Bicircular Field Research Articles

Valley selections and control of topological phases by bicircular laser field in transition-metal dichalcogenides

The energy spectra of transition metal dichalcogenides are influenced by three orbitals, forming a three-band model with strong spin-orbit interaction. Analyzing these bands through a two-band projection suffices for exploring electronic and optical properties. We examine topological phases and the spin-valley Hall effect, derived from spin-valley Chern numbers. Spin-orbit interaction breaks inversion symmetry but preserves time-reversal symmetry, resulting in non-zero spin-valley-dependent Hall conductivities, crucial for both spin and valley Hall effects. Interestingly, direct optical manipulation of the valley degree of freedom can be achieved using a trefoil field generated by a bicircular field. Selectable valley conductivity occurs when the field orientation matches the lattice symmetry, leading to a quantum anomalous Hall effect without magnetization. This approach suggests the potential for valley selection via field orientation, with applications in valleytronics and spintronics devices, enabling qubit encoding.

Programmable generation of counterrotating bicircular light pulses in the multi-terahertz frequency range

The manipulation of solid states using intense infrared or terahertz light fields is a pivotal area in contemporary ultrafast photonics research. While conventional circular polarization has been well explored, the potential of counterrotating bicircular light remains widely underexplored, despite growing interest in theory. In the mid-infrared or multi-terahertz region, experimental challenges lie in difficulties in stabilizing the relative phase between two-color lights and the lack of available polarization elements. Here, we successfully generated phase-stable counterrotating bicircular light pulses in the 14–39 THz frequency range circumventing the above problems. Employing spectral broadening, polarization pulse shaping with a spatial light modulator, and intra-pulse difference frequency generation leveraging a distinctive angular-momentum selection rule within the nonlinear crystal, we achieved direct conversion from near-infrared pulses into the designed counterrotating bicircular multi-terahertz pulses. Use of the spatial light modulator enables programmable control over the shape, orientation, rotational symmetry, and helicity of the bicircular light field trajectory. This advancement provides a novel pathway for the programmable manipulation of light fields, and marks a significant step toward understanding and harnessing the impact of tailored light fields on matter, particularly in the context of topological semimetals.

Probing H_{2} Double Ionization with Bicircular Laser Fields.

We present a kinematically complete study on strong-field double ionization of H_{2} molecules in two-color bicircular laser fields. The releasing times of electrons and protons are recorded with the double-hand attoclock. We observe the relative emission angles of two electrons oscillate with the kinetic energy release of protons, indicating the internal concerted four-body fragmentation. Using a three-dimensional molecular semiclassical ensemble model, we have disentangled the attosecond correlated electron emission in H_{2} double ionization. This work reveals the strong electron-nuclear coupling in the molecular bond breaking and may open up a new approach to experimentally accessing the intramolecular electron and bond dynamics with bicircular fields.

Anomalous Hall conductivity in a honeycomb topological insulator under counter-rotating bicircular laser field.

We investigate the interaction between the counter-rotating bicircular field and the trivial and topological insulator with anomalous Hall conductivity (AHC) to show the effect of the asymmetric spin band and topological invariant. We show that the reaction of the system to the counter-rotating bicircular field is classified into the high-field and low-field regimes. In the high-field regime, it is shown that the AHC of the system is controlled by the phase difference between the ω0 and 2ω0 fields. We also show that in the low-field regime, the AHC of the topological insulator is determined by the helicity of the laser, while the AHC is negligible in the trivial insulator. For the spin-orbit coupling (SOC), it is demonstrated that the high SOC increases the required field amplitude for the transition from the low-field to the high-field regime. Also, we show that strong SOC leads to an additional sign change of the AHC in the high-field regime, but with different origins in the trivial and topological insulator.

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.

Orbital-resolved photoelectron momentum distributions of F- ions in a counter-rotating bicircular field.

