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Role of Resonant $\mathbf{k}$-Points in the Transient Optical Response of Pumped Germanium
Authors:
Amir Eskandari-asl,
Giacomo Inzani,
Matteo Lucchini,
Adolfo Avella
Abstract:
Pump-induced transient optical properties combine contributions from electronic states throughout the Brillouin zone, but the relative relevance of off-resonant and l-photon resonant crystal momenta has remained unexplored. We address this issue in pumped germanium by resolving the transient absorptive response into momentum-space classes defined by the presence or absence of 1-, 2-, and 3-photon…
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Pump-induced transient optical properties combine contributions from electronic states throughout the Brillouin zone, but the relative relevance of off-resonant and l-photon resonant crystal momenta has remained unexplored. We address this issue in pumped germanium by resolving the transient absorptive response into momentum-space classes defined by the presence or absence of 1-, 2-, and 3-photon resonances with respect to the pump. Using the Dynamical Projective Operatorial Approach together with the related generalized linear response theory, we compute the differential imaginary part of the dielectric function and evaluate the contributions of each resonance class. Resonant regions account for nearly the entire optical response, whereas points outside the identified resonance sets contribute only negligibly. Nevertheless, the 2-photon-resonant set, although containing more than 98% of the residual (post-pump) excitation population, does not reproduce the full transient spectrum. Conversely, resonance classes with very small residual populations generate non-negligible contributions to the transient optical properties. This mismatch shows that the transient optical weight is not determined solely by the real-charge dynamics (which results in post-pulse residual excitation population) and is consistent with substantial virtual pump-induced contributions, whose dominant optical weight nevertheless arises from the resonant regions of momentum space. The class-resolved phase of the dominant 2$ω_{\mathrm{pu}}$ oscillations further shows that, whenever a class contributes appreciably, the phase of its oscillatory component follows that of the corresponding full signal. The resulting decomposition provides a momentum-resolved connection among multi-photon resonances and transient optical observables in a realistic material.
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Submitted 22 July, 2026;
originally announced July 2026.
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Extreme-ultraviolet optical response of atomically-thin molybdenum disulfide
Authors:
G. Fiorentini,
N. Di Palo,
G. Inzani,
G. L. Dolso,
S. Bonetti,
Q. Li,
F. Liu,
X. Zhu,
A. Giglia,
N. Mahne,
L. Pasquali,
M. D'Alessandro,
M. Malakhov,
M. Camarasa-Gómez,
J. J. Esteve-Paredes,
J. J. Palacios,
R. Borrego-Varillas,
M. Nisoli,
A. Picón,
D. Sangalli,
M. Lucchini
Abstract:
We report multi-angle reflectivity measurements in the extreme-ultraviolet (XUV) range for mono- and bilayer MoS$_2$ on a Si$_3$N$_4$ substrate. Using a single-sheet 2D conductivity model, we extract the complex optical response of the MoS$_2$ bilayer between 25 and 90 eV and derive an effective refractive index by introducing a thickness equal to the interlayer spacing. The MoS$_2$ monolayer resp…
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We report multi-angle reflectivity measurements in the extreme-ultraviolet (XUV) range for mono- and bilayer MoS$_2$ on a Si$_3$N$_4$ substrate. Using a single-sheet 2D conductivity model, we extract the complex optical response of the MoS$_2$ bilayer between 25 and 90 eV and derive an effective refractive index by introducing a thickness equal to the interlayer spacing. The MoS$_2$ monolayer response is consistently reproduced either by halving the 2D conductivity or the effective thickness, indicating a robust scaling with layer number. The resulting optical constants display a broad resonance at the Mo N$_{2,3}$ edge with no signatures of sharp core-exciton features despite the reduced dimensionality. First-principles calculations reproduce the experimental results and show that local-field (Hartree) effects dominate the XUV response, while screened-exchange (SEX) contributions remain weak and mainly induce spectral shifts. Our analysis demonstrates that excitonic effects play a minor role in the XUV optical response of atomically thin MoS$_2$, highlighting key differences with respect to the visible and infrared regimes, and calling for a reassessment of the use of Mo-based transition metal dichalcogenides in attosecond spectroscopy and XUV excitonics.
