Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2512.13140

Intense-Laser Nondipole-Induced Symmetry Breaking in Solids

Asger Weeth, Lars Bojer Madsen

quant-phcond-mat.mtrl-sciphysics.opticsSubmitted Dec 15, 2025• Announced Dec 16, 2025
arXivHTMLPDF

Abstract

High-harmonic spectroscopy in solids gives insight into the inner workings of solids, such as reconstructing band structures or probing the topological phase of materials. High-harmonic generation (HHG) is a highly non-linear phenomena and simulations guide interpretation of experimental results. These simulations often rely on the electric dipole approximation, even though the driving fields enter regimes that challenge its accuracy. Here, we investigate effects of including nondipole terms in the light-matter coupling in simulations of HHG in materials with both topologically trivial and non-trivial phases. We show how the inclusion of nondipole terms breaks dipole selection rules, allowing for new polarizations of the generated light. Specifically we find that helicity, completely absent in the dipole approximation, is induced by the nondipole extension, and that this helicity is dependent on the topological phase of the material.

Comments
5 pages, 4 figures

Related papers

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

Christian Saugbjerg Lange, Lars Bojer Madsen

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-pharXiv:2602.16454•Feb 19, 2026

Geometric Control of Cat States in High Harmonic Generation

Arti Gaharwar, Rocío Borrego-Varillas, Marcelo F. Ciappina +6 more

High-harmonic generation (HHG) provides a powerful platform for exploring the interaction between intense laser fields and matter on ultrafast timescales. Beyond its conventional description in terms of emitted radiation and electron dynamics, a fully quantum treatment of HHG reveals that the nonlinear light-matter interaction can modify the quantum state of the driving field itself, establishing correlations between the fundamental and harmonic modes. This perspective opens new possibilities for using HHG as a tool to engineer and control nonclassical states of light. In this work, we investigate the geometric properties of optical Schroedinger cat states generated in HHG via conditioning and post-selection. By analyzing the coherent-state displacements induced by different structured driving fields, we characterize the resulting phase-space evolution and the associated geometric phases of the generated quantum states. Particular emphasis is placed on how the polarization and spatial-mode structure of the driving light influence the geometry and evolution of displaced coherent states. Our results demonstrate that structured light offers a versatile means of controlling the geometric dynamics of HHG-generated cat states across the parameter space. Furthermore, we discuss the prospects for realizing genuinely topological optical cat states by exploiting more complex structured light configurations.

physics.opticsCross-listedarXiv:2608.20119•Aug 21, 2026•0 citations

High Harmonic Generation in Strongly Correlated Systems

Markus Lysne

In recent years, the study of phenomena pertaining to non-linear properties of materials has seen a major upswing - especially in the context of High Harmonic Generation (HHG). In this thesis, an account of the current state of research in this area will be given. In addition, we seek to combine two seemingly disparate areas of research, both of which have been the subject of numerous years of intense research - namely those of HHG in solid state materials, and the optical response of strongly correlated quantum systems. To this end we will rely on solving the Fermi-Hubbard model coupled to an electromagnetic field under time propagation. With the aid of both numerical work and simple energy level analyses, we are able to explain most of the characteristics of our calculated spectra. High field strength will induce a Mott insulator to metal phase transition whose imprints will be established through time resolved high harmonic emission and doublon and spin correlation functions. The various HHG spectra, together