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Statistical Characteristics of Tunneling States in Strong-Field Atomic Ionization
Authors:
M. W. Cao,
Z. Y. Chen,
J. N. Wu,
S. Q. Shen,
S. Wang,
W. Y. Li,
J. Y. Che,
Y. J. Chen
Abstract:
The state of the tunneling electron under the potential barrier is important in strong laser-atom interaction but is difficult to identify. Recent experiments showed that the tunneling electron may be located in a bound state with high symmetry [Phys. Rev. Lett. 134, 213201 (2025)]. However, the quantitative characteristic of the tunneling state in a tunneling event remains unclear. Here, we study…
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The state of the tunneling electron under the potential barrier is important in strong laser-atom interaction but is difficult to identify. Recent experiments showed that the tunneling electron may be located in a bound state with high symmetry [Phys. Rev. Lett. 134, 213201 (2025)]. However, the quantitative characteristic of the tunneling state in a tunneling event remains unclear. Here, we study tunneling ionization of atoms in strong circular laser fields. The calculated photoelectron momentum distribution (PMD) through numerical solution of time-dependent Schrödinger equation (TDSE) presents an isotropic ring-shaped distribution and the most probable momentum (MPM) along the ring can be easily identified. The kinetic energy related to MPM is remarkably smaller than that predicted by the strong-field approximation (SFA) that ignores Coulomb potential. Surprisingly, for different target atoms and laser parameters, the kinetic energy difference of MPM between TDSE and SFA is always close to half of the corresponding Coulomb potential at the tunnel exit. This phenomenon can be well described by a proposed model, which indicates that the tunneling electron is in an exit-position-dependent quasibound state agreeing with the virial theorem. These results quantitatively reveal the characteristics of tunneling states from a statistical perspective.
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Submitted 24 June, 2026;
originally announced June 2026.
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Single-photon ionization of H$_2^+$ in near-circular laser fields with lower photon energy
Authors:
Z. Y. Chen,
S. Q. Shen,
M. Q. Liu,
J. Y. Che,
Y. J. Chen
Abstract:
We study single-photon ionization of aligned H$_2^+$ in low-intensity near-circular laser fields with lower photon energy numerically and analytically. The photoelectron momentum distribution (PMD) within the laser polarization plane, obtained by numerical simulations, shows a remarkable offset angle, which changes with changing the internuclear distance and the laser frequency. This phenomenon is…
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We study single-photon ionization of aligned H$_2^+$ in low-intensity near-circular laser fields with lower photon energy numerically and analytically. The photoelectron momentum distribution (PMD) within the laser polarization plane, obtained by numerical simulations, shows a remarkable offset angle, which changes with changing the internuclear distance and the laser frequency. This phenomenon is different from that observed in recent experiments [Science 370, 339 (2020)] which is related to the PMD along the propagation direction of the laser. This phenomenon holds even for H$_2^+$ with short-range Coulomb potentials but disappears for atoms, different from that observed in attoclock experiments. We show that the molecular Coulomb potential near the two atomic centers plays an important role here and theory models associated with more accurate continuum wave function of the molecule are needed for reproducing this phenomenon. This phenomenon can be useful for ultrafast probing of molecules with high resolution of several attoseconds or even zeptoseconds.
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Submitted 12 May, 2025;
originally announced May 2025.
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Two-Color Attosecond Chronoscope
Authors:
J. N. Wu,
J. Y. Che,
F. B. Zhang,
C. Chen,
W. Y. Li,
G. G. Xin,
Y. J. Chen
Abstract:
We study ionization of atoms in strong orthogonal two-color ($ω,2ω$) (OTC) laser fields numerically and analytically. The calculated photoelectron momentum distribution shows two typical structures: a rectangular-like structure and a shoulder-like structure, the positions of which depend on the laser parameters. Using a strong-field model which allows us to quantitatively evaluate the Coulomb effe…
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We study ionization of atoms in strong orthogonal two-color ($ω,2ω$) (OTC) laser fields numerically and analytically. The calculated photoelectron momentum distribution shows two typical structures: a rectangular-like structure and a shoulder-like structure, the positions of which depend on the laser parameters. Using a strong-field model which allows us to quantitatively evaluate the Coulomb effect, we show that these two structures arise from attosecond response of electron inside an atom to light in OTC-induced photoemission. Some simple mappings between the locations of these structures and response time are derived, with which we are able to establish two-color attosecond chronoscope with high resolution for timing electron emission in OTC-based precise manipulation.
