, generating direct and scattered electron wave packets. The direct electron wave packet accelerates and oscillates in the laser field before reaching the detector, while the scattered electron wave packet returns to the parent ion under the influence of the laser field, collides and scatters with the parent nucleus, and then reaches the detector again. These two types of electron wave packets coherently superimpose on the detector, ultimately forming a photoelectron holographic interference, the principle of which is very similar to holographic interference in optics. Furthermore, this study indicated that photoelectron holographic interference technology holds promise for obtaining ultrafast dynamics information about atomic and molecular structures and their internal electrons. This result was published in *Science*, and subsequently, many researchers have focused on photoelectron holographic interference technology. How to use strong-field photoelectron holographic interference technology to detect the migration of ultrafast electrons within molecules has attracted widespread attention.

[0004] Recently, research based on strong-field photoelectron holographic interferometry has proposed that the evolution of superposition-state electron wave packets can be observed by analyzing the phase of holographic interference in the electron momentum distribution. However, in practical applications, the detection steps of this method are complex, and the holographic interference fringes far from the laser field polarization axis in the photoelectron momentum spectrum are unclear. Furthermore, the blanket-like interference in the momentum spectrum makes it difficult to extract the holographic interference phase in this region, resulting in less than ideal observation results. Therefore, how to accurately detect the motion of superposition-state electron wave packets using a simple and feasible method is an urgent problem to be solved. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the problems of complex steps and inaccurate observation results in the existing methods for observing the evolution process of superposition state electron wave packets based on strong field photoelectron holographic interferometry.

[0006] To address the aforementioned technical problems, this invention provides a method for detecting intramolecular electron migration motion based on photoelectron holographic interferometry, the specific steps of which include:

[0007] S1. Use mid-infrared or near-infrared femtosecond lasers to ionize the ground-state electron wave packet in molecules, making the laser field polarization direction ninety degrees with the molecular axis to obtain the first electron momentum distribution.

[0008] S2. Excite the ground-state molecule with a femtosecond laser in the ultraviolet band to obtain an electron wave packet that is superimposed on the ground state and the excited state. Then, use the mid-infrared or near-infrared femtosecond laser to ionize the superimposed electron wave packet in the molecule again, so that the polarization direction of the laser field is at ninety degrees to the molecular axis, and obtain the second electron momentum distribution.

[0009] S3. Analyze the measured momentum distributions of the first and second electrons, and extract the momentum shift of the holographic interference in the second electron momentum distribution relative to the holographic interference in the first electron momentum distribution.

[0010] S4. Based on the momentum shift, obtain the change of the most probable density distribution of the electron wave packet at the molecular tunneling ionization exit with time, and the proportion of excited states in the superposition state electron wave packet.

[0011] In one embodiment of the present invention, in step S3, the first and second electron momentum distributions obtained by analysis and measurement are used to extract the momentum shift of the holographic interference in the second electron momentum distribution relative to the holographic interference in the first electron momentum distribution. The specific steps include:

[0012] The first holographic interference fringes are obtained based on the first electron momentum distribution, and the second holographic interference fringes are obtained based on the second photoelectron momentum spectrum.

[0013] The momentum of each order of interference fringes is retrieved in the first holographic interference and the second holographic interference, respectively;

[0014] The momentum shift of each level of interference in the second holographic interference is obtained by subtracting the momentum of each level of interference in the first holographic interference from the momentum of each level of interference in the second electron momentum distribution.

[0015] In one embodiment of the present invention, obtaining a first holographic interference fringe based on the first electron momentum distribution and obtaining a second holographic interference fringe based on the second photoelectron momentum spectrum includes:

[0016] Within the target region of the first electron momentum distribution, the final momentum in the laser field polarization direction is retrieved as... The electron production at the point is used to obtain the first transverse momentum distribution; Gaussian function fitting is performed on the first transverse momentum distribution, and the first transverse momentum distribution is divided by the Gaussian function to obtain the first holographic interference fringe; and the second holographic interference fringe is obtained in the same way.

[0017] In one embodiment of the present invention, the final momentum in the laser field polarization direction is retrieved within the target region of the first electron momentum distribution. The method for electron production at the location is as follows: the target region of the first electron momentum distribution is uniformly cut several times, and each segment is extracted along the laser field polarization direction. The electron production at the location; in the same way, within the target region of the second electron momentum distribution, the final momentum in the laser field polarization direction is retrieved. Electron production at the location.

[0018] In one embodiment of the present invention, the expression for the first transverse momentum distribution is: in Let $\mathbf{a}$ be the amplitude of the first transverse momentum distribution, $\mathbf{a}$ be the first holographic interference, and $\mathbf{a}$ be the phase of the first holographic interference. The expression is:

[0019] The expression for the second transverse momentum distribution is as follows: in Let $\mathbf{a}$ be the amplitude of the second transverse momentum distribution, $\mathbf{b}$ be the second holographic interference, and $\mathbf{b}$ be the phase of the second holographic interference. The expression is:

[0020] in, and These are the transverse momentum of the first electron and the transverse momentum of the second electron, respectively, t r t0 is the instantaneous moment when electrons scatter with the parent ion, t0 is the instantaneous moment when electrons are at the tunnel exit, and α is the scattering amplitude and phase of the parent ion. The intermediate momentum of the scattered electrons generated by the tunneling ionization of the ground-state electron wave packet. It represents the intermediate momentum of scattered electrons generated by the tunneling ionization of the superposition state electron wave packet.