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Submitted 12 June, 2026;
originally announced June 2026.
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Subcycle videography of lightwave-driven Landau-Zener-Majorana transitions in graphene
Authors:
Vincent Eggers,
Giacomo Inzani,
Manuel Meierhofer,
Lasse Münster,
Jakob Helml,
Robert Wallauer,
Sarah Zajusch,
Suguru Ito,
Leon Machtl,
Hao Yin,
Christian Kumpf,
François C. Bocquet,
Changhua Bao,
Jens Güdde,
F. Stefan Tautz,
Rupert Huber,
Ulrich Höfer
Abstract:
Strong light fields have unlocked previously unthinkable possibilities to tailor coherent electron trajectories, engineer band structures and shape emergent phases of matter all-optically. Unravelling the underlying quantum mechanisms requires a visualisation of the lightwave-driven electron motion directly in the band structure. While photoelectron momentum microscopy has imaged optically excited…
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Strong light fields have unlocked previously unthinkable possibilities to tailor coherent electron trajectories, engineer band structures and shape emergent phases of matter all-optically. Unravelling the underlying quantum mechanisms requires a visualisation of the lightwave-driven electron motion directly in the band structure. While photoelectron momentum microscopy has imaged optically excited electrons averaged over many cycles of light, actual subcycle band-structure videography has been limited to small electron momenta. Yet lightwave-driven elementary processes in quantum materials often occur throughout momentum space. Here, we introduce attosecond-precision, subcycle band-structure videography covering the entire first Brillouin zone (BZ) and visualize one of the most fundamental but notoriously elusive strong-field processes: non-adiabatic Landau-Zener-Majorana (LZM) tunnelling. The interplay of field-driven acceleration within the Dirac-like band structure of graphene and periodic LZM interband tunnelling manifest in a coherent displacement and distortion of the momentum distribution at the BZ edge. The extremely non-thermal electron distributions also allow us to disentangle competing scattering processes and assess their impact on coherent electronic control through electron redistribution and thermalization. Our panoramic view of strong-field-driven electron motion in quantum materials lays the foundation for a microscopic understanding of some of the most discussed light-driven phenomena in condensed matter physics.
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Submitted 13 February, 2026;
originally announced February 2026.
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Field-driven attosecond photoinjection dynamics in semiconductors
Authors:
Giacomo Inzani,
Lyudmyla Adamska,
Amir Eskandari-asl,
Nicola Di Palo,
Gian Luca Dolso,
Bruno Moio,
Luciano Jacopo D'Onofrio,
Alessio Lamperti,
Alessandro Molle,
Rocío Borrego-Varillas,
Mauro Nisoli,
Stefano Pittalis,
Carlo Andrea Rozzi,
Adolfo Avella,
Matteo Lucchini
Abstract:
The route towards manipulation of the optoelectronic properties of matter beyond the current limits of electronics starts from a comprehensive study of the ultrafast dynamics triggered by interaction with light. Among them, a fundamental role is played by charge photoinjection, a complex process that stems from the interplay of many different physical phenomena, which cannot be easily disentangled…
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The route towards manipulation of the optoelectronic properties of matter beyond the current limits of electronics starts from a comprehensive study of the ultrafast dynamics triggered by interaction with light. Among them, a fundamental role is played by charge photoinjection, a complex process that stems from the interplay of many different physical phenomena, which cannot be easily disentangled. Single- and multi-photon absorption, diabatic tunnelling, intra-band motion, and field-driven band dressing, all concur in determining the overall excited electron population, dictating the electro-optical properties of a material. Here we investigate ultrafast photoinjection in a prototypical semiconductor (monocrystalline germanium) by using attosecond transient reflection spectroscopy. The precise pump-field characterization ensured by a simultaneous attosecond streaking experiment, in tandem with a comprehensive theoretical approach, allowed us to disentangle the different physical phenomena unfolding at different positions in the reciprocal space and at different timing within the envelope of the pump pulse. Moreover, we found that intra-band phenomena hinder charge injection, in contrast to what was previously observed for resonant, direct band-gap semiconductors. Therefore, besides other known parameters as the central wavelength and peak intensity, our results indicate that the pulse temporal envelope and the local band structure probed by intra-band effects are of key importance to achieve an optimal control over the ultrafast carrier injection process and tailor the complex optical and electronic properties of a semiconductor on the few- to sub-femtosecond time scale.
