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Sample geometry and laser spectrum a, Scanning-electron-microscope image of the sample (false-coloured). The graphene strip is aligned parallel to the terrace steps. Scale bar is 2 μm. The triangles found in the electrodes are alignment markers. b, Map of the (CEP-independent) photocurrent as a function of the laser spot position. When the laser spot hits the graphene–metal junction, photo carriers are generated in the graphene that result in a photocurrent owing to the built-in potential at the junction originating from the mismatch of the work functions. c, Laser spectrum, recorded with an optical spectrum analyser. The instrumental noise floor is visible at the spectral extrema. d, Second-harmonics interferometric autocorrelation trace of the compressed laser pulse. The blue circles are measured data points, and the red curve shows a trace calculated from the spectrum assuming a flat spectral phase. The signal is normalized so that the intensity for sufficiently large delay (>40 fs) becomes the unity.
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Ultrafast electron dynamics in solids under strong optical fields has recently found particular attention. In dielectrics and semiconductors, various light-field-driven effects have been explored, such as high-harmonic generation, sub-optical-cycle interband population transfer and nonperturbative increase of transient polarizability. In contrast,...
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Citations
... It has a potential for probing and controlling ultrafast carrier dynamics and material properties. Among them, the light-induced phenomena including high-harmonic generation [1][2][3][4][5][6][7][8][9][10][11][12] and field-driven current [13][14][15] provide routes for exploring electron-photon coupling [16,17], electron-density information [18], energyband structure [19][20][21], Berry curvature [22] and more. So far, the underlying electronic dynamics have been extensively studied and two main mechanisms were proposed to understand these processes: interband polarization and intraband current [23][24][25]. ...
We investigate theoretically the laser intensity dependent valley polarization in gapped graphene driven by the circularly polarized pulse. The results show that the valley polarization without considering decoherence displays a nonmonotonic behavior as a function of the laser intensity. By analyzing the conduction-band electron distribution, we demonstrate that the decrease of the valley polarization in low laser intensity is caused by the change of dominant physical mechanisms, i.e., from few-photon to diabatic tunneling transitions. While in high laser intensity, the analysis of electron dynamics trajectories indicates that the intercycle interference determines the different k-resolved electron distributions in K and K′ valleys, influences the valley polarization, finally leads to the formation of a peak. Moreover, when the decoherence is considered, although the interference structure of the k-resolved electron distribution becomes blurred, the oscillation of valley polarization with the laser intensity is still present. Our work illustrates that the laser intensity can significantly influence the field-driven electron dynamics processes and can be as a knob to adjust the valley polarization in gapped graphene.
... We extend the use of the Naimark dilation method to a time-dependent non-PT -symmetric NHH in order to simulate the pseudo-Hermitian Landau-Zener-Stückelberg-Majorana (LZSM) model [43] on a superconducting quantum processor. The LZSM model finds use in the description of transitions in a large variety of two-level systems, such as the valence/conduction bands in graphene [44], molecular states in ultracold Cs 2 [45], electron transfer between two As or P donors in a silicon nanowire transistor [46], and even the in-plane and out-of-plane resonator modes of a classical nanomechanical resonator [47]. The pseudo-Hermitian extension of the LZSM model can be applied to, e.g., the description of two electromagnetic modes traveling to opposite directions in a waveguide [48], and boosting a weak signal with a stronger one in the sum-frequency generation process [49]. ...
While the Hamiltonians used in standard quantum mechanics are Hermitian, it is also possible to extend the theory to non-Hermitian Hamiltonians. Particularly interesting are non-Hermitian Hamiltonians satisfying parity–time ( P T ) symmetry, or more generally pseudo-Hermiticity, since such non-Hermitian Hamiltonians can still exhibit real eigenvalues. In this article, we present a quantum simulation of the time-dependent non-Hermitian non- P T -symmetric Hamiltonian used in a pseudo-Hermitian extension of the Landau–Zener–Stückelberg–Majorana (LZSM) model. The simulation is implemented on a superconducting processor by using Naimark dilation to transform a non-Hermitian Hamiltonian for one qubit into a Hermitian Hamiltonian for a qubit and an ancilla; postselection on the ancilla state ensures that the qubit undergoes nonunitary time evolution corresponding to the original non-Hermitian Hamiltonian. We observe properties such as the dependence of transition probabilities on time and the replacement of conservation of total probability by other dynamical invariants in agreement with predictions based on a theoretical treatment of the pseudo-Hermitian LZSM system.