[0021] In one embodiment of the present invention, the step of retrieving the momentum of each order of interference fringes in the first holographic interference and the second holographic interference respectively includes:

[0022] Setting the midpoint of the first holographic interference as the origin, and counting from either the left or right, the nth... 1 The transverse momentum of the electron at the nth maximum value is... 1 Maximum momentum of polar interference, m-th moment of the first holographic interference 1 The transverse momentum of the electron at each minimum value is the m-th minimum value. 1 Extreme interference minimum momentum;

[0023] The first holographic interference fringes and electron transverse momentum The relationship is in

[0024] Similarly, setting the midpoint of the second holographic interference as the origin, and counting from either the left or right, the nth digit of the second holographic interference... 2 At the nth maximum, the transverse momentum of the electron is... 2 Maximum momentum of polar interference, m-th moment of the second holographic interference 2 At each minimum value, the transverse momentum of the electron is at the m-th minimum. 2 Extreme interference minimum momentum;

[0025] The second holographic interference fringes and electron transverse momentum The relationship is in

[0026] In one embodiment of the present invention, in S2, the expression for the superposition state electron wave packet is:

[0027]

[0028] Where |Ψ1(t)> and |Ψ2(r)> represent the ground state and excited state of the electron wave packet, respectively, c1 and c2 are their expansion coefficients, E1 and E2 are their electronic state energies, and θ0 is the initial relative phase of the ground state and excited state of the electron wave packet.

[0029] In one embodiment of the present invention, the momentum shift of the holographic interference in the second electron momentum distribution relative to the holographic interference in the first electron momentum distribution is: Since ground-state electron wave packet tunneling ionization always exists, get

[0030] In one embodiment of the present invention, obtaining the change of the most probable density distribution of the electron wave packet at the molecular tunneling ionization exit over time based on the momentum shift includes:

[0031] The most probable spatial location of the electron wave packet density distribution at the molecular tunneling ionization exit point y0(t) and Δp y The relationship is The most probable density distribution of the electron wave packet at the molecular tunneling ionization exit point is obtained as y0(t)=Δp over time. y / (tr - t0).

[0032] In one embodiment of the present invention, the change y0(t) of the most probable density distribution of the electron wave packet at the molecular tunneling ionization exit with time is analyzed, the extreme value of the change is found, and the proportion of excited states in the superposition electron wave packet is determined by comparing this value with the dependence of the most probable density distribution on the proportion of excited states in the superposition state.

[0033] The technical solution of the present invention has the following advantages over the prior art:

[0034] The present invention discloses a method for detecting intramolecular electron migration motion based on photoelectron holographic interferometry. By analyzing the offset of each level of holographic interference obtained by ionizing the superposition state electron wave packet of a linearly polarized laser field relative to the level of holographic interference obtained by ionizing the ground state electron wave packet of a laser field, the method achieves attosecond time-resolved detection of intramolecular electron migration motion and detection of the proportion of excited states in the superposition state of electron wave packets. The detection method is simpler and the detection results are more accurate.

[0035] The present invention discloses a method for detecting intramolecular electron migration based on photoelectron holographic interferometry. The calculated offsets of interference fringes at all levels are identical, therefore the detection of electron migration is independent of the order of the interference fringes, demonstrating the stability of this invention. Compared to existing methods that directly analyze the phase of holographic interference in the electron momentum distribution to detect the evolution of superposition-state electron wave packets, this invention utilizes ground-state electron wave packets ionized by a laser field. Even when holographic interference fringes far from the laser field polarization axis in the photoelectron momentum spectrum are unclear, the evolution of superposition-state electron wave packets can still be detected, thus exhibiting greater feasibility and universality. Attached Figure Description

[0036] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein...

[0037] Figure 1 This is a flowchart of a method for detecting intramolecular electron migration based on photoelectron holographic interferometry according to the present invention;

[0038] Figure 2 These are the laser field and the first and second electron momentum distributions used in the embodiments of the present invention;

[0039] Figure 2 In this embodiment, (a) is the few-period linearly polarized laser field used in the present invention.

[0040] Figure 2 (b) in the diagram is a schematic diagram illustrating the formation principle of molecular tunneling ionization photoelectron holographic interference;

[0041] Figure 2(c) in the figure is the momentum distribution diagram of molecular tunneling ionization photoelectron holographic interference provided in the embodiment of the present invention;

[0042] Figure 2 (d) in the figure is the first electron momentum distribution diagram provided in Embodiments 1, 2 and 3 of the present invention;

[0043] Figure 2 (e) in the figure is the second electron momentum distribution diagram provided in Embodiment 1 and Embodiment 3 of the present invention;

[0044] Figure 3 These are the first and second holographic interferences extracted in the embodiments of the present invention;

[0045] Figure 3 In Example (a), the electron momentum p extracted from the photoelectric momentum distribution in Embodiment 1 of this invention is... x Electron transverse momentum distribution at -1 atomic unit;

[0046] Figure 3 In (b), the electron momentum p extracted from the photoelectric momentum distribution in Embodiment 1 of the present invention is... x Transverse momentum distribution at -1.4 atomic units;

[0047] Figure 3 (c) in the figure represents the holographic interference extracted from the second electron momentum distribution provided in Embodiments 1 and 3 of the present invention;

[0048] Figure 3 In the figure (d), the holographic interference extracted from the second electron momentum distribution provided in Embodiment 2 of the present invention is shown.

