Recent experimental advancements in ultrafast pump-probe setups drive a growing need for efficient and insightful theoretical methods. This study will delve into the intricacies of our newly developed approach, the Dynamical Projective Operatorial Approach (DPOA). DPOA stands out as a highly efficient model-Hamiltonian method capable of calculating a wide range of single/multi-time single/multi-particle properties, such as excitation populations, out-of-equilibrium Green's functions, TR-ARPES signals, and various response functions. When dealing with transient optical properties, utilizing the DPOA formulation and capitalizing on the weak intensity of the probe pulse, we efficiently compute the linear response of the pumped system to a generic probe pulse, significantly accelerating calculations. Alongside the theoretical framework, we present noteworthy results that experimentalists can utilize to establish connections between observed effects and their underlying physical phenomena.
Recent experimental advancements in ultrafast pump-probe setups drive a growing need for efficient and insightful theoretical methods. This study will delve into the intricacies of our newly developed approach, the Dynamical Projective Operatorial Approach (DPOA). DPOA stands out as a highly efficient model-Hamiltonian method capable of calculating a wide range of single/multi-time single/multi-particle properties, such as excitation populations, out-of-equilibrium Green's functions, TR-ARPES signals, and various response functions. When dealing with transient optical properties, utilizing the DPOA formulation and capitalizing on the weak intensity of the probe pulse, we efficiently compute the linear response of the pumped system to a generic probe pulse, significantly accelerating calculations. Alongside the theoretical framework, we present noteworthy results that experimentalists can utilize to establish connections between observed effects and their underlying physical phenomena.
We develop a general theoretical framework for computing the time-resolved magneto-optical Kerr effect in ultrafast pump-probe setups, formulated within the Dynamical Projective Operatorial Approach (DPOA) and its application to the generalized linear-response theory for pumped systems. Furthermore, we exploit this formalism to express the post-pump optical conductivity and consequently the Kerr rotation in terms of the time-evolved single-particle density matrix (SPDM), providing a transparent and computationally efficient description of photo-excited multi-band systems. This extension, in addition to its lower computational cost, has the advantage of allowing the inclusion of phenomenological damping. We illustrate the formalism using both (i) a two-band tight-binding model, which captures the essential physics of ultrafast spin-charge dynamics and the Kerr rotation, and (ii) weakly spin-polarized germanium, as a realistic playground with a complex band structure. The results demonstrate that, by exploiting DPOA and/or its SPDM extension, one can reliably reproduce both the short-time features under the pump-pulse envelope and the long-time dynamics after excitation, offering a versatile framework for analyzing time-resolved magneto-optical Kerr effect experiments in complex materials. Moreover, this analysis clearly shows that the Kerr rotation can be used to deduce experimentally the relevant n-photon resonances for a given specific material.
We employ the Dynamical Projective Operatorial Approach (DPOA) to investigate the ultrafast optical excitations of germanium under intense, ultrashort pump pulses. The method has very low resource demand relative to many other available approaches and enables detailed calculation of the residual electron and hole populations induced by the pump pulse. It provides direct access to the energy distribution of excited carriers and to the total energy transferred to the system. By decomposing the response into contributions from different multi-photon resonant processes, we systematically study the dependence of excited-carrier density and absorbed energy on key pump-pulse parameters: duration, amplitude, and photon energy. Our results reveal a complex interplay between these parameters, governed by resonant Rabi-like dynamics and competition between different multi-photon absorption channels. For the studied germanium setup, we find that two-photon processes are generally dominant, while one- and three-photon channels become significant under specific conditions of pump-pulse frequency, duration, and intensity. This comprehensive analysis offers practical insights for optimizing ultrafast optical control in semiconductors by targeting specific multi-photon pathways.
Quasiparticles are fundamental in describing the complex many-body interactions underlying single-particle excitations, playing a key role in understanding the macroscopic properties of quantum materials. Recent advancements in ultrafast laser technology, combined with various detection methods, have enabled precise monitoring and manipulation of quantum states and their dynamic processes. These developments not only enhance our comprehension of quasiparticle excitation mechanisms but also facilitate driving materials into non-equilibrium states, uncovering novel physical phenomena and advancing the design and application of innovative functional materials. The computational approach based on real-time time-dependent density functional theory (rt-TDDFT) transcends the limitations of linear response theory, enabling first-principles simulations of the dynamic response of strongly coupled quasiparticles under non-equilibrium conditions. The proposed method provides accurate predictions of highly nonlinear phenomena induced by strong laser fields, offering deeper insights into the underlying physical mechanisms. These theoretical insights are crucial for optimizing the performance of optoelectronic devices. This paper introduces the theoretical foundations of Ehrenfest dynamics within the framework of rt-TDDFT and presents case studies on the evolution of various quasiparticles under laser excitation. The results demonstrate the significant potential of ultrafast lasers for probing and controlling the properties of quantum materials, while also underscoring the vital role of dynamic simulations for studying non-equilibrium states and their time-domain characteristics.