Published by the American Physical Society 2024
... About a decade ago, HHG has been first demonstrated in a bulk semiconductor [8] and more recently has been explored in a wider variety of materials such as dielectrics [9,10], twodimensional semiconductors [11,12], and nanostructures [13,14]. Its discovery has also laid the foundation of attosecond science in condensed matter [15][16][17][18][19]. HHG in solids has also attracted attention as a method for reconstructing band structural properties such as energy bands [20], transition dipole moments (TDMs) [21], and Berry curvature [22,23]. ...
... In other words, the Berry connection plays the role of a gauge field in a periodic solid, and its non-trivial gauge dependence [Eq. (17)] cancels the gauge dependence of the gradient in Eq. (18). Further, the matrix elements of the position operator are also covariant, as it is readily seen from Eq. (10) that nk |x| mk = iD nm (k). ...
... In this section we use one-body SBEs to study HHG in gapped graphene, which is a non-centrosymmetric system comprising two distinct atomic species on a honeycomb lattice [18,35]. In previous work [51] we studied HHG in the more general Haldane model [61], which is also based on the honeycomb lattice but lacks time-reversal symmetry and can exhibit non-trivial topology. ...
The semiconductor Bloch equations (SBEs) are a well-established model for optical interactions in condensed matter. In particular, the SBEs in the electromagnetic length gauge preserve the band picture of periodic crystals and thus provide an intuitive and numerically efficient model of high harmonic generation (HHG) in solids. For materials with broken inversion or time-reversal symmetry, the length gauge SBEs involve complex transition dipole moments (TDMs), which depend on the choice of Bloch gauge. The numerical and conceptual complications resulting from this gauge freedom have impeded interpretation and key applications of HHG, such as the tomographic reconstruction of crystal band structure. We derive gauge invariant SBEs (GI-SBEs) that contain only gauge invariant structural quantities: the absolute value of TDMs, the shift vector, and for more than two bands a triple product of TDM phases. The GI-SBEs provide insight into the physics of HHG in solids with broken inversion symmetry, which we demonstrate in gapped graphene.
... On the other hand, in solids, scattering by other electrons or other degrees of freedom occurs under driving. When the typical scattering timescale is longer than the period of the driving field, the electron motion can be regarded as coherent and ballistic, as in atoms [2,[8][9][10][11]. On the other hand, when the typical scattering time is shorter than the driving period, scattering disrupts the ballistic electron motion (called a drift-diffusive regime) [12] and prevents the formation of nonequilibrium states. ...
Electron-electron scattering on the order of a few to tens of femtoseconds plays a crucial role in the ultrafast electron dynamics of conventional metals. When mid-infrared light is used for driving and the period of light field is comparable to the scattering time in metals, unique light-driven states and nonlinear optical responses associated with the scattering process are expected to occur. Here, we use high-harmonics spectroscopy to investigate the effect of electron-electron scattering on the electron dynamics in thin film 2 H − NbSe 2 driven by a mid-infrared field. We observed odd-order high harmonics up to 9th order as well as a broadband emission from hot electrons in the energy range from 1.5 to 4.0 eV. The electron-electron scattering time in 2H- NbSe 2 was estimated from the broadband emission to be almost the same as the period of the mid-infrared light field. A comparison between experimental results and a numerical calculation reveals that competition and cooperation between the driving and scattering enhances the nonperturbative behavior of high harmonics in metals, causing a highly nonequilibrium electronic state corresponding to several thousand Kelvin.