[0049] Figure 4 This refers to the extraction process of momentum shift and the detection process of intramolecular electron migration in the embodiments of the present invention.

[0050] Figure 4 In this context, (a) represents the lateral offset Δp provided in Embodiments 1 and 3 of the present invention. y The relationship between momentum and the direction of laser polarization;

[0051] Figure 4 (b) in the figure is the lateral offset Δp provided in Embodiment 2 of the present invention. y The relationship between momentum and the direction of laser polarization;

[0052] Figure 4 (c) is a graph showing the evolution of the most probable density distribution of electron wave packets at the molecular tunneling ionization exit point over time, provided in an embodiment of the present invention.

[0053] Figure 4In the figure (d), the electron wave packet density distribution diagram of the electron wave function at 1.25 times the laser period provided in the embodiment of the present invention is shown.

[0054] Figure 4 (e) in the figure is the density distribution of electron wave packets at 1.45 times the laser period provided in Embodiment 1 of the present invention;

[0055] Figure 5 This is the detection process of the proportion of excited states in the superposition state of electron wave packets in the embodiments of the present invention;

[0056] Figure 5 (a) is a graph showing the change of the spatial position extreme value corresponding to the most probable density distribution at different spatial positions perpendicular to the laser field oscillation direction as a function of the proportion of excited states in the superposition state of the electron wave packet, provided in Embodiment 1 of the present invention.

[0057] Figure 5 (b) is a graph provided in Embodiment 1 of the present invention showing the change of the spatial position extremum corresponding to the most probable density distribution of the electron wave packet at the tunnel exit x0 = 16a.u. with the proportion of excited states in the superposition state of the electron wave packet. Detailed Implementation

[0058] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention. The terms "first" and "second" are used only to distinguish different objects and are not intended to indicate or imply numbers or order.

[0059] When an ultrafast and ultra-intense laser field interacts with matter, the atoms and molecules in the matter undergo tunneling ionization. The released electrons accelerate in the laser field, and some electrons can return and collide with the parent ion for scattering. This scattered electron wave packet coherently superimposes with the direct electron wave packet that did not interact with the parent ion in the photoelectron momentum spectrum, producing strong-field photoelectron holographic interference.

[0060] This invention provides a method for detecting intramolecular electron migration based on photoelectron holographic interferometry, referring to... Figure 1 As shown, the specific steps include:

[0061] S1. High-intensity mid-infrared or near-infrared femtosecond lasers are used to ionize the ground-state electron wave packet in molecules, making the laser field polarization direction ninety degrees with the molecular axis, to obtain the first electron momentum distribution.

[0062] In embodiments of the present invention, the laser field is selected as a near-infrared or mid-infrared laser field with an intensity range of 5.0 × 10⁻⁶. 13 W / cm 2 Up to 5.0×10 14 W / cm 2Molecules are arranged in a cold-target recoil particle momentum imaging spectrometer or particle velocity imager. A polarizer is then used to align the laser beam polarization direction with the molecular axis at a 90-degree angle, and the beam is applied to the molecule. During molecule ionization, electrons escape the binding force of the parent nucleus through tunneling ionization. The momentum distribution of these electrons can be measured using an electron detector. This first electron momentum distribution is a two-dimensional electron momentum distribution.

[0063] S2. Excite the ground-state molecule with a femtosecond laser in the ultraviolet band to obtain an electron wave packet that is superimposed on the ground state and the excited state. Then, use the mid-infrared or near-infrared femtosecond laser to ionize the superimposed electron wave packet within the molecule again, so that the polarization direction of the laser field is at a 90-degree angle to the molecular axis, and obtain a second electron momentum distribution.

[0064] The expression for the superposition state electron wave packet is:

[0065]

[0066] Where |Ψ1(r)> and |Ψ2(r)> represent the ground state and excited state of the electron wave packet, respectively, c1 and c2 are their expansion coefficients, E1 and E2 are their electronic state energies, and θ0 is the initial relative phase of the ground state and excited state of the electron wave packet.

[0067] S3. Analyze the measured momentum distributions of the first and second electrons, and extract the momentum shift of the holographic interference in the second electron momentum distribution relative to the holographic interference in the first electron momentum distribution. Specific steps include:

[0068] S310. The first holographic interference fringe is obtained based on the first electron momentum distribution, and the second holographic interference fringe is obtained based on the second photoelectron momentum spectrum.

