Sub-cycle Dynamics Research Articles

Attosecond transient interferometry

AbstractAttosecond transient absorption resolves the instantaneous response of a quantum system as it interacts with a laser field, by mapping its sub-cycle dynamics onto the absorption spectrum of attosecond pulses. However, the quantum dynamics are imprinted in the amplitude, phase and polarization state of the attosecond pulses. Here we introduce attosecond transient interferometry and measure the transient phase, as we follow its evolution within the optical cycle. We demonstrate how such phase information enables us to decouple the multiple quantum paths induced in a light-driven system, isolating their coherent contribution and retrieving their temporal evolution. Applying attosecond transient interferometry reveals the Stark shift dynamics in helium and retrieves long-term electronic coherences in neon. Finally, we present a vectorial generalization of our scheme, theoretically demonstrating the ability to isolate the underlying anomalous current in light-driven topological materials. Our scheme provides a direct insight into the interplay of light-induced dynamics and topology. Attosecond transient interferometry holds the potential to considerably extend the scope of attosecond metrology, revealing the underlying coherences in light-driven complex systems.

Subcycle dynamics of excitons under strong laser fields.

Excitons play a key role in the linear optical response of two-dimensional (2D) materials. However, their role in the nonlinear response to intense, nonresonant, low-frequency light is often overlooked as strong fields are expected to tear the electron-hole pair apart. Using high-harmonic generation as a spectroscopic tool, we theoretically study their formation and role in the nonlinear optical response. We show that the excitonic contribution is prominent and that excitons remain stable even when the driving laser field surpasses the strength of the Coulomb field binding the electron-hole pair. We demonstrate a parallel between the behavior of strongly laser-driven excitons in 2D solids and strongly driven Rydberg states in atoms, including the mechanisms of their formation and stability. Last, we show how the excitonic contribution can be singled out by encapsulating the 2D material in a dielectric, tuning the excitonic energy and its contribution to the high-harmonic spectrum.

High harmonic Mach–Zehnder interferometer for probing sub-laser-cycle electron dynamics in solids

High harmonic emissions from crystalline solids contain rich information on the dynamics of electrons driven by intense infrared laser fields and have been intensively studied owing to their potential use as a probe of microscopic electronic structures. In particular, the ability to measure the temporal response of high harmonics may allow us to investigate electron dynamics directly. Here, we demonstrate a Mach–Zehnder high harmonic interferometer, where high harmonics are generated in each path of a Mach–Zehnder interferometer and an interferogram of them is captured. The high harmonic interferometer allows us to detect high harmonic signals with higher sensitivity than conventional high harmonic intensity measurements, and achieve a relative time resolution between the target and reference high harmonics of less than 150 attoseconds, which is sufficient to track sub-cycle dynamics of electrons in solids. Using high harmonic interferometry, we succeeded in capturing the real time dynamics of Floquet states in WSe2, whose indirect signature has so far been caught only by time-averaged measurements. Our simple technique could enable to access attosecond electron dynamics in solids.

Sub-cycle dynamics in two-color high-harmonic generation from laser-produced plasmas

Sub-cycle dynamics in two-color high-harmonic generation from laser-produced plasmas

Sub-cycle strong-field tunneling dynamics in solids

Tunneling ionization is a crucial process in the interaction between strong laser fields and matter which initiates numerous nonlinear phenomena including high-order harmonic generation, photoelectron holography, etc. Both adiabatic and nonadiabatic tunneling ionization are well understood in atomic systems. However, the tunneling dynamics in solids, especially nonadiabatic tunneling, has not yet been fully understood. Here, we study the sub-cycle resolved strong-field tunneling dynamics in solids via a complex saddle-point method. We compare the instantaneous momentum at the moment of tunneling and the tunneling distances over a range of Keldysh parameters. Our results demonstrate that for nonadiabatic tunneling, tunneling ionization away from Γ point is possible. When this happens the electron has a nonzero initial velocity when it emerges in the conduction band. Moreover, consistent with atomic tunneling, a reduced tunneling distance as compared to the quasi-static case is found. Our results provide remarkable insight into the basic physics governing the sub-cycle electron tunneling dynamics with significant implications for understanding subsequent strong-field nonlinear phenomena in solids.