Published by the American Physical Society 2024
... As an illustrative example, we propose a strong-field ARPES experiment on Rabi oscillations and Landau-Zehner-Stückelberg interferences in the excited state population in graphene, resulting from the interaction with few-cycle NIR pulses with a peak electric field strength E 0 in the Vnm −1 range. The study is motivated by recently performed photocurrent control experiments in graphene using the carrier-envelope phase (CEP) of few-cycle NIR laser pulses as a control parameter [83,84]. Numerical simulations showed that the detected net photocurrent observed for E 0 ≳ 2 Vnm −1 arises from suboptical-cycle Landau-Zener-Stückelberg interferences, consisting of coherent repeated Landau-Zener transitions on the femtosecond time scale [see Figure 7a]. ...
... The off-resonant populations, which show a clear asymmetry with respect to k x = 0, are due to CEPmodulated Landau-Zener-Stückelberg interferences. The net photocurrent observed in [83] is a direct consequence of this asymmetry. Note that dissipative processes due to carriercarrier scattering and carrier-phonon scattering were not considered in the simulations. ...
... (c) E 0 of few-cycle 800 nm laser pulses as a function of pulse duration and the square root of the incident pump fluence F. Constant values of E 0 in units of Vnm −1 are marked by the gray dashed lines. The solid red line marks the boundary between the weak-field and the strong-field regime in graphene (E 0 = 1.8 Vnm −1 , γ ≈ 1) reported in Ref. [83]. The blue circled points indicate the experimental laser pulse parameters used in trARPES experiments on graphite [67] and graphene [12]. ...
Over the last two decades, time- and angle-resolved photoemission spectroscopy (trARPES) has become a mature and established experimental technique for the study of ultrafast electronic and structural dynamics in materials. To date, most trARPES investigations have focused on the investigation of processes occurring on time scales of ≳30 fs, in particular, relaxation and thermalization, and have therefore been blind to the initial sub-10 fs dynamics related to electronic coherence and correlation effects. In this article, we illustrate how current trARPES setups reach their limits when it comes to addressing such extraordinarily short time scales and present an experimental configuration that provides the time, energy, and momentum resolutions required to monitor few-femtosecond dynamics on the relevant energy and momentum scales. We discuss the potential capabilities of such an experiment to study the electronic response of materials in the strong-field interaction regime at PHz frequencies and finally review a theoretical concept that may in the future even overcome the competing resolution limitations of trARPES experiments, as imposed by the time–bandwidth product of the probing laser pulse. Our roadmap for ultrafast trARPES indicates a path to break new experimental ground in quantum nonequilibrium electronic dynamics, from which new possibilities for ultrafast control of optical and electronic signals in quantum materials can be explored.
... In recent years, the stacking and twisting of atom-thin structures with matching crystal symmetry has provided a unique way to create new superlattice structures in which new properties emerge 1,2 . In parallel, control over the temporal characteristics of strong light fields has allowed researchers to manipulate coherent electron transport in such atom-thin structures on sublaser-cycle timescales 3,4 . Here we demonstrate a tailored light-wave-driven analogue to twisted layer stacking. ...
... Previous works have shown using Floquet theory that the frequency, intensity and helicity of long-pulse-duration electric fields can be exploited as additional degrees of freedom to modify the Hamiltonian parameters of a crystal during an interaction [21][22][23][24] on the timescale of the pulse duration 25 . In light-wave electronics 3,4,[26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] , one exploits control over the temporal characteristics of strong light fields, such as the carrier envelope phase of single-cycle pulses or the time delay between multicolour fields, to manipulate coherent electronic transport on timescales shorter than one laser cycle. ...