[0069] S311. Within the target region of the first electron momentum distribution, the final momentum in the laser field polarization direction is retrieved. The electron production at the location is used to obtain the first transverse momentum distribution; the final momentum in the laser field polarization direction is uniformly searched within the target region of the second electron momentum distribution. The electron production is used to obtain the second transverse momentum distribution.

[0070] The method for retrieving electron production is as follows: the target region of the first electron momentum distribution is uniformly cut several times, and each segment is extracted along the laser field polarization direction. The electron production at the point is used to obtain the first transverse momentum distribution; similarly, the target region of the second electron momentum distribution is uniformly cut several times, and each segment is extracted along the laser field polarization direction. The electron production at that location yields the second transverse momentum distribution.

[0071] In an embodiment of the present invention, the target region is px =1.3 atomic units to -0.35 atomic units; within this target range, a complete and clear holographic interference can be obtained from the photoelectron momentum spectrum. The target regions of the first and second electron momentum distributions are both uniformly cut 1024 times.

[0072] The first expression for the transverse momentum distribution is: in Let $\mathbf{a}$ be the amplitude of the first transverse momentum distribution, $\mathbf{a}$ be the first holographic interference, and $\mathbf{a}$ be the phase of the first holographic interference. The expression is:

[0073] The expression for the second transverse momentum distribution is as follows: in Let $\mathbf{a}$ be the amplitude of the second transverse momentum distribution, $\mathbf{b}$ be the second holographic interference, and $\mathbf{b}$ be the phase of the second holographic interference. The expression is:

[0074] in, and These are the transverse momentum of the first electron and the transverse momentum of the second electron, respectively, t r t0 is the instantaneous moment when electrons scatter with the parent ion, t0 is the instantaneous moment when electrons are at the tunnel exit, and α is the scattering amplitude and phase of the parent ion. The intermediate momentum of the scattered electrons generated by the tunneling ionization of the ground-state electron wave packet. It represents the intermediate momentum of scattered electrons generated by the tunneling ionization of the superposition state electron wave packet.

[0075] S312. Perform Gaussian function fitting on the first transverse momentum distribution, and divide the first transverse momentum distribution by the Gaussian function to obtain the first holographic interference fringes; similarly, perform Gaussian function fitting on the second transverse momentum distribution, and divide the second transverse momentum distribution by the Gaussian function to obtain the second holographic interference fringes.

[0076] S320. Retrieve the momentum of each level of interference fringes in the first holographic interference and the second holographic interference, respectively.

[0077] S321. Set the midpoint of the first holographic interference as the origin, and count from either the left or the right, the nth... 1 The transverse momentum of the electron at the nth maximum value is... 1 Maximum momentum of polar interference, m-th moment of the first holographic interference 1 The transverse momentum of the electron at each minimum value is the m-th minimum value. 1 Extreme interference minimal momentum.

[0078] Similarly, setting the midpoint of the second holographic interference as the origin, and counting from either the left or right, the nth digit of the second holographic interference...2 At the nth maximum, the transverse momentum of the electron is... 2 Maximum momentum of polar interference, m-th moment of the second holographic interference 2 At each minimum value, the transverse momentum of the electron is at the m-th minimum. 2 Extreme interference minimal momentum.

[0079] S322. Establish the first holographic interference fringes and electron transverse momentum. The relationship is in

[0080] Establish the second holographic interference fringes at various levels and the electron transverse momentum The relationship is in

[0081] S330. Subtract the momentum of each level of interference fringes of the second holographic interference from the momentum of each level of interference fringes of the first holographic interference to obtain the momentum shift of each level of interference in the second electron momentum distribution relative to each level of interference in the first electron momentum distribution.

[0082] The momentum shift is

[0083] Reference Figure 2 (c) and Figure 2 As shown in (d), existing research results have demonstrated that, due to the persistent tunneling ionization of the ground-state electron wave packet, the momenta position of the interference center obtained by the linearly polarized laser field ionizing the ground-state electron wave packet for the first photoelectron holographic interference is... It is always 0. Therefore, when n = 0 and α = 0, there exists Therefore there is And thus obtain

[0084] S4. Based on the momentum shift, obtain the change of the most probable density distribution of the electron wave packet at the molecular tunneling ionization exit with time, and the proportion of excited states in the superposition state electron wave packet.

[0085] S410. Establish the spatial location y0(t) of the most probable electron wave packet density distribution at the molecular tunneling ionization exit and Δp. y Relationship: Combination The most probable density distribution of the electron wave packet at the molecular tunneling ionization exit can be obtained as y0(t)=Δp over time. y / (t r -t0).

[0086] S420. Analyze the change y0(t) of the most probable density distribution of the electron wave packet at the molecular tunneling ionization exit with time, find the extreme value of the change, and determine the proportion of excited states in the superposition electron wave packet by comparing this value with the dependence of the most probable density distribution on the proportion of excited states in the superposition state.

[0087] The present invention discloses a method for detecting intramolecular electron migration motion based on photoelectron holographic interferometry. By analyzing the offset of each level of holographic interference obtained by ionizing the superposition state electron wave packet of a linearly polarized laser field relative to the level of holographic interference obtained by ionizing the ground state electron wave packet of a laser field, the method achieves attosecond time-resolved detection of intramolecular electron migration motion and detection of the proportion of excited states in the superposition state of electron wave packets. The detection method is also simpler.