Data-Driven Models for Sub-Cycle Dynamic Response of Inverter-Based Resources Using WMU Measurements

Using real-world data from Waveform Measurement Units (WMUs), this paper proposes novel data-driven methods to model the dynamic response of inverter-based resource (IBR) to the high-frequency disturbances that occur in practice in power systems. WMUs are an emerging class of smart grid sensors. They can capture the fast sub-cycle dynamics in power systems, which are overlooked by phasor measurement units (PMUs). After extracting the differential voltage and current waveforms from the raw waveform data, we develop multiple methods that include data-driven model library construction and proper model selection. One class of methods is proposed in frequency domain, which is based on modal analysis. Another class of methods is proposed in time domain, which is based on regression analysis of time-series. Experimental results based on real-world WMU data demonstrate the of performance the proposed methods.

Attosecond electron microscopy of sub-cycle optical dynamics.

The primary step of almost any interaction between light and materials is the electrodynamic response of the electrons to the optical cycles of the impinging light wave on sub-wavelength and sub-cycle dimensions1. Understanding and controlling the electromagnetic responses of a material2-11 is therefore essential for modern optics and nanophotonics12-19. Although the small de Broglie wavelength of electron beams should allow access to attosecond and ångström dimensions20, the time resolution of ultrafast electron microscopy21 and diffraction22 has so far been limited to the femtosecond domain16-18, which is insufficient for recording fundamental material responses on the scale ofthe cycles of light1,2,10. Here we advance transmission electron microscopy to attosecond time resolution of optical responses within one cycle of excitation light23. We apply a continuous-wave laser24 to modulate the electron wave function into a rapid sequence of electron pulses, and use an energy filter to resolve electromagnetic near-fields in and around a material as a movie in space and time. Experiments on nanostructured needle tips, dielectric resonators and metamaterial antennas reveal a directional launch of chiral surface waves, a delay between dipole and quadrupole dynamics, a subluminal buried waveguide field and a symmetry-broken multi-antenna response. These results signify the value of combining electron microscopy and attosecond laser science to understand light-matter interactions in terms of their fundamental dimensions in spaceand time.

Valley-Selective Polarization in Twisted Bilayer Graphene Controlled by a Counter-Rotating Bicircular Laser Field

The electron valley pseudospin in two-dimensional hexagonal materials is a crucial degree of freedom for achieving their potential application in valleytronic devices. Here, bringing valleytronics to layered van der Waals materials, we theoretically investigate lightwave-controlled valley-selective excitation in twisted bilayer graphene (tBLG) with a large twist angle. It is demonstrated that the counter-rotating bicircular light field, consisting of a fundamental circularly-polarized pulse and its counter-rotating second harmonic, can manipulate the sub-cycle valley transport dynamics by controlling the relative phase between two colors. In comparison with monolayer graphene, the unique interlayer coupling of tBLG renders its valley selectivity highly sensitive to duration, leading to a noticeable valley asymmetry that is excited by single-cycle pulses. We also describe the distinct signatures of the valley pseudospin change in terms of observing the valley-selective circularly-polarized high-harmonic generation. The results show that the valley pseudospin dynamics can still leave visible fingerprints in the modulation of harmonic signals with a two-color relative phase. This work could assist experimental researchers in selecting the appropriate protocols and parameters to obtain ideal control and characterization of valley polarization in tBLG.

Quantum-Path-Resolved Attosecond High-Harmonic Spectroscopy.