We present a theoretical study of the orbital-resolved photoelectron momentum distributions (PMDs) of F- ions by a two-color counter-rotating circularly polarized field. We show that the PMDs of F- ions can be modulated from an isotropic symmetric distribution into a three-lobe one by adding a weak fundamental counter-rotating field to the intense second harmonic circularly polarized field, and this modulation strongly depends on the initial atomic orbital. The PMDs simulated by the strong-field approximation method show good agreement with those obtained by solving the time-dependent Schrödinger equation. Based on the strong-field approximation method, we find that the radial momentum shift of PMDs for different orbitals is the fingerprint of orbital-dependent initial momentum at the tunnel exit. More importantly, we demonstrate that the lobes in PMDs appear in sequential order, highlighting that the scheme can be viewed as controllable rotating temporal Young's two-slit interferometer.

Elliptically polarized attosecond pulse generation by corotating bicircular laser fields

We revisit high-order-harmonic generation (HHG) in corotating bicircular fields, which possess high optical chirality, and extend the study to a frequency ratio higher than 1:2. By analyzing the classical trajectories in the corotating bicircular fields in the rotating frame, we show that the Coriolis-force effect that hinders HHG decreases with the frequency ratio. Given these features, we propose a method for producing highly elliptically polarized attosecond pulses (with ellipticity up to $\ensuremath{\epsilon}=0.88$) using the corotating bicircular field with a frequency ratio of 1:3. A comparison is also made with the extensively studied counter-rotating configurations with a frequency ratio of 1:2 considering various laser parameters. The results affirm the validity and superiority of the corotating configurations, from which both the ellipticity and yield of generated attosecond pulses are higher than those from the counter-rotating configurations.

Valley-resolved interband excitation and emission in gapped graphene

We theoretically investigate the electronic dynamics in gapped graphene driven by a bicircular field. The results indicate that the residual population on the conduction band is obviously asymmetric in the K and ${\mathrm{K}}^{\ensuremath{'}}$ valleys. Through analyzing the electron trajectory, we find that the interband transitions are determined by the compensation of two phases: the dynamic phase and the full dipole phase (including the transition dipole phase and the Berry phase). When the rates of change of the dynamic phase and the full dipole phase nearby the ionization time have the inverse signs, the unidirectional interband transition from the valence band (VB) to the conduction band (CB) results in the constructive interference of the population. In contrast, when they have the same signs, the bidirectional transition (CB$\ensuremath{\rightarrow}$VB and VB$\ensuremath{\rightarrow}$CB) results in the destructive interference. The constructive interference and the destructive interference lead to the asymmetric distribution of the CB population. Moreover, we also investigate the harmonic emission and find that only the $3n+2$ harmonics are generated in the cutoff region. This phenomenon can be attributed to the asymmetric distribution of the CB population and the trefoil vector potential of the electric field. Due to the dependence on population distribution, the harmonics can be a promising optical way to detect the valley excitation of the gapped graphene.

Coulomb effects in the high-energy part of above-threshold-ionization spectra in intense bicircular laser fields

Coulomb effects in the high-energy part of photoelectron spectra produced through the above-threshold ionization of an atom subject to intense short laser pulses are analyzed. The analysis is carried out for linearly polarized and tailored bicircular laser pulses consisting of the fundamental and the second-harmonic components. We include the Coulomb effects in the analytic semiclassical description of the photoelectron rescattering plateau using the recently developed adiabatic approach [Phys. Rev. A 104, 033109 (2021)] and the expression for the Coulomb phase derived for description of the high harmonic generation [J. Phys. B: At., Mol. Opt. Phys. 51, 144006 (2018)]. Comparisons between predictions of the analytic approach and numerical solutions of the time-dependent Schr\"odinger equation are presented. They allow the identification of the contribution of the Coulomb interaction to photoelectron spectra for different laser pulse forms. We show that the Coulomb effects appear more pronounced for bicircular fields, where they demonstrate considerable sensitivity to the photoelectron emission angle. Instead, for linear polarization, the Coulomb effect in the high-energy plateau is generally insignificant.