[0088] Example 1

[0089] Strong-field photoelectron momentum spectra were obtained from the ground-state and superposition-state electron wave packets of hydrogen molecular ions ionized by a few-period linearly polarized laser field. The initial relative phase of the superposition state was θ0 = 0, and the proportion of excited states in the superposition state was 0.2. The laser field wavelength was 1000 nm, and the intensity was 2.5 × 10⁻⁶. 14 W / cm 2 By analyzing the momentum shift of the zero-order maxima of holographic interference fringes in the photoelectron momentum spectrum, attosecond-resolved detection of intramolecular electron migration and the proportion of excited states in the superposition of electron wave packets can be achieved.

[0090] Figure 2 This is the strong field photoelectron momentum distribution obtained when the laser field polarization direction is at a 90-degree angle to the hydrogen molecule axis in this embodiment. Figure 2 In Figure (a), the laser field is a few-period linearly polarized laser field. The solid black line represents the electric field of the laser pulse, and the dashed line represents the vector potential of the laser pulse. The horizontal axis represents the motion time of the electron wave packet, and the vertical axis represents the values ​​of the laser electric field and vector potential at the instant of molecular ionization. The gray box in the figure represents the ionization window, and the scattered electrons and direct electron wave packets (two arrows) are generated by the ionization window. Figure 2 (b) in the diagram illustrates the formation principle of intramolecular photoelectron holographic interference. Under the influence of a few-period laser field, electrons break free from the parent ion, generating an electron wave packet. Accelerated by the laser field, some electrons in this wave packet return to the parent ion, collide with the molecular center, and then reach the detector, as shown in Figure 1. Figure 2 The solid line with an arrow in (c) shows this. Another portion of the electron wave packet reaches the detector directly without interacting with the parent nucleus, such as... Figure 2 As shown by the dashed line with an arrow in (c) of the diagram. These two electron wave packets coherently superimpose on the detector, forming a holographic interference. Figure 2 In (c), the polarization direction of the laser field is at ninety degrees to the molecular axis. Figure 2In the figure, (d) represents the strong field photoelectron momentum distribution obtained by the ground state electron wave packet of hydrogen molecular ions ionized by a few-period linearly polarized laser field. Figure 2 In the figure (e), the strong field photoelectron momentum distribution is obtained by the superposition state electron wave packet of hydrogen molecular ions ionized by a few-period linear polarized laser field. The white dashed line represents the zero-order maximum fringe momentum of the holographic interference.

[0091] from Figure 2 (d) and Figure 2 In (e), a forked holographic interference structure can be observed in the photoelectron momentum distribution, and it is clear and stable within a momentum region ranging from -1.3 to -0.35 atomic units in the laser oscillation direction. Therefore, in Figure 2 (d) and Figure 2 The momentum is uniformly selected within the momentum region in (e) and for each value, a photoelectron momentum distribution perpendicular to the laser field polarization direction is obtained, i.e., the transverse momentum distribution.

[0092] Figure 3 From Figure 2 Holographic interference extracted from it. Figure 3 In the figure, (a) represents the electron momentum extracted from the photoelectric momentum distribution, which is p. x The transverse momentum distribution of electrons at a position of -1 atomic unit is shown in the figure. The solid and dashed lines in the figure represent the results of the ground state electron wave packet and the superposition state electron wave packet, respectively. Figure 3 (b) represents the electron momentum p extracted from the photoelectric momentum distribution. x = -1.4 atomic units, transverse momentum distribution. The solid and dashed lines in the figure represent the results of the ground state electron wave packet and the superposition state electron wave packet, respectively.

[0093] Gaussian function fitting is performed on the photoelectron momentum distribution to eliminate the amplitude of the electron momentum distribution and obtain the holographic interference cos(ΔΦ). Figure 3 (c) in the middle is from Figure 2 Holographic interference extracted from the momentum distribution shown in (e); from Figure 3 As can be seen in (c), for the superposition wave packet, the initial relative phase is θ0 = 0, the proportion of excited states in the superposition is 0.2, and the zero-order maxima of the holographic interference will be relative to the laser field oscillation axis p. x =0 to p y The negative direction offset, the magnitude of the offset is related to p x The value is related. Since the offset of the zero-order maxima of the strong-field photoelectron interference obtained by ionizing the ground-state electron wave packet of molecules by a few-period linearly polarized laser field is 0, the final momentum of the photoelectrons perpendicular to the laser polarization direction corresponding to the maximum value of the holographic interference is the offset Δp of the zero-order maxima of the holographic interference. y .

