arXiv subjects

Christian Saugbjerg Lange

Publications and source records attributed to Christian Saugbjerg Lange.

8 recordsLinked to original sources

arXiv2026

Edge states and quantum optical high-harmonic generation from topological insulators

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.

quant-ph↗

arXiv2026

Limitations of an approximative phase-space description in strong-field quantum optics

In recent years, strong-field processes such as high-order harmonic generation (HHG) and above-threshold ionization driven by nonclassical states of light have become an increasingly popular field of study. The theoretical modeling of these processes often applies an approximate phase-space expansion of the nonclassical driving field in terms of coherent states, which has been shown to accurately predict the harmonic spectrum. However, its accuracy for the computation of quantum optical observables like the degree of squeezing and photon statistics has not been thoroughly considered. In this work, we introduce this approximative phase-space description and discuss its accuracy, and we find that it mischaracterizes the quantum optical properties of the driving laser by making it an incoherent mixture of classical states. We further show that this error in the driving field description maps onto the light emitted from HHG, as neither sub-Poissonian photon statistics nor quadrature squeezing below vacuum fluctuations can be captured by the approximative phase-space description. Lastly, to benchmark the approximative phase-space description, we consider the quantum HHG from a one-band model, which yields an exact analytical solution. Using the approximative phase-space representation with this specific model, we find a small quantitative error in the quadrature variance of the emitted field that scales with pulse duration and emitter density. Our results show that using this approximative phase-space description can mischaracterize quantum optical observables. Attributing physical meaning to such results should therefore be accompanied by a quantitative analysis of the error.

quant-ph↗

arXiv2025

High-Order Harmonic Generation with Beyond-Semiclassical Emitter Dynamics: A Strong-Field Quantum Optical Heisenberg Picture Approach

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.

quant-ph↗

arXiv2025

Excitonic Enhancement of Squeezed Light in Quantum-Optical High-Harmonic Generation From a Mott Insulator

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. So far, however, no clear nonclassical signal at a distinct and unambiguous frequency has been predicted. 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. 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.

quant-ph↗

arXiv2025

High-Harmonic Generation in a Crystal Driven by Quantum Light

We study intraband high-harmonic generation (HHG) in a crystal driven by quantum light. Previous theoretical studies have developed a framework based on coherent state expansions in terms of P distributions to consider nonclassical driving fields for HHG in atoms. Here, we adapt this framework to the context of solids and consider an intraband model of ZnO. We investigate the effect of the quantum optical nature of the driving field on the harmonic spectra including the cutoff and the intensity scaling of the harmonics with driving field intensity. Based on analytical calculations in the Floquet limit, we explain why driving with thermal light or bright-squeezed vacuum (BSV) produces a much higher cutoff than when driving with fields described by coherent or Fock states. Further, we derive an expression for the generated time-dependent electric field and its fluctuations and find that it inherits characteristics of the driving field. Finally, we discuss the limitations of an approximative positive P representation, which is introduced to be able to reduce the numerical complexity for Fock and BSV driving fields.

quant-ph↗

arXiv2024

Hierarchy of approximations for describing quantum light from high-harmonic generation: A Fermi-Hubbard model study

The quantum optical description of high-order harmonic generation where both the electrons of the generating medium and the driving and generated light fields are described quantum mechanically has been of significant interest in the past years. The quantum optical formulation leads to equations of motion for the generated light field in which the quantum optical field couples to the time-dependent current of the electronic medium irrespectively of the specifics of the electronic system being an atom, molecule, or solid. These equations of motion are not solvable for any realistic system and accurate and verified approximations are hence needed. In this work, we present a hierarchy of approximations for the equations of motion for the photonic state. At each level in this hierarchy, we compare it to the previous level justifying the validity using the Fermi-Hubbard model as an example of an electronic system with correlations. This model allows us to perform an accurate simulation of the electron motion of all the required states. We find that for the typical experimental situation of weak quantized-light-matter-coupling constant and at intensities well below the damage threshold, an explicit expression for the generated quantum light, referred to as the Markov-state approximation (MSA), captures the high-harmonic spectrum quantitatively and describes the single-mode quantum properties of the generated light as characterized by the Mandel-Q parameter and the degree of squeezing qualitatively.

quant-ph↗

arXiv2024

Noninteger high-harmonic generation from extended correlated systems

The spectra produced by high-harmonic generation (HHG) typically exhibit well-defined peaks at odd integers times the laser frequency. However, in recent investigations of HHG from correlated materials, spectra exhibit signals at noninteger harmonics which do not conform to the well-known symmetry-based selection rules for HHG-spectra. Here, we use the Fermi-Hubbard model to study HHG from a linear chain of atoms. This model allows us to study both the correlated and uncorrelated phases through a specification of the amount of onsite electron-electron repulsion. The presence of signal at noninteger harmonics can be interpreted as originating from the population of multiple Floquet states. We show how this coupling to different Floquet states depends on the characteristics of the driving pulse and the strength of the electron-electron interaction in the system.

physics.atom-ph↗

arXiv2023

Electron-correlation induced nonclassicallity of light from high-harmonic generation

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.

quant-ph↗