The strong-field induced generation of nonclassical states of light is not only a subject of fundamental research but also has potential usage in quantum information science and technology. The emerging field of strong-field quantum optics has developed ways of generating nonclassical states of light from the process of high-harmonic generation (HHG) at much wider frequency ranges and intensities than is typical for quantum optics. Here, we study the response from an exciton in a Mott-insulating system, using the extended Hubbard model. We find that the exciton plays a key role in the nonclassical response and generates squeezing at the exciton energy, showing a clear mapping between the quantum nature of the electronic system and the quantum nature of emitted radiation. We relate this nonclassical response to the nonvanishing time correlations of the current operator in the system. Our work defines a direction for experimental work to search for squeezed light from HHG in a spectrally confined region defined by the exciton energy.
The strong-field induced generation of nonclassical states of light is not only a subject of fundamental research but also has potential usage in quantum information science and technology. The emerging field of strong-field quantum optics has developed ways of generating nonclassical states of light from the process of high-harmonic generation (HHG) at much wider frequency ranges and intensities than is typical for quantum optics. Here, we study the response from an exciton in a Mott-insulating system, using the extended Hubbard model. We find that the exciton plays a key role in the nonclassical response and generates squeezing at the exciton energy, showing a clear mapping between the quantum nature of the electronic system and the quantum nature of emitted radiation. We relate this nonclassical response to the nonvanishing time correlations of the current operator in the system. Our work defines a direction for experimental work to search for squeezed light from HHG in a spectrally confined region defined by the exciton energy.
We study the effect of electron-electron correlations on the quantum state of the light emitted from high-harmonic generation (HHG). The quantum state of the emitted light is obtained by using a fully quantum mechanical description of both the optical modes as well as the electronic system. This is different from the usual semiclassical description of HHG, which only treats the electronic target system quantum mechanically. Using the generic Fermi-Hubbard model, the strength of the electron-electron correlation can be treated as a parameter enabling us to investigate the two limiting cases of a completely uncorrelated phase and a correlated Mott-insulating phase. In the completely uncorrelated phase, the model reduces to a single-band tight-binding model in which only intraband currents contribute to the spectrum. In this limit, we analytically find that the emitted light is in a classical coherent state. In the Mott-insulating phase, a consideration of the photon statistics and squeezing of the emitted photonic state shows that the inter-Hubbard-subband current generates nonclassical light. In this sense, we show that electron-electron correlation can induce the generation of nonclassical states of light.
The strong-field process of high-harmonic generation (HHG) has, in recent years, been treated from a quantum optical perspective in the emerging research area of strong-field quantum optics. These investigations show that HHG radiation is, in general, in a nonclassical state of light. However, the quantum optical treatment of HHG from topological nontrivial materials is missing. Here, we aim to address this gap in current knowledge and consider the quantum optical HHG response from the Su-Schrieffer-Heeger model, a finite chain of atoms with both a topologically trivial and nontrivial insulating phase, the latter supporting edge states. We find that HHG from both topological phases is squeezed at the band-gap frequency. Interestingly, while the harmonic spectrum discriminates the two topological phases of the system, the degree of squeezing only discriminates the phases for smaller chain lengths. We attribute this difference to a relative increase in overlap between bulk and edge states in the topological nontrivial phase for smaller systems. Our findings reveal how the strength of dipole couplings governs the nonclassical HHG response and define new research questions on topologically protected generation of quantum light in strong-field physics.
High-order harmonic generation (HHG) is a significant nonlinear phenomenon triggered by the interaction of intense laser fields with matter. As a high-quality coherent light source, it has found extensive applications in areas such as attosecond pulse generation and ultrafast spectroscopy. Recent studies have revealed the prevalent existence of nonclassical effects in high-harmonic radiation, including nonclassical photon statistics, intermodal correlations, and entanglement. It holds broad development prospects in directions including the generation of nonclassical states with high photon numbers, precise control of entanglement in solid-state systems, and integration with cavity quantum electrodynamics. This review systematically summarizes the research progress concerning the nonclassical effects in HHG. It begins with an overview of the semiclassical model and strong-field quantum theory, clarifying the differences in the quantum properties of harmonic fields when driven by coherent states versus nonclassical states. Subsequently, it focuses on various physical schemes for generating nonclassical optical field states, such as optical cat states and squeezed states, via this process. Research on strong-field HHG not only deepens our understanding of the fundamental nature of intense laser physics but also opens new avenues for the generation and application of quantum light sources in the extreme ultraviolet to X-ray spectral regions.
Quantum-optical descriptions of strong-field processes have attracted significant attention in recent years. Typically, the theoretical modeling has been conducted in the Schrödinger picture, where results are only obtainable under certain approximations, while, in contrast, the Heisenberg picture has remained relatively unexplored. In this work, we develop an accurately controlled perturbative expansion of the time-evolution operator in the Heisenberg picture and derive beyond-semiclassical corrections to the emitter dynamics due to the coupling to the quantized electromagnetic field, capturing effects of the quantum fluctuations present in the latter. We focus on high-order harmonic generation (HHG), where the approach is accurate in parameter regimes of current interest and it gives closed-form expressions for key observables. This formulation not only simplifies numerical calculations compared to the Schrödinger-picture approach but also provides a clear correspondence between nonclassical features of the emitted light and the underlying induced dynamics of the generating medium including quantum fluctuations. Moreover, the Heisenberg framework naturally yields scaling relations with the number of independent emitters, enabling us to assess whether nonclassical behavior should persist under typical experimental conditions involving large emitter ensembles. Interestingly, we find that the degree of squeezing increases with the number of emitters, whereas the photon statistics approaches a classical Poissonian distribution in the many-emitter limit. We also find that the beyond-semiclassical emitter dynamics significantly enhances the degree of squeezing of the emitted light. Our work advances the theoretical understanding of quantum-optical HHG and introduces an accessible and well-controlled framework to describe realistic experiments.
High-harmonic generation (HHG) has emerged as a pivotal process in strong-field physics, yielding extreme ultraviolet radiation and attosecond pulses for a wide range of applications. Furthermore, its emergent connection with the field of quantum optics has revealed its potential for generating nonclassical states of light. Here, we investigate the process of high-harmonic generation in semiconductors under a quantum optical perspective while using a Bloch-based solid-state description. Through the implementation of quantum operations based on the measurement of high-order harmonics, we demonstrate the generation of nonclassical light states similar to those found when driving atomic systems. These states are characterized using diverse quantum optical observables and quantum information measures, showing the influence of electron dynamics on their properties. Additionally, we analyze the dependence of their features on solid characteristics such as the dephasing time and crystal orientation, while also assessing their sensitivity to changes in driving field strength. This paper provides insights into HHG in semiconductors and its potential for generating nonclassical light sources.
To study excitonic effects on high-harmonic generation (HHG) in Mott insulators, we investigate pumped nonequilibrium dynamics in the one-dimensional extended Hubbard model. By employing time-dependent calculations based on the exact diagonalization and infinite time-evolving block decimation methods, we find the strong enhancement of the HHG intensity around the exciton energy. The subcycle analysis in the sub-Mott-gap regime shows that the intensity region of the time-resolved spectrum around the exciton energy splits into two levels and oscillates following the driving electric field. This excitonic dynamics is qualitatively different from the dynamics of free doublon and holon but favorably contributes to HHG in the Mott insulator.