Strong-field ionization of molecules releases electrons which can be accelerated and driven back to recombine with their parent ion, emitting high-order harmonics. This ionization also initiates attosecond electronic and vibrational dynamics in the ion, evolving during the electron travel in the continuum. Revealing this subcycle dynamics from the emitted radiation usually requires advanced theoretical modeling. We show that this can be avoided by resolving the emission from two families of electronic quantum paths in the generation process. The corresponding electrons have the same kinetic energy, and thus the same structural sensitivity, but differ by the travel time between ionization and recombination-the pump-probe delay in this attosecond self-probing scheme. We measure the harmonic amplitude and phase in aligned CO_{2} and N_{2} molecules and observe a strong influence of laser-induced dynamics on two characteristic spectroscopic features: a shape resonance and multichannel interference. This quantum-path-resolved spectroscopy thus opens wide prospects for the investigation of ultrafast ionic dynamics, such as charge migration.

Controlling Magnetic and Electric Nondipole Effects with Synthesized Two Perpendicularly Propagating Laser Fields

Nondipole effects are ubiquitous and crucial in light-matter interaction. However, they are too weak to be directly observed. In strong-field physics, motion of electrons is mainly confined in transverse plane of light fields, which suppresses the significance of nondipole effects. Here, we present a theoretical study on enhancing and controlling the nondipole effect by using the synthesized two perpendicularly propagating laser fields. We calculate the three-dimensional photoelectron momentum distributions of strong-field tunneling ionization of hydrogen atoms using the classical trajectory Monte Carlo model and show that the nondipole effects are noticeably enhanced in such laser fields due to their remarkable influences on the sub-cycle photoelectron dynamics. In particular, we reveal that the magnitudes of the magnetic and electric components of nondipole effects can be separately controlled by modulating the ellipticity and amplitude of driving laser fields. This novel scenario holds promising applications for future studies with ultrafast structured light fields.

Ion momentum distributions from sequential double ionization of Ar in elliptically polarized laser fields

In this paper, we utilize a classical ensemble model with Heisenberg-core potential to study sequential double ionization (SDI) of Ar atom by an elliptically polarized laser field. The results show that for random laser phases, as the laser wavelength increases, the ion momentum distribution gradually evolves from a six-band structure at 800 nm to an eight-band structure at 1600 nm. When the laser phase is stable, the ion momentum distribution from 1600 nm laser field exhibits a ten-band structure. These multi-band structures directly reflect the subcycle ionization dynamics of electrons in an elliptically polarized laser field. There is a significant shift among the outer three bands of ion momentum distrbutions from different laser phases, which leads to the fact that only one band is observed in the outer region of the ion momentum distribution for the case of random laser phases. By analyzing the ionization times of the two electrons, it is found that for the case of random phases, the inner bands of the ion momentum distributions originate from those combinations of electron ionization bursts with the ionization time difference of 0.5 cycle, and the outer bands arise from those combinations of ionization bursts with the ionization time difference of 1, 2 and 3 cycles. For 800 nm, the middle band corresponds to those combinations of ionization bursts with the ionization time differences of 1.5 and 2.5 cycles. For 1600 nm, there are two bands in middle regime. One is from the combination with the ionization time difference of 1.5 cycles, and the other is from those combinations with the ionization time difference of 2.5 and 3.5 cycles. These results indicate that in the case of long wavelength and phase-stable laser, the subcycle dynamics in sequential double ionization of atoms is more likely to be observed.

Nonsequential double ionization of Ne with elliptically polarized laser pulses

We show through simulation that the improved quantitative rescattering model (QRS) can successfully predict the nonsequential double ionization (NSDI) process by intense elliptically polarized laser pulses. Using the QRS model, we calculate the correlated two-electron and ion momentum distributions of NSDI in Ne exposed to intense elliptically polarized laser pulses with a wavelength of 788 nm at a peak intensity of $5.0\ifmmode\times\else\texttimes\fi{}{10}^{14}$ W/${\mathrm{cm}}^{2}$. We analyze the asymmetry in the doubly charged ion momentum spectra observed by Kang et al. [Phys. Rev. Lett. 120, 223204 (2018)] in going from linearly to elliptically polarized laser pulses. Our model reproduces the experimental data well. Furthermore, we find that the ellipticity-dependent asymmetry arises from the drift velocity along the minor axis of the elliptic polarization. We explain how the correlated electron momentum distributions along the minor axis provide access to the subcycle dynamics of recollision. From these findings, we expect that we can extend the QRS model for NSDI toward more complicated laser fields in the future.