[0094] Figure 4This is the evolution of the most probable density distribution of electron wave packets at the molecular tunneling ionization exit point over time in this embodiment. Figure 4 The black circle in (a) is from Figure 3 The zero-order maxima offset Δp extracted from the holographic interferometry shown in (c) is an example. y According to the formula Δp y =y0(t) / (t) r -t0), through analysis of Δp y The evolution of the most probable density distribution of the electron wave packet over time, y0(t), can be calculated, and the results are as follows: Figure 4 The gray circle in (c) is shown. Figure 4 In the figure (c), the evolution of the most probable density distribution of electron wave packets at the molecular tunneling ionization exit over time is shown. The horizontal axis represents the evolution time, the vertical axis represents the spatial position perpendicular to the laser oscillation direction, and the black dashed line represents the spatial position perpendicular to the laser field oscillation direction corresponding to the maximum value of the electron wave packet density distribution. Figure 4 (d) and Figure 4 Figure (e) shows the electron wave packet density distribution at 1.25 and 1.45 times the laser period, respectively. As can be seen from the figure, the electron wave packet density distribution changes over time, and the spatial location corresponding to the most probable density distribution of the electron wave packet shifts, i.e., "electron migration".

[0095] The results obtained by the method of the present invention are as follows Figure 4 As shown by the gray circle in (c), the evolution of the most probable electron wave packet density distribution at the molecular tunneling ionization exit over time in real-world conditions is as follows: Figure 4 As shown by the black dashed line in (c) of the diagram. From Figure 4 As can be seen in (c), the results obtained by the method of the present invention are consistent with the evolution of the most probable density distribution of the electron wave packet at the molecular tunneling ionization exit over time under real conditions. This confirms that the present invention accurately detects the evolution of the most probable density distribution of the electron wave packet at the molecular tunneling ionization exit over time.

[0096] The spatial location corresponding to the most probable density distribution of the electron wave packet changes over time. The amplitude of the spatial location corresponding to the most probable density distribution is modulated by the proportion of excited states in the superposition of the electron wave packet.

[0097] Figure 5 This is the process of detecting the proportion of excited states in the superposition of electron wave packets in this embodiment. Figure 5 In (a), the spatial extrema corresponding to the most probable density distribution at different spatial locations perpendicular to the oscillation direction of the laser field change with the proportion of excited states in the superposition of electron wave packets. Figure 5(b) represents the spatial extremum of the most probable density distribution of the electron wave packet at the tunnel exit x0 = 16 a.u., which varies with the proportion of excited states in the superposition of the electron wave packet, where x0 = -I p / E(t), I p E(t) represents the molecular ionization energy, and E(t) represents the laser electric field.

[0098] Depend on Figure 4 From (c) in the figure, we can obtain that, based on the holographic interference offset Δp y The calculated extreme value of the most probable density distribution of the electron wave packet over time is 2.3 atomic units. This result is compared with... Figure 5 Comparing with (b) in the previous example, the proportion of excited states in the superposition of electron wave packets is 0.2. This value is consistent with the superposition state used in this embodiment, which confirms that the present invention accurately detects the proportion of excited states in the superposition of intramolecular electron wave packets.

[0099] Example 2

[0100] The strong-field photoelectron momentum distribution was obtained by ionizing the ground-state and superposition-state electron wave packets of hydrogen molecular ions using a few-period linearly polarized laser field. The initial relative phase of the superposition-state was θ0 = π, the proportion of excited states in the superposition-state was 0.2, the laser field wavelength was 1000 nm, and the intensity was 2.5 × 10⁻⁶. 14 W / cm 2 By analyzing the momentum shift of the zero-order maxima of holographic interference fringes in the photoelectron momentum spectrum, attosecond time-resolved detection of intramolecular electron migration and the proportion of excited states in the superposition of electron wave packets can be achieved.

[0101] Figure 3 In this embodiment, (d) represents the photoelectron holographic interference corresponding to the superposition state. Figure 3 As can be observed in (d), for this superposition wave packet, the zeroth-order maxima of the holographic interference will be relative to the laser field oscillation axis p. x =0 towards Δp y The offset is in the positive direction. Since the offset of the zero-order maxima of the strong-field photoelectron holographic interference obtained by ionizing the ground-state electron wave packet of molecules by a few-period linearly polarized laser field is 0, the final momentum of the photoelectrons perpendicular to the laser oscillation direction corresponding to the maximum value of the holographic interference is the offset Δp of the zero-order maxima fringe of the holographic interference. y .

[0102] Figure 4 The black circle in (b) is from Figure 3 The offset Δp of the zeroth-order maxima fringe extracted from the holographic interference shown in (d) is... y According to the formula Δp y =y0(t) / (t) r -t0), through analysis of Δp yThe evolution of the most probable density distribution of the electron wave packet over time, y0(t), can be obtained. The results are as follows: Figure 4 The black circle in (c) is shown. Figure 4 In the figure (c), the most probable density distribution of electron wave packets at the molecular tunneling ionization exit changes with time, where the horizontal axis is the evolution time, the vertical axis is the spatial position perpendicular to the laser oscillation direction, and the black dashed line represents the spatial position perpendicular to the laser field polarization direction corresponding to the maximum value of the electron wave packet density distribution.

[0103] The results obtained by the method of the present invention are as follows Figure 4 As shown by the black circle in (c), the evolution of the most probable density distribution of the electron wave packet at the molecular tunneling ionization exit over time in real-world conditions is as follows: Figure 4 As shown by the black dashed line in (c) of the diagram. From Figure 4 As can be seen in (c), the results obtained by the method of the present invention are consistent with the evolution of the most probable density distribution of the electron wave packet at the molecular tunneling ionization exit over time under real conditions. This confirms that the present invention accurately detects the evolution of the most probable density distribution of the electron wave packet at the molecular tunneling ionization exit over time.