In recent years, the stacking and twisting of atom-thin structures with matching crystal symmetry has provided a unique way to create new superlattice structures in which new properties emerge1,2. In parallel, control over the temporal characteristics of strong light fields has allowed researchers to manipulate coherent electron transport in such atom-thin structures on sublaser-cycle timescales3,4. Here we demonstrate a tailored light-wave-driven analogue to twisted layer stacking. Tailoring the spatial symmetry of the light waveform to that of the lattice of a hexagonal boron nitride monolayer and then twisting this waveform result in optical control of time-reversal symmetry breaking⁵ and the realization of the topological Haldane model⁶ in a laser-dressed two-dimensional insulating crystal. Further, the parameters of the effective Haldane-type Hamiltonian can be controlled by rotating the light waveform, thus enabling ultrafast switching between band structure configurations and allowing unprecedented control over the magnitude, location and curvature of the bandgap. This results in an asymmetric population between complementary quantum valleys that leads to a measurable valley Hall current⁷, which can be detected by optical harmonic polarimetry. The universality and robustness of our scheme paves the way to valley-selective bandgap engineering on the fly and unlocks the possibility of creating few-femtosecond switches with quantum degrees of freedom.
... In order to fully capitalize on these capabilities, it is essential to understand the fundamental electron dynamics that supports the steady-state out-of-equilibrium phase. Inevitably, such dynamics are responsible for emerging observables such as transport phenomena [33][34][35] or high harmonic generation (HHG) [36,37]. The most direct methodology that allows exploring Floquet phases of matter is time-and angleresolved photoelectron spectroscopy (Tr-ARPES), whereby a short probe pulse ionizes the sample while it is irradiated by a dressing pump laser pulse (which can also be applied in a spin-resolved manner). ...
... It should also form a basis for future work to further analyze and measure non-Floquet bands. Beyond Tr-ARPES, this work should impact neighboring fields that rely on light-driven electron dynamics such as HHG [36,37], photogalvanic currents [35,82,88], and ultrafast magnetism [89,90], where either Houston or Floquet states are used as basis sets for analyzing the dynamics. The results presented here should pave the way to a hybrid basis set for attosecond charge dynamics that combines both Houston and Floquet states, thus incorporating all physical effects on equal footing. ...
Floquet engineering has recently emerged as a technique for controlling material properties with light. Floquet phases can be probed with time- and angle-resolved photoelectron spectroscopy (Tr-ARPES), providing direct access to the laser-dressed electronic bands. Applications of Tr-ARPES to date focused on observing the Floquet-Bloch bands themselves, and their build-up and dephasing on sub-laser-cycle timescales. However, momentum and energy resolved sub-laser-cycle dynamics between Floquet bands have not been analyzed. Given that Floquet theory strictly applies in time-periodic conditions, the notion of resolving sub-laser-cycle dynamics between Floquet states seems contradictory – it requires probe pulse durations below a laser cycle that inherently cannot discern the time-periodic nature of the light-matter system. Here we propose to employ attosecond pulse train probes with the same temporal periodicity as the Floquet-dressing pump pulse, allowing both attosecond sub-laser-cycle resolution and a proper projection of Tr-ARPES spectra on the Floquet-Bloch bands. We formulate and employ this approach in ab-initio calculations in light-driven graphene. Our calculations predict significant sub-laser-cycle dynamics occurring within the Floquet phase with the majority of electrons moving within and in-between Floquet bands, and a small portion residing and moving outside of them in what we denote as ‘non-Floquet’ bands. We establish that non-Floquet bands arise from the pump laser envelope that induces non-adiabatic electronic excitations during the pulse turn-on and turn-off. By performing calculations in systems with poly-chromatic pumps we also show that Floquet states are not formed on a sub-laser-cycle level. This work indicates that the Floquet-Bloch states are generally not a complete basis set for sub-laser-cycle dynamics in steady-state phases of matter.
... The establishment of a technology to control the carrier envelope phase of an optical wave (optical frequency comb) [1] has brought about revolutionary developments in optical frequency standards followed by high-resolution laser spectroscopy [2], as well as in its counterpart, attosecond science [3]; this is likely the most symbolic example in a recent development of optical science. Other developments include programmable waveform generation [4][5][6][7] by employing a spatial light modulator, time-dependent polarization control [8][9][10][11][12], pulse shaping with metasurfaces [13], controlling terahertz waveforms [14][15][16], and the use of these technologies to control molecular ionization [9,10], photocurrent in solids [17][18][19], magnetization vectors [20,21], and tunneling currents [22,23]. ...