Excited-state dynamics in condensed matter systems plays a crucial role in determining their properties. Understanding and controlling ultrafast dynamics across multiple dimensions—such as time, space, energy, momentum, and spin—has become a key emerging direction in modern condensed matter physics. In recent decades, time-resolved ultrafast laser technology based on pump-probe techniques has advanced significantly. This technology has been integrated with various experimental methods, leading to developments in ultrafast spectroscopy, time- and angle-resolved photoemission spectroscopy (TR-ARPES), ultrafast scanning tunneling microscopy (STM), ultrafast electron diffraction (UED), and ultrafast X-ray techniques, enabling the study of lattice, electron, and spin dynamics. Meanwhile, to provide a clearer physical picture of ultrafast dynamics, real-time first-principles methods have been developed by combining electronic structure methods with dynamic approaches, allowing the study of multidimensional lattice, electron, and spin behaviors. This article reviews recent progress in the field and discusses its future challenges and opportunities.
The exploration of ultrafast phenomena is a frontier of condensed matter research, where the interplay of theory, computation, and experiment is unveiling new opportunities for understanding and engineering quantum materials. With the advent of advanced experimental techniques and computational tools, it has become possible to probe and manipulate nonequilibrium processes at unprecedented temporal and spatial resolutions, providing insights into the dynamical behavior of matter under extreme conditions. These capabilities have the potential to revolutionize fields ranging from optoelectronics and quantum information to catalysis and energy storage. This roadmap captures the collective progress and vision of leading researchers, addressing challenges and opportunities across key areas of ultrafast science and condensed matter. Contributions in this roadmap span the development of ab initio methods for time-resolved spectroscopy, the dynamics of driven correlated systems, the engineering of materials in optical cavities, and the adoption of FAIR principles for data sharing and analysis. Together, these efforts highlight the interdisciplinary nature of ultrafast research and its reliance on cutting-edge methodologies, including quantum electrodynamical density-functional theory, correlated electronic structure methods, nonequilibrium Green’s function approaches, quantum and ab initio simulations.
For decades, ultrafast light-matter interactions have provided a powerful means to observe electrons in motion across a wide range of physical systems. This dissertation builds new theoretical frameworks to make sense of the emergent phenomena that arise when light drives matter into the strong-field regime, spanning atomic, molecular, and condensed-matter systems. The resulting dynamics leave their fingerprints on a variety of observables, such as photoionization spectra, high-harmonic generation, and nonlinear spectroscopic signals, each of which provides a different window onto the underlying electronic motion. The work is organized into two parts.The first part focuses on the electric-field observables of nonlinear optical signals. Because both the amplitude and phase of the emitted field are experimentally accessible through techniques such as spectral interferometry and electro-optic sampling, the full field itself serves as a rich observable for characterizing nonlinear responses in atomic, molecular, and condensed-matter systems. Leveraging this, the simulations presented here uncover novel and largely unexplored physical phenomena encoded in these field observables. The second part turns to optical spectroscopy with quantum light. Although nonlinear optical processes are conventionally modeled within a semiclassical framework, treating the matter quantum mechanically while the driving ultrafast fields remain classical, the resulting signals can nonetheless exhibit intrinsically non-classical properties. Building on this insight, a framework for interpreting experimental data is introduced and used to show that four-wave mixing driven by ultrafast femtosecond laser pulses generates bright squeezed light. Beyond squeezed light, strong field-matter interactions can also produce attosecond entangled photons, a distinct form of quantum light. Several strategies are proposed to enhance the efficiency of their generation, with the developed theory predicting rates of energy-time entangled biphoton production orders of magnitude beyond those achievable with conventional spontaneous parametric down-conversion (SPDC) sources. The studies presented here are initial steps toward investigating quantum properties of these systems through quantum phynonlinear spectroscopy, which is not achievable with classical light.