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Submitted 28 January, 2023;
originally announced January 2023.
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Response time of electron inside a molecule to light in strong-field ionization
Authors:
J. Y. Che,
Y. G. Peng,
F. B. Zhang,
X. J. Xie,
G. G. Xin,
Y. J. Chen
Abstract:
We study ionization of aligned H$_2^+$ in strong elliptically-polarized laser fields numerically and analytically. The calculated offset angle in photoelectron momentum distribution is several degrees larger for the molecule than a model atom with similar ionization potential at diverse laser parameters. Using a strong-field model that considers the properties of multi-center and single-center Cou…
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We study ionization of aligned H$_2^+$ in strong elliptically-polarized laser fields numerically and analytically. The calculated offset angle in photoelectron momentum distribution is several degrees larger for the molecule than a model atom with similar ionization potential at diverse laser parameters. Using a strong-field model that considers the properties of multi-center and single-center Coulomb potentials, we are able to quantitatively reproduce this angle difference between the molecule and the atom. Further analyses based on this model show that the response time of electron to light which is encoded in the offset angle and is manifested as the time spent in tunneling ionization, is about 15 attoseconds longer for the molecule than the atom. This time difference is further enlarged when increasing the internuclear distance of the molecule.
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Submitted 2 January, 2023;
originally announced January 2023.
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Roles of laser ellipticity in attoclock
Authors:
J. Y. Che,
J. Y. Huang,
F. B. Zhang,
C. Chen,
G. G. Xin,
Y. J. Chen
Abstract:
We study ionization of atoms in strong elliptically-polarized laser fields numerically and analytically. We focus on effects of laser ellipticity on the offset angle in photoelectron momentum distribution. This angle is considered to encode time information of tunneling ionization in attoclock experiments. The calculated offset angle increases with the decrease of ellipticity but the momentum alon…
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We study ionization of atoms in strong elliptically-polarized laser fields numerically and analytically. We focus on effects of laser ellipticity on the offset angle in photoelectron momentum distribution. This angle is considered to encode time information of tunneling ionization in attoclock experiments. The calculated offset angle increases with the decrease of ellipticity but the momentum along the major axis of laser polarization related to this angle changes slowly, in agreement with experiments. With a Coulomb-included strong-field model, the scaling laws for ellipticity dependence of this angle and relevant momentum components are obtained, and the ellipticity dependence of Coulomb-induced ionization time lag encoded in this angle is also addressed.
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Submitted 19 December, 2022;
originally announced December 2022.
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Coulomb scattering inducing time lag in strong-field tunneling ionization
Authors:
Y. G. Peng,
J. Y. Che,
C. Chen,
G. G. Xin,
Y. J. Chen
Abstract:
We study ionization of atoms in strong elliptically-polarized laser fields. We focus on the physical origin of the offset angle in the photoelectron momentum distribution and its possible relation to a specific time. By developing a model which is based on strong-field approximation and considers the classical Coulomb scattering, we are able to quantitatively explain recent attoclock experiments i…
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We study ionization of atoms in strong elliptically-polarized laser fields. We focus on the physical origin of the offset angle in the photoelectron momentum distribution and its possible relation to a specific time. By developing a model which is based on strong-field approximation and considers the classical Coulomb scattering, we are able to quantitatively explain recent attoclock experiments in a wide region of laser and atomic parameters. The offset angle can be understood as arising from the scattering of the electron by the ionic potential when the electron exits the laser-Coulomb-formed barrier through tunneling. The scattering time is manifested as the Coulomb-induced ionization time lag and is encoded in the offset angle.
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Submitted 9 December, 2022;
originally announced December 2022.
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Single-photon ionization of aligned H$_2^+$ with lower photon energy
Authors:
F. B. Zhang,
J. Y. Che,
W. Y. Li,
C. Chen,
Y. J. Chen
Abstract:
We study single-photon ionization of aligned H$_2^+$ in a high-frequency low-intensity laser field. We focus on the case where the laser frequency is not far larger than the ionization potential of the target. The calculated photoelectron momentum distribution through numerical solution of time-dependent Schrödinger equation shows clear interference patterns. By developing a theory model applicabl…
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We study single-photon ionization of aligned H$_2^+$ in a high-frequency low-intensity laser field. We focus on the case where the laser frequency is not far larger than the ionization potential of the target. The calculated photoelectron momentum distribution through numerical solution of time-dependent Schrödinger equation shows clear interference patterns. By developing a theory model applicable for high-frequency laser field, we show that the interference patterns can not be explained by the interference of the electronic wave with the observed momentum between these two atomic centers of the molecule. The Coulomb potential influences remarkably on the momentum of the emitting electronic wave responsible for this interference. Our results suggest a manner for probing the structure and the electron dynamics of the molecule in single-photon ionization.