[0104] Depend on Figure 4 From (b) in the figure, we can obtain that, based on the holographic interference offset Δp y The calculated extreme value of the most probable density distribution of the electron wave packet over time is -2.3 atomic units, and its size is 2.3 atomic units. This result is compared with... Figure 5 Comparing with (b) in the previous example, the proportion of excited states in the superposition of electron wave packets is 0.2. This value is consistent with the superposition state used in this embodiment, which confirms that the present invention accurately detects the proportion of excited states in the superposition of intramolecular electron wave packets.

[0105] Therefore, the method for detecting intramolecular electron migration based on photoelectron holographic interferometry provided by this invention yields more accurate results and is feasible.

[0106] Example 3

[0107] The strong-field photoelectron momentum distribution was obtained by ionizing the ground-state and superposition-state electron wave packets of hydrogen molecular ions using a few-period linearly polarized laser field. The initial relative phase of the superposition-state was θ0 = 0, the proportion of excited states in the superposition-state was 0.2, the laser field wavelength was 1000 nm, and the intensity was 2.5 × 10⁻⁶. 14 W / cm 2 By analyzing the momentum shift of the first-order maxima and minima in the holographic interference of photoelectron momentum distribution, attosecond time-resolved detection of intramolecular electron migration and the proportion of excited states in the superposition of electron wave packets can be achieved.

[0108] Figure 4 (a) in the middle is from Figure 3 The momentum shift Δp of the first-order maxima and minima of the holographic interference extracted from the holographic interference shown in (c) is... y The black rhombus represents the momentum shift at the first-order maximum of the holographic interference, and the black solid line represents the momentum shift at the first-order minimum of the holographic interference.

[0109] This result is obtained by subtracting the momentum of the first-order maxima and minima of the holographic interference obtained from the superposition state of ionized hydrogen molecular ions in a linearly polarized laser field from the momentum of the first-order maxima and minima of the holographic interference obtained from the ground state of ionized hydrogen molecular ions. The result is completely consistent with the zero-order maxima shift of the holographic interference. According to the formula Δp y =y0(t) / (t) r -t0), different orders of interference fringes have the same Δp y By analyzing Δp y The evolution of the most probable density distribution of the electron wave packet over time, y0(t), can be calculated. By comparing the extreme value of the calculated evolution of the most probable density distribution of the electron wave packet over time with the dependence of the most probable density distribution on the proportion of excited states in the superposition state, the proportion of excited states in the superposition state of the electron wave packet can be determined.

[0110] In this example, the offset Δp of the first-order maxima and minima of the holographic interference is... y Completely consistent with the zero-order maximum offset of holographic interference, the evolution of the most probable density distribution of the electron wave packet over time and the proportion of excited states in the superposition state of the electron wave packet are the same as in Example 1. This confirms that the present invention is stable and the detection of electron migration motion does not depend on the order of the interference fringes.

[0111] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for detecting intramolecular electron migration based on photoelectron holographic interferometry, characterized in that, The specific steps include: S1. Use mid-infrared or near-infrared femtosecond lasers to ionize the ground-state electron wave packet in molecules, making the laser field polarization direction ninety degrees with the molecular axis to obtain the first electron momentum distribution. S2. Excite the ground-state molecule with a femtosecond laser in the ultraviolet band to obtain an electron wave packet that is superimposed on the ground state and the excited state. Then, use the mid-infrared or near-infrared femtosecond laser to ionize the superimposed electron wave packet in the molecule again, so that the polarization direction of the laser field is at ninety degrees to the molecular axis, and obtain the second electron momentum distribution. S3. Analyze the measured momentum distributions of the first and second electrons, and extract the momentum shift of the holographic interference in the second electron momentum distribution relative to the holographic interference in the first electron momentum distribution. S4. Based on the momentum shift, obtain the change of the most probable density distribution of the electron wave packet at the molecular tunneling ionization exit with time, and the proportion of excited states in the superposition state electron wave packet.

2. The method for detecting intramolecular electron migration based on photoelectron holographic interferometry according to claim 1, characterized in that, In S3, the first and second electron momentum distributions obtained by analysis and measurement are used to extract the momentum shift of the holographic interference in the second electron momentum distribution relative to the holographic interference in the first electron momentum distribution. Specific steps include: The first holographic interference fringes are obtained based on the first electron momentum distribution, and the second holographic interference fringes are obtained based on the second photoelectron momentum spectrum. The momentum of each order of interference fringes is retrieved in the first holographic interference and the second holographic interference, respectively; The momentum shift of each level of interference in the second holographic interference is obtained by subtracting the momentum of each level of interference in the first holographic interference from the momentum of each level of interference in the second electron momentum distribution.