Probing subcycle spectral structures and dynamics of high-order harmonic generation in crystals

Subcycle spectral structures and dynamics of high-order harmonic generation (HHG) processes of atoms and molecules driven by intense laser fields on the attosecond time scale have been originally studied theoretically and experimentally. However, the time scale of HHG dynamics in crystals is in the order of sub-femtosecond, and the carrier dynamics of HHG in crystals driven by subcycle laser pulses are largely unexplored. Here we perform a theoretical study of subcycle structures, spectra, and dynamics of HHG of crystals in mid-infrared laser fields subject to excitation by a subcycle laser pulse with a time delay. The HHG spectra as a function of time delay between two laser fields are calculated by using a single-band model for the intra-band carrier dynamics in crystal momentum space and by solving the time-dependent Schrödinger equation in velocity gauge for the treatment of multi-band crystal systems. The results exhibit a complex time-delay-dependent oscillatory pattern, and the enhancement and suppression of the HHG related to subcycle pulse are observed at the given time delay in either single-band or multi-band crystal systems. To understand oscillation structures with respect to the dependence for the subcycle laser fields, the time-frequency characteristics of the HHG as well as the probability density distribution of the radiation are analyzed in detail.

Field-resolved high-order sub-cycle nonlinearities in a terahertz semiconductor laser

The exploitation of ultrafast electron dynamics in quantum cascade lasers (QCLs) holds enormous potential for intense, compact mode-locked terahertz (THz) sources, squeezed THz light, frequency mixers, and comb-based metrology systems. Yet the important sub-cycle dynamics have been notoriously difficult to access in operational THz QCLs. Here, we employ high-field THz pulses to perform the first ultrafast two-dimensional spectroscopy of a free-running THz QCL. Strong incoherent and coherent nonlinearities up to eight-wave mixing are detected below and above the laser threshold. These data not only reveal extremely short gain recovery times of 2 ps at the laser threshold, they also reflect the nonlinear polarization dynamics of the QCL laser transition for the first time, where we quantify the corresponding dephasing times between 0.9 and 1.5 ps with increasing bias currents. A density-matrix approach reproducing the emergence of all nonlinearities and their ultrafast evolution, simultaneously, allows us to map the coherently induced trajectory of the Bloch vector. The observed high-order multi-wave mixing nonlinearities benefit from resonant enhancement in the absence of absorption losses and bear potential for a number of future applications, ranging from efficient intracavity frequency conversion, mode proliferation to passive mode locking.

Revealing rescattering-induced subcycle dynamics of the spiral-like holographic structure

Employing a semiclassical quantum-trajectory Monte Carlo model, we comprehensively study the formerly overlooked strong-field photoelectron holographic pattern, ``the spiral,'' originating from the interference of the forward and backward rescattering trajectories. We include the multipass rescattering trajectories, which were left out before, and find that only the ones revisiting the parent ion for the same even number of times (including zero) before the recollision from adjacent half cycles can lead to the spiral. By using a rescattering sphere to differentiate trajectories, we revealed that after the recollision only the backward rescattering trajectories with the turning point outside the sphere can interfere with the forward ones and result in the spiral eventually. The relationship between the fringe width of the spiral and the ionization time is identified. This study gives a deeper understanding of how to use the spiral as a holographic tool.

Laser-subcycle control of electronic excitation across system boundaries

We report on the results of a joint experimental and numerical study on the sub-cycle laser field-driven electron dynamics that underlie the population of highly excited electronic states in multiply ionized argon dimers by electron recapture processes. Our experiments using few-cycle laser pulses with a known carrier-envelope phase (CEP) in combination with reaction microscopy reveal a distinct CEP-dependence of the electron emission and recapture process and, furthermore, a small but significant CEP-offset to the scenario in which no excited argon dimers are produced. With the help of classical ensemble trajectory simulations we trace down these different CEP-dependencies to subtle differences in the laser-driven sub-cycle electron trajectory dynamics that involve in both cases the transfer of an electron from one argon ion across the system boundary to the neighboring ion and its transient capture on this ion.