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Submitted 5 December, 2022;
originally announced December 2022.
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Reconstruction of ultrafast exciton dynamics with a phase-retrieval algorithm
Authors:
Bruno Moio,
Gian Luca Dolso,
Giacomo Inzani,
Nicola Di Palo,
Shunsuke A. Sato,
Rocío Borrego-Varillas,
Mauro Nisoli,
Matteo Lucchini
Abstract:
The first step to gain optical control over the ultrafast processes initiated by light in solids is a correct identification of the physical mechanisms at play. Among them, exciton formation has been identified as a crucial phenomenon which deeply affects the electro-optical properties of most semiconductors and insulators of technological interest. While recent experiments based on attosecond spe…
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The first step to gain optical control over the ultrafast processes initiated by light in solids is a correct identification of the physical mechanisms at play. Among them, exciton formation has been identified as a crucial phenomenon which deeply affects the electro-optical properties of most semiconductors and insulators of technological interest. While recent experiments based on attosecond spectroscopy techniques have demonstrated the possibility to observe the early-stage exciton dynamics, the description of the underlying exciton properties remains non-trivial. In this work we propose a new method called extended Ptychographic Iterative engine for eXcitons (ePIX), capable of reconstructing the main physical properties which determine the evolution of the quasi-particle with no prior knowledge of the exact relaxation dynamics or the pump temporal characteristics. By demonstrating its accuracy even when the exciton dynamics is comparable to the pump pulse duration, ePIX is established as a powerful approach to widen our knowledge of solid-state physics.
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Submitted 17 July, 2021;
originally announced July 2021.
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Time-frequency mapping of two-colour photoemission driven by harmonic radiation
Authors:
Bruno Moio,
Gian Luca Dolso,
Giacomo Inzani,
Nicola Di Palo,
Rocío Borrego-Varillas,
Mauro Nisoli,
Matteo Lucchini
Abstract:
The use of few-femtosecond, extreme ultraviolet (XUV) pulses, produced by high-order harmonic generation, in combination with few-femtosecond infrared (IR) pulses in pump-probe experiments has great potential to disclose ultrafast dynamics in molecules, nanostructures and solids. A crucial prerequisite is a reliable characterization of the temporal properties of the XUV and IR pulses. Several tech…
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The use of few-femtosecond, extreme ultraviolet (XUV) pulses, produced by high-order harmonic generation, in combination with few-femtosecond infrared (IR) pulses in pump-probe experiments has great potential to disclose ultrafast dynamics in molecules, nanostructures and solids. A crucial prerequisite is a reliable characterization of the temporal properties of the XUV and IR pulses. Several techniques have been developed. The majority of them applies phase reconstruction algorithms to a photoelectron spectrogram obtained by ionizing an atomic target in a pump-probe fashion. If the ionizing radiation is a single harmonic, all the information is encoded in a two-color two-photon signal called sideband (SB). In this work, we present a simplified model to interpret the time-frequency mapping of the SB signal and we show that the temporal dispersion of the pulses directly maps onto the shape of its spectrogram. Finally, we derive an analytical solution, which allows us to propose a novel procedure to estimate the second-order dispersion of the XUV and IR pulses in real time and with no need for iterative algorithms.
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Submitted 18 June, 2021;
originally announced June 2021.