We report an optical method of generating arbitrary polarization states by manipulating the thicknesses of a pair of uniaxial birefringent plates, the optical axes of which are set at a crossing angle of π/4. The method has the remarkable feature of being able to generate a distribution of arbitrary polarization states in a group of highly discrete spectra without spatially separating the individual spectral components. The target polarization-state distribution is obtained as an optimal solution through an exploration. Within a realistic exploration range, a sufficient number of near-optimal solutions are found. This property is also reproduced well by a concise model based on a distribution of exploration points on a Poincaré sphere, showing that the number of near-optimal solutions behaves exponentially with respect to the number of spectral components of concern. As a typical example of an application, by applying this method to a set of phase-locked highly discrete spectra, we numerically demonstrate the continuous generation of a vectorlike optical electric field waveform, the helicity of which is alternated within a single optical cycle in the time domain.
... In the context of solid state physics, a strong short optical pulse modifies both the transport and optical properties of solids [20][21][22][23][24][25][26][27][28][29][30][31][32][33]. In terms of electron dynamics, an ultrashort optical pulse induces two distinct dynamics known as interband and intraband electron dynamics which unfolds the process of HHG through the interactive interactions of these two distinct dynamics [12-14, 18, 19, 34]. ...
We study theoretically the generation of high harmonics in disk graphene quantum dots placed in linearly polarized short pulse.
The quantum dots are described within an effective model of the Dirac type and the length gauge was used to describe the interaction of quantum dots with an optical pulse. The generated radiation spectra of graphene quantum dots can be controlled by varying the quantum dot size, i.e., its radius. With increasing the quantum dot radius, the intensities of low harmonics mainly decrease, while the cutoff frequency increases. The sensitivity of the cutoff frequency to the QD size increases with the intensity of the pulse.
... Controlled charge flows are fundamental to many areas of science and technology, serving as carriers of energy and information, as probes of material properties and dynamics 1 and as a means of revealing 2,3 or even inducing 4,5 broken symmetries. Emerging methods for light-based current control [5][6][7][8][9][10][11][12][13][14][15][16] offer particularly promising routes beyond the speed and adaptability limitations of conventional voltage-driven systems. However, optical generation and manipulation of currents at nanometre spatial scales remains a basic challenge and a crucial step towards scalable optoelectronic systems for microelectronics and information science. ...
Controlled charge flows are fundamental to many areas of science and technology, serving as carriers of energy and information, as probes of material properties and dynamics¹ and as a means of revealing2,3 or even inducing4,5 broken symmetries. Emerging methods for light-based current control5–16 offer particularly promising routes beyond the speed and adaptability limitations of conventional voltage-driven systems. However, optical generation and manipulation of currents at nanometre spatial scales remains a basic challenge and a crucial step towards scalable optoelectronic systems for microelectronics and information science. Here we introduce vectorial optoelectronic metasurfaces in which ultrafast light pulses induce local directional charge flows around symmetry-broken plasmonic nanostructures, with tunable responses and arbitrary patterning down to subdiffractive nanometre scales. Local symmetries and vectorial currents are revealed by polarization-dependent and wavelength-sensitive electrical readout and terahertz (THz) emission, whereas spatially tailored global currents are demonstrated in the direct generation of elusive broadband THz vector beams¹⁷. We show that, in graphene, a detailed interplay between electrodynamic, thermodynamic and hydrodynamic degrees of freedom gives rise to rapidly evolving nanoscale driving forces and charge flows under the extremely spatially and temporally localized excitation. These results set the stage for versatile patterning and optical control over nanoscale currents in materials diagnostics, THz spectroscopies, nanomagnetism and ultrafast information processing.