Yield enhancement of elliptical high harmonics driven by bicircular laser pulses

We theoretically investigate the yield enhancement of elliptical high harmonics in the interaction of molecules with bicircular laser pulses by solving the time-dependent Schrödinger equation. It is shown that by adjusting the relative intensity ratio of the two bicircular field components in specific ranges the yield of the molecular high harmonics for the plateau and cutoff regions can be respectively enhanced. To analyze this enhancement phenomenon, we calculate the weights of the electron classical trajectories. Additionally, we also study the ellipticity distribution of harmonics for different intensity ratios. We find that these enhanced harmonics are elliptically polarized, which we mainly attribute to the recombination dipole moment of the major weighted trajectories. These enhanced elliptical extreme ultraviolet and soft x-ray radiations may serve as essential tools for exploring the ultrafast dynamics in magnetic materials and chiral media.

Macroscopic effects in high-order harmonic generation - a focal-averaging method based on the integral solution of the wave equation.

A macroscopic theory of high-order harmonic generation (HHG) is presented, which applies a focal-averaging method based on the integral solution of the wave equation. The macroscopic high-harmonic yield is the coherent superposition of the single-atom contributions of all atoms of the generating medium, which are positioned at different spatial points of the laser focus and exposed to the space-time-dependent laser pulse. The HHG spectrum obtained in our macroscopic simulations is qualitatively different from the one obtained using the microscopic or single-atom theory of HHG. Coherent intensity focal averaging, the simpler and more approximate of two methods we introduced, gives the spectrum which forms a declining plateau with the same cutoff position as that of the microscopic spectrum. The second, more precise method, which we call coherent spatio-temporal focal averaging, shows that it is possible, changing the macroscopic conditions, to obtain an observable peak in the harmonic spectrum at an energy much lower than the microscopic cutoff energy. Generally, the high-harmonic yield appears to be dominated by the contributions of laser-pulse spatio-temporal regions with lower intensities as well as by interference, so that the high-energy plateau and its sharp cutoff are quenched in the theoretical simulation and, presumably, in the experiment. The height and position of this peak strongly depend on the macroscopic conditions. We confirmed these findings by applying our macroscopic theory to simulate two recent experiments with mid-infrared laser fields, one with a linearly polarized field and the other one with a bicircular field.

Dynamical symmetry and valley-selective circularly polarized high-harmonic generation in monolayer molybdenum disulfide

Circularly polarized high harmonics (CHHs) have been observed in several solid targets under single-color circularly polarized excitation. However, experimental observations show that CHHs cannot be efficiently generated in monolayer molybdenum disulphide (${\text{MoS}}_{2}$) driving by a single-color circularly polarized laser, thus letting its unique valley-selective circular dichroism (VSCD) to remain unexploited in the high harmonic generation process. Here we demonstrate that the efficient generation of CHHs in monolayer ${\text{MoS}}_{2}$ driven by counterrotating bicircular (CRB) fields and the broken inversion symmetry of monolayer ${\text{MoS}}_{2}$ leads to the generation of forbidden $3n$ ($n\ensuremath{\in}\mathbb{N}$) harmonic orders. Interestingly, we find that the VSCD lead to a distinctive valley selection of harmonic orders, while the valley selection caused by the trefoil orientation relative to the lattice is also observed. Dynamical symmetry analyses show that the rotational symmetry of the crystals can be decoded by the combination of a linearly polarized excitation scheme and CRB excitation scheme via the lowest common multiple rule. Additionally, VSCD leaves unique fingerprints in the ellipticity of harmonics.

Enhancing circularly polarized XUV vortices from bicircular Laguerre-Gaussian fields.

In this work, we theoretically study the generation of circularly polarized XUV vortices from high harmonic generation driven by bicircular Laguerre-Gaussian (LG) fields with different frequency ratios, by using the strong-field approximation theory. Our simulation shows that the amplitude of the generated vortices from the ω-3ω bicircular LG field is about one order of magnitude larger than that from the ω-2ω field, irrespective of the harmonic order and the orbital angular momentum of the bicircular driving fields. Our analysis shows that the great increase of the vortex amplitude for the ω-3ω field originates from the harmonic enhancement of a single atom. Furthermore, in terms of quantum-orbit theory, the underlying physics of the harmonic enhancement of the single atom for the ω-3ω field is revealed. Our work provides a simple and robust method to increase the amplitude of the circularly polarized XUV vortices.