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Submitted 1 December, 2022;
originally announced December 2022.
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Response time of photoemission at quantum-classic boundary
Authors:
C. Chen,
J. Y. Che,
W. Y. Li,
S. Wang,
X. J. Xie,
J. Y. Huang,
Y. G. Peng,
G. G. Xin,
Y. J. Chen
Abstract:
The response time of the electron to light in photoemission is difficult to define and measure. Tunneling ionization of atoms, a strong-laser-induced photoemission process, provides a semiclassical case for visiting the problem. Here, we show that the response time can be determined at the boundary between quantum and classic. Specifically, tunneling is instantaneous but a finite response time (ab…
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The response time of the electron to light in photoemission is difficult to define and measure. Tunneling ionization of atoms, a strong-laser-induced photoemission process, provides a semiclassical case for visiting the problem. Here, we show that the response time can be determined at the boundary between quantum and classic. Specifically, tunneling is instantaneous but a finite response time (about 100 attoseconds) is needed for the state of the tunneling electron to evolve into the ionized state around tunnel exit. This time can be well described with a compact expression related to some basic laser and atomic parameters. Moreover, it can be directly mapped to and easily decoded from photoelectron momentum with a simple mapping, allowing an unambiguous measurement. These results shed light on definition and measurement of the response time of photoemission.
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Submitted 19 December, 2022; v1 submitted 16 November, 2021;
originally announced November 2021.
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Measuring Coulomb-Induced Ionization Time Lag with a Calibrated Attoclock
Authors:
J. Y. Che,
C. Chen,
S. Wang,
G. G. Xin,
Y. J. Chen
Abstract:
Electrons in atoms and molecules can not react immediately to the action of intense laser field. A time lag (about 100 attoseconds) between instants of the field maximum and the ionization-rate maximum emerges. This lag characterizes the response time of the electronic wave function to the strong-field ionization event and has important effects on subsequent ultrafast dynamics of the ionized elect…
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Electrons in atoms and molecules can not react immediately to the action of intense laser field. A time lag (about 100 attoseconds) between instants of the field maximum and the ionization-rate maximum emerges. This lag characterizes the response time of the electronic wave function to the strong-field ionization event and has important effects on subsequent ultrafast dynamics of the ionized electron. The absolute time lag is not accessible in experiments. Here, a calibrated attoclock procedure, which is related to a simple Coulomb-induced temporal correction to electron trajectories, is proposed to measure the relative lag of two different ionization events. Using this procedure,the difference (i.e., the relative lag) between the ionization time lags of polar molecules in two consecutive half laser cycles can be probed with a high accuracy.
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Submitted 31 March, 2021;
originally announced March 2021.
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Tracing origins of asymmetric momentum distribution for polar molecules in strong linearly-polarized laser fields
Authors:
S. Wang,
J. Y. Che,
C. Chen,
G. G. Xin,
Y. J. Chen
Abstract:
We study the ionization dynamics of oriented HeH$^+$ in strong linearly-polarized laser fields by numerically solving the time-dependent Schrödinger equation. The calculated photoelectron momentum distributions for parallel orientation show a striking asymmetric structure. With a developed model pertinent to polar molecules, we trace the electron motion in real time. We show that this asymmetric s…
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We study the ionization dynamics of oriented HeH$^+$ in strong linearly-polarized laser fields by numerically solving the time-dependent Schrödinger equation. The calculated photoelectron momentum distributions for parallel orientation show a striking asymmetric structure. With a developed model pertinent to polar molecules, we trace the electron motion in real time. We show that this asymmetric structure arises from the interplay of the Coulomb effect and the permanent dipole in strong laser fields. This structure can be used to probe the degree of orientation which is important in ultrafast experiments for polar molecules. we also check our results for other polar molecules such as CO and BF.
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Submitted 15 August, 2020; v1 submitted 18 September, 2019;
originally announced September 2019.