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Unravelling the intertwined atomic and bulk nature of localised excitons by attosecond spectroscopy
Authors:
Matteo Lucchini,
Shunsuke A. Sato,
Giacinto D. Lucarelli,
Bruno Moio,
Giacomo Inzani,
Rocío Borrego-Varillas,
Fabio Frassetto,
Luca Poletto,
Hannes Hübener,
Umberto De Giovannini,
Angel Rubio,
Mauro Nisoli
Abstract:
The electro-optical properties of most semiconductors and insulators of technological interest are dominated by the presence of electron-hole quasiparticles called excitons. The manipulation of these hydrogen-like quasi-particles in dielectrics, has received great interest under the name excitonics that is expected to be of great potential for a variety of applications, including optoelectronics a…
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The electro-optical properties of most semiconductors and insulators of technological interest are dominated by the presence of electron-hole quasiparticles called excitons. The manipulation of these hydrogen-like quasi-particles in dielectrics, has received great interest under the name excitonics that is expected to be of great potential for a variety of applications, including optoelectronics and photonics. A crucial step for such exploitation of excitons in advanced technological applications is a detailed understanding of their dynamical nature. However, the ultrafast processes unfolding on few-femtosecond and attosecond time scales, of primary relevance in view of the desired extension of electronic devices towards the petahertz regime, remain largely unexplored. Here we apply attosecond transient reflection spectroscopy in a sequential two-foci geometry and observe sub-femtosecond dynamics of a core-level exciton in bulk MgF$_2$ single crystals. With our unique setup, we can access absolute phase delays which allow for an unambiguous comparison with theoretical calculations based on the Wannier-Mott model. Our results show that excitons surprisingly exhibit a dual atomic- and solid-like character which manifests itself on different time scales. While the former is responsible for a femtosecond optical Stark effect, the latter dominates the attosecond excitonic response and originates by the interaction with the crystal. Further investigation of the role of exciton localization proves that the bulk character persists also for strongly localised quasi-particles and allows us to envision a new route to control exciton dynamics in the close-to-petahertz regime.
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Submitted 29 June, 2020;
originally announced June 2020.
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Novel beamline for attosecond transient reflection spectroscopy in a sequential two-foci geometry
Authors:
Giacinto D. Lucarelli,
Bruno Moio,
Giacomo Inzani,
Nicola Fabris,
Liliana Moscardi,
Fabio Frassetto,
Luca Poletto,
Mauro Nisoli,
Matteo Lucchini
Abstract:
We present an innovative beamline for extreme ultraviolet (XUV)-infrared (IR) pump-probe reflection spectroscopy in solids with attosecond temporal resolution. The setup uses an actively stabilized interferometer, where attosecond pulse trains or isolated attosecond pulses are produced by high-order harmonic generation in gases. After collinear recombination, the attosecond XUV pulses and the femt…
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We present an innovative beamline for extreme ultraviolet (XUV)-infrared (IR) pump-probe reflection spectroscopy in solids with attosecond temporal resolution. The setup uses an actively stabilized interferometer, where attosecond pulse trains or isolated attosecond pulses are produced by high-order harmonic generation in gases. After collinear recombination, the attosecond XUV pulses and the femtosecond IR pulses are focused twice in sequence by toroidal mirrors, giving two spatially separated interaction regions. In the first region, the combination of a gas target with a time-of-flight spectrometer allows for attosecond photoelectron spectroscopy experiments. In the second focal region, an XUV reflectometer is used for attosecond transient reflection spectroscopy (ATRS) experiments. Since the two measurements can be performed simultaneously, precise pump-probe delay calibration can be achieved, thus opening the possibility for a new class of attosecond experiments on solids. Successful operation of the beamline is demonstrated by the generation and characterization of isolated attosecond pulses, the measurement of the absolute reflectivity of SiO2, and by performing simultaneous photoemission/ATRS in Ge.
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Submitted 25 February, 2020;
originally announced February 2020.