3. The method for detecting intramolecular electron migration based on photoelectron holographic interferometry according to claim 2, characterized in that, The process of obtaining the first holographic interference fringe based on the first electron momentum distribution and the second holographic interference fringe based on the second photoelectron momentum spectrum includes: Within the target region of the first electron momentum distribution, the final momentum in the laser field polarization direction is retrieved as... The electron production at the point is used to obtain the first transverse momentum distribution; Gaussian function fitting is performed on the first transverse momentum distribution, and the first transverse momentum distribution is divided by the Gaussian function to obtain the first holographic interference fringe; and the second holographic interference fringe is obtained in the same way.

4. The method for detecting intramolecular electron migration based on photoelectron holographic interferometry according to claim 3, characterized in that, Within the target region of the first electron momentum distribution, the final momentum in the laser field polarization direction is retrieved. The method for electron production at the location is as follows: the target region of the first electron momentum distribution is uniformly cut several times, and each segment is extracted along the laser field polarization direction. The electron production at the location; in the same way, within the target region of the second electron momentum distribution, the final momentum in the laser field polarization direction is retrieved. Electron production at the location.

5. The method for detecting intramolecular electron migration based on photoelectron holographic interferometry according to claim 3, characterized in that, The expression for the first transverse momentum distribution is: ,in The amplitude of the first transverse momentum distribution. For the first holographic interference, The first holographic interference phase is expressed as follows: ; The expression for the second transverse momentum distribution is as follows: ,in This represents the amplitude of the second transverse momentum distribution. For the second holographic interference, The second holographic interference phase is expressed as follows: ; in, and These are the transverse momentum of the first electron and the transverse momentum of the second electron, respectively. The instantaneous moment of electron scattering with the parent ion. For the instantaneous moment when the electron is at the tunnel exit, The scattering amplitude and phase of the parent ion; The intermediate momentum of the scattered electrons generated by the tunneling ionization of the ground-state electron wave packet. It represents the intermediate momentum of scattered electrons generated by the tunneling ionization of the superposition state electron wave packet.

6. The method for detecting intramolecular electron migration based on photoelectron holographic interferometry according to claim 5, characterized in that, The step of retrieving the momentum of each order of interference fringes in the first holographic interference and the second holographic interference respectively includes: Setting the midpoint of the first holographic interference as the origin, counting from either left or right, the first holographic interference... The transverse momentum of the electron at the i-th maximum is the i-th Extreme interferometry maximum momentum, the first holographic interferometry... The transverse momentum of the electron corresponding to the i-th minimum is the i-th Extreme interference minimum momentum; The first holographic interference fringes and electron transverse momentum The relationship is ,in The first holographic interference phase, The intermediate momentum of the scattered electrons generated by the tunneling ionization of the ground-state electron wave packet; Similarly, setting the midpoint of the second holographic interference as the origin, and counting from either the left or right, the second holographic interference... At the i-th maximum, the electron's transverse momentum is the th... Extreme interference maximum momentum, the second holographic interference of the second holographic interference At the th minimum, the transverse momentum of the electron is the th... Extreme interference minimum momentum; The second holographic interference fringes and electron transverse momentum The relationship is ,in The second holographic interference phase, It represents the intermediate momentum of scattered electrons generated by the tunneling ionization of the superposition state electron wave packet.

7. The method for detecting intramolecular electron migration based on photoelectron holographic interferometry according to claim 1, characterized in that, In S2, the expression for the superposition state electron wave packet is: ,in and These represent the ground state and excited state of the electron wave packet, respectively. and These are their expansion coefficients, and Their respective electronic state energies, The initial relative phase of the electron wave packet ground state and excited state is given. To reduce Planck's constant, the value is approximately 1 × 10⁻³ 4 Joule second.

8. The method for detecting intramolecular electron migration motion based on photoelectron holographic interferometry according to claim 1, characterized in that, The momentum shift of the holographic interference in the second electron momentum distribution relative to the holographic interference in the first electron momentum distribution is: Since ground-state electron wave packet tunneling ionization always exists, therefore ,get ,in, and These are the transverse momentum of the first electron and the transverse momentum of the second electron, respectively. The intermediate momentum of the scattered electrons generated by the tunneling ionization of the ground-state electron wave packet. It represents the intermediate momentum of scattered electrons generated by the tunneling ionization of the superposition state electron wave packet.

9. The method for detecting intramolecular electron migration motion based on photoelectron holographic interferometry according to claim 1, characterized in that, The step of obtaining the most probable density distribution of the electron wave packet at the molecular tunneling ionization exit over time based on the momentum shift includes: Spatial location of the most probable density distribution of electron wave packet at the exit of molecular tunneling ionization and The relationship is The most probable density distribution of the electron wave packet at the molecular tunneling ionization exit point was obtained as a function of time. ,in, The instantaneous moment of electron scattering with the parent ion. For the instantaneous moment when the electron is at the tunnel exit, It represents the intermediate momentum of scattered electrons generated by the tunneling ionization of the superposition state electron wave packet.

10. The method for detecting intramolecular electron migration based on photoelectron holographic interferometry according to claim 9, characterized in that, Analyze the change in the most probable density distribution of the electron wave packet at the molecular tunneling ionization exit over time. The extreme value of the change is found, and the proportion of excited states in the superposition electron wave packet is determined by comparing this value with the dependence of the most probable density distribution on the proportion of excited states in the superposition state.

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