Probing Molecular Frame Wigner Time Delay and Electron Wavepacket Phase Structure of CO Molecule

The time delay of photoelectron emission serves as a fundamental building block to understand the ultrafast electron emission dynamics in strong-field physics. Here, we study the photoelectron angular streaking of CO molecules by using two-color ( 400 + 800 nm) corotating circularly polarized fields. By coincidently measuring photoelectrons with the dissociative ions, we present molecular frame photoelectron angular distributions with respect to the instantaneous driving electric field signatures. We develop a semiclassical nonadiabatic molecular quantum-trajectory Monte Carlo (MO-QTMC) model that fully captures the experimental observations and further ab initio simulations. We disentangle the orientation-resolved contribution of the anisotropic ionic potential and the molecular orbital structure on the measured photoelectron angular distributions. Furthermore, by analyzing the photoelectron interference patterns, we extract the sub-Coulomb-barrier phase distribution of the photoelectron wavepacket and reconstruct the orientation- and energy-resolved Wigner time delay in the molecular frame. Holographic angular streaking with bicircular fields can be used for probing polyatomic molecules in the future.

Probing tunneling dynamics of dissociative H2 molecules using two-color bicircularly polarized fields

Probing and manipulating the electronic motion in the ultrafast laser molecular interaction provides the pathways for quantum imaging and controlling chemical reactions. Recently, the emerging application of attosecond metrology of ultrafast electron dynamics has accessed the time scale of the most fundamental processes in molecular chemical reactions. Here, we probe the tunneling dynamics of internuclear-dependent dissociative reaction of ${\mathrm{H}}_{2}$ with angular streaking using two-color bicircularly polarized femtosecond laser pulses. By measuring high-resolution photoelectron spectroscopy, we disentangle the orientation and internuclear-distance dependent effect of the long-range Coulomb potential and the initial phase on molecular-frame photoelectron momentum distributions, and stereo extract the phase gradient of the tunneling electron wave packets and Wigner time delay during the dissociative ionization using two-color bicircular fields. The work has an insight into the clocking of ultrafast spatiotemporal photoelectron dynamics and the quantum control of molecular chemical processes via sculptured circular fields, which can be applied to polyatomic molecules.

Symmetries and Selection Rules of the Spectra of Photoelectrons and High-Order Harmonics Generated by Field-Driven Atoms and Molecules

Using the strong-field approximation we systematically investigate the selection rules for high-order harmonic generation and the symmetry properties of the angle-resolved photoelectron spectra for various atomic and molecular targets exposed to one-component and two-component laser fields. These include bicircular fields and orthogonally polarized two-color fields. The selection rules are derived directly from the dynamical symmetries of the driving field. Alternatively, we demonstrate that they can be obtained using the conservation of the projection of the total angular momentum on the quantization axis. We discuss how the harmonic spectra of atomic targets depend on the type of the ground state or, for molecular targets, on the pertinent molecular orbital. In addition, we briefly discuss some properties of the high-order harmonic spectra generated by a few-cycle laser field. The symmetry properties of the angle-resolved photoelectron momentum distribution are also determined by the dynamical symmetry of the driving field. We consider the first two terms in a Born series expansion of the T matrix, which describe the direct and the rescattered electrons. Dynamical symmetries involving time translation generate rotational symmetries obeyed by both terms. However, those that involve time reversal generate reflection symmetries that are only observed by the direct electrons. Finally, we explain how the symmetry properties, imposed by the dynamical symmetry of the driving field, are altered for molecular targets.

