Cam-Tu Le

Studying the effects caused by core electrons of highly polarizable atoms and molecules is essential since interactions between external fields and matter primarily occur in the outer electron shell, but the contribution of the core electrons has been revealed in recent studies. Therefore, investigating the core-electron polarization effect (MEP) in the high-order harmonic generation (HHG) spectrum of matter when interacting with intense, ultrashort laser pulses has attracted significant attention. In our latest work, we have shown that when interacting with a few-cycle laser pulse, MEP induces significant shifts in the HHG peaks of the CO molecules. However, the laser's parameter ranges of the laser pulse, allowing the observation of these peak shifts, have not yet been thoroughly examined. In this paper, by simulating the HHG emitted from the CO molecule under interactions with few-cycle laser pulses of different parameters, we demonstrate that the laser pulse duration should be greater than three cycles and less than six cycles. Furthermore, the carrier-envelope phase of the laser pulse should be within the ranges of ($2\pi/3$,~$7\pi/6$) and ($5\pi/3$,~$2\pi$). These optimal regions guide experiments in choosing laser settings to observe core-electron effects on the HHG spectrum via peak shifts.

Odd-even harmonic generation contains the system's dynamical symmetry breaking, and its decoding is desirable not only in understanding physics but also for applications of dynamics extraction. In this work we discover a simple universal relation between the odd-even harmonics and the asymmetry of the terahertz (THz)-assisted laser-atomic system: atoms in a primary midinfrared laser pulse combined with a THz laser. We demonstrate numerically and then derive analytically the dependence of the harmonic even-to-odd ratio on the THz electric field. Notably, the functional form of this dependency reveals a universal scaling independent of the parameters of both the primary pulse and atomic target. This universality inspires us to propose a pump-probe scheme for THz waveform sampling from the even-to-odd ratio, accessible from conventional compact setups.

It is argued that the dynamic core-electron polarization (DCEP) in polar molecules primarily affects harmonic processes at the ionization step only. This manifestation can also be understood in view of the strong-field assumption that the parent ion's potential becomes irrelevant when the electron is accelerated in the continuum-energy region. However, the scenario becomes vastly different, especially in the case of long-wavelength lasers as shown in this paper, where we demonstrate a complete physical picture of the DCEP on the harmonic process from asymmetric carbon monoxide (CO) molecules comprising the propagation step. To do so, we develop a visualization method for the harmonic process with and without DCEP based on Bohmian mechanics. As tracer particles evolving along quantum trajectories, Bohmian trajectories provide an intuitive picture of the “harmonic process from the CO molecules. Remarkably, when the change of the harmonic intensity with respect to the DCEP inclusion cannot be explained by the instantaneous ionization rate, the Bohmian trajectories can attribute this change to the difference in the number of returning events and returning time of the electron after the propagation stage. By analyzing the dynamics of individual Bohmian trajectories (the acceleration and the time-frequency profile), we show that the DCEP alters nonlocally the innermost trajectories, which encode all the dynamics of the harmonic process. This insight into the DCEP effect necessitates a careful reinvestigation into other strong-field physics theories on the role of the target over the propagation stage.

Retrieving atomic and molecular properties from entangling macroscopic measurements is an ambitious task. In particular, the phase difference between the adjacent attosecond bursts emitted from polar molecules is of interest and has been reconstructed from measured high-order harmonic generation (HHG) when molecules are exposed to an intense laser pulse. However, besides the ratio of intensities between the even and odd harmonic orders which can be measured directly, the suggested construction method requires nonmeasured parameters that can be supplied through theoretical calculations. The complexity or comprehensiveness of this theory clearly affects the accuracy of the retrieval procedure. In this study we propose a robust parameter-free method to retrieve the subtle molecular asymmetry, i.e., both the spectral phase difference and intensity ratio of two adjacent attosecond bursts, from purely experimental measurements of HHG. For this purpose, we first figure out that the phase difference is an intrinsic feature of polar molecules, almost independent of the external laser's parameters. After that, we design a detailed procedure to quantitatively extract these features via the time-frequency profile from the intensity and phase measurements of HHG emitted from partially oriented molecular samples. In this step, we develop the analytical formula to convert the phase difference and intensity ratio of a partially oriented sample to those of a single molecule. The accuracy and robustness of the methods are validated by numerical data.

It has been known that the broadband of continuum harmonics, a regular periodicity or a wide smooth range, is essential for generating attosecond pulses. However, the high-order rescatterings of electrons (HOR) can significantly affect this important part of high-order harmonic spectra. In the present work, we apply the method suggested in our previous studies to limit the HOR effect on the continuum harmonics by using up-chirped pulses with frequency increasing in time to regulate the high-order harmonic generation of an asymmetric molecule such as CO subjected to a near-infrared laser. To do so, we numerically calculate the high-order harmonic spectra using the time-dependent wave functions obtained within the framework of the single-active electron approximation. To analyze and regulate the HOR effect, we use the time-frequency analysis together with the kinetic energy maps obtained from the equation of electron motion in the laser electric field. These techniques reveal the high-order harmonic dynamics, especially the effect of chirped pulse on the manifestation of continuum harmonics. Based on this, we release the notice on choosing appropriate parameters to obtain the optimal continuum range of harmonics. Although the detailed analysis is given for the CO molecule, the method suggested is applicable for other polar molecules.

The underlying physics of high-order harmonic generation of carbon monoxide (CO) in a multicycle near-infrared laser: multiple rescatterings and their effect through time-frequency analysis and classical electron trajectories.

Dynamic core-electron polarization (DCeP) is a correction to the single-active electron (SAE) approximation by considering a response of the core electrons to the time-dependent laser field. Despite being initially construed as a perturbative correction, in some cases especially atoms and molecules with large polarizabilities, DCeP can qualitatively alter predictions produced by the bare SAE theory. In this study, we unambiguously demonstrate the nonperturbative role of DCeP in the resolved odd-even high-order harmonic generation (HHG) of the CO molecule. In particular, we find that the even-to-odd ratio, i.e., the ratio between the harmonic intensities of even order and average of the two adjacent odd orders, changes by as much as one order of magnitude when DCeP is included, making the theoretically predicted values remarkably consistent with the experimental ones. This strong manifestation allows us to verify the DCeP role in HHG by experimental data. Furthermore, our analysis of the harmonic time profile shows that this agreement is not an artifact of the numerical method but reflects relevant physics, establishing that DCeP must be incorporated into the standard framework for strong-field physics.