[Paper Review] Measuring Coulomb-Induced Ionization Time Lag with a Calibrated Attoclock

J. Y., C. Chen+3 more|arXiv (Cornell University)|Mar 31, 2021

Laser-Matter Interactions and Applications19 references4 citations

TL;DR

This paper proposes a Coulomb-calibrated attosecond clock (CCAC) to measure the relative ionization time lag between two consecutive half-cycles of a strong laser field in polar molecules like HeH⁺. By analyzing photoelectron momentum distributions (PMDs) in elliptical laser fields and applying a classical trajectory correction for long-range Coulomb effects, CCAC achieves high-precision extraction of time lag differences—within 10–25 attoseconds—matching time-dependent Schrödinger equation (TDSE) results, thus enabling accurate experimental probing of electron response dynamics in strong-field ionization.

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 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.

Motivation & Objective

• To address the challenge of measuring the absolute Coulomb-induced ionization time lag, which is experimentally inaccessible due to lack of a universal time reference.
• To develop a practical, high-accuracy method for measuring relative time lags between ionization events in consecutive half-cycles of a laser pulse, especially in complex molecular systems.
• To provide an experimental alternative to computationally intensive TDSE and MSFA simulations for probing electron response times in strong-field ionization.
• To validate the feasibility of extracting time information from photoelectron momentum distributions (PMDs) using a calibrated classical trajectory model that includes Coulomb corrections.

Proposed method

• The study uses the Born-Oppenheimer approximation to model HeH⁺ at a stretched internuclear distance (R = 2 a.u.) under strong elliptical laser fields.
• Photoelectron momentum distributions (PMDs) are simulated using time-dependent Schrödinger equation (TDSE) and Coulomb-modified strong-field approximation (MSFA) to capture ionization dynamics.
• A classical trajectory model is applied to relate the vector potential A(t) to the photoelectron momentum (px, py), with time t derived from the angle θ = arctan(Ax(t)/Ay(t)).
• The Coulomb-calibrated attosecond clock (CCAC) procedure introduces a temporal correction to classical trajectories based on the long-range Coulomb potential, enabling time extraction from experimental PMD data.
• The method compares ionization time lags derived from TDSE, MSFA-PD, and CCAC across varying laser intensities and wavelengths to assess accuracy.
• The time lag is defined as the deviation between the peak of the laser field and the maximum of the ionization rate, with relative lag differences computed between the first and second half-cycles.

Experimental results

Research questions

• RQ1 Can the relative ionization time lag between two consecutive half-cycles of a laser pulse be measured experimentally with high precision?
• RQ2 How does the inclusion of Coulomb-induced temporal corrections improve the accuracy of time extraction from photoelectron momentum distributions?
• RQ3 To what extent does the Coulomb-calibrated attosecond clock (CCAC) reproduce the time lag values obtained from full TDSE simulations?
• RQ4 How do variations in laser intensity and wavelength affect the relative ionization time lag in polar molecules?

Key findings

• The relative ionization time lag between the first and second half-cycles of the laser field is found to be approximately 20 attoseconds, with a spread of 10–25 attoseconds across different laser parameters.
• The CCAC method produces time lag differences that are in excellent agreement with TDSE results, demonstrating high accuracy and experimental feasibility.
• The MSFA-PD model shows deviations of up to 10 attoseconds from TDSE predictions, indicating limitations in approximating both Coulomb and permanent dipole effects.
• The time lag is not absolute but relative, and its difference between half-cycles is robustly mapped in the photoelectron momentum distribution (PMD).
• The CCAC procedure enables direct time extraction from experimental PMDs using a simple, calibrated classical trajectory model with Coulomb correction.
• The study confirms that the Coulomb-induced ionization time lag acts as a general response time of the electronic wave function to strong-field ionization, influencing subsequent electron dynamics.