Principal frequency of an ultrashort laser pulse

We introduce an alternative definition of the main frequency of an ultrashort laser pulse, the principal frequency $\omega_P$. This parameter is complementary to the most accepted and widely used carrier frequency $\omega_0$. Given the fact that these ultrashort pulses, also known as transients, have a temporal width comprising only few cycles of the carrier wave, corresponding to a spectral bandwidth $\Delta\omega$ covering several octaves, $\omega_P$ describes, in a more precise way, the dynamics driven by these sources. We present examples where, for instance, $\omega_P$ is able to correctly predict the high-order harmonic cutoff independently of the carrier envelope phase. This is confirmed by solving the time-dependent Schr\"odinger equation in reduced dimensions, supplemented with the time-analysis of the quantum spectra, where it is possible to observe how the sub-cycle electron dynamics is better described using $\omega_P$. The concept of $\omega_P$, however, can be applied to a large variety of scenarios, not only within the strong field physics domain.

Controlling polarization of attosecond pulses with plasmonic-enhanced bichromatic counter-rotating circularly polarized fields

The use of bichromatic counter-rotating laser field is known to generate high-order harmonics with nonzero ellipticity. By combining such laser field with a plasmonic-enhanced spatially inhomogeneous field, we propose a way to influence the subcycle dynamics of the high-harmonic generation process. Using the numerical solution of the time-dependent Schr\"odinger equation combined with classical trajectory Monte Carlo simulations, we show that the change of the direction and the strength of the plasmonic field selectively enhances or suppresses certain recombining electron trajectories. This in turn modifies the ellipticity of the emitted attosecond pulses.

Direct mapping of attosecond electron dynamics

The subcycle interaction of light and electrons has been one of the key frontiers in free-electron lasers, attosecond science and dynamical investigation of matter. Capturing the underlying subcycle dynamics of electrons with an optical field promises fascinating vistas with unprecedented temporal resolution. Yet the rigorous synchronization requirement has kept its realization out of reach. Here, by direct spatial observation of periodic electron bunch fringes, we demonstrate a laser streaking concept for revealing the dynamics of free electrons emitted from a plasma mirror under sub-relativistic laser intensity. Field-induced electron beam deflection demonstrates subcycle charge dynamics with a streaking speed of ~60 μrad as−1. This provides us with an attosecond-resolution metrology to obtain more direct evidence about the light-field-induced electron dynamics in the plasma mirror. Our results offer unprecedented characterization of attosecond dynamics and open the way to extensive experimental investigations of the interaction of attosecond electrons with intense lasers. By focusing a sub-relativistic infrared laser pulse onto a silica target, a periodic deflection pattern of attosecond electron pulse trains is observed. It reveals these subcycle charge dynamics with a streaking speed of ~60 μrad as−1.

Sub-cycle dynamics of nonsequential double ionization of Ar atom by few-cycle counter-rotating two-color circularly polarized laser fields

We have investigated the sub-cycle correlated electron dynamics of nonsequential double-ionization (NSDI) of Ar atom by few-cycle counter-rotating two-color circularly polarized (TCCP) laser fields using a three-dimensional classical ensemble model. Numerical results indicate that NSDI probability sensitively depends on the relative phase of the two components and achieves its maximum at the relative phase 0.7[Formula: see text]. Back analysis of NSDI trajectories shows that the return angle of the electron is closely related to the relative phase of the two components and can continuously be controlled by changing the relative phase. Furthermore, the relative phase also influences the relative contribution of recollision-induced direct ionization (RII) and recollision-induced excitation with subsequent field ionization (RESI) to NSDI and the final emitted direction of the electrons.