Attoclock with bicircular laser fields as a probe of velocity-dependent tunnel-exit positions

Strong-field ionization of atoms can be investigated on the attosecond time scale by using the attoclock method, i.e. by observing the peak of the photoelectron momentum distribution (PMD) after applying a laser pulse with a two-dimensional polarization form. Examples for such laser fields are close-to-circular or bicircular fields. Here, we report numerical solutions of the time-dependent Schrödinger equation for bicircular fields and a comparison with a compact classical model to demonstrate that the tunnel-exit position, i.e. the position where the electron emerges after tunnel ionization, is encoded in the PMD. We find that the tunnel-exit position depends on the transverse velocity of the tunneling electron. This gives rise to a momentum-dependent attoclock shift, meaning that the momentum shift due to the Coulomb force on the outgoing electron depends on which slice of the momentum distribution is analysed. Our finding is supported by a momentum-space-based implementation of the classical backpropagation method.

Probing the Spin-Orbit Time Delay of Multiphoton Ionization of Kr by Bicircular Fields.

We study multiphoton ionization of Kr atoms by circular 400-nm laser fields and probe its photoelectron circular dichroism with the weak corotating and counterrotating circular fields at 800nm. The unusual momentum- and energy-resolved photoelectron circular dichroisms from the ^{2}P_{1/2} ionic state are observed as compared with those from ^{2}P_{3/2} ionic state. We identify an anomalous ionization enhancement at sidebands related to the ^{2}P_{1/2} ionic state on photoelectron momentum distribution when switching the relative helicity of the two fields from corotating to counterrotating. By performing the two-color intensity-continuously-varying experiments and the pump-probe experiment, we find a specific mixed-photon populated resonant transition channel in counterrotating fields that contributes to the ionization enhancement. We then probe the time delay between the two spin-orbit coupled ionic states (^{2}P_{1/2} and ^{2}P_{3/2}) using bicircular fields and reveal that the resonant transition has an insignificant effect on the relative spin-orbit time delay.

Analytic description of the above-threshold detachment in the adiabatic limit

Strong-field above-threshold detachment (ATD) is analyzed in the low-frequency (or adiabatic) limit. The explicit form of ATD amplitude is obtained within a developed low-frequency approximation. We show that in the low-frequency limit, the atomic structure effects are introduced in the ATD amplitude through the $T$ matrix, which in the limiting case coincides with the amplitude of elastic electron scattering. The rescattering part of ATD amplitude is evaluated in terms of the closed real classical electron trajectories. We further discuss the behavior of ATD amplitude near the caustic rescattering energies (classical energies for which two trajectories merge into a single one) of photoelectrons. Comparison of developed analytic theory with the numerical solution of time-dependent Schr\"odinger equation is presented for linearly polarized and time-delayed bicircular fields. Based on the analytical description, we predict an enhancement of ATD yield for time-delayed bicircular fields, which is similar to previous findings for the high harmonic yield [M.V. Frolov et al., Phys. Rev. Lett. 120, 263203 (2018)].

High-order harmonic generation by bi-elliptical orthogonally polarized two-color fields

Based on the strong-field approximation, we report results for high-order harmonic generation by bi-elliptical orthogonally polarized two-color (BEOTC) fields with frequency ratios of 2:1 and 3:1 and fundamental wavelengths of 800 and 1800 nm. A BEOTC field denotes the superposition of two copropagating counter-rotating elliptically polarized fields with different wavelengths and orthogonal semimajor axes. Its two limiting cases are the bicircular field and the linearly polarized orthogonal two-color field [D. B. Milo\ifmmode \check{s}\else \v{s}\fi{}evi\ifmmode \acute{c}\else \'{c}\fi{} and W. Becker, Phys. Rev. A 100, 031401(R) (2019)]. A detailed analysis of the high-order harmonic intensities and ellipticities as functions of the harmonic order, the ellipticity, and the relative phase between the two driving-field components is presented. Regions of the parameter space are identified where the harmonic ellipticities are very high. Surprisingly, this can be the case already for very small ellipticity (as small as $\ensuremath{\varepsilon}=0.01$) of the driving field. This can be important for practical applications. In the opposite limit where the BEOTC field is close to bicircular, the selection rules that govern the latter case can also be very quickly invalidated. For the 2:1 case, this can result in an apparent shift of the selection rules by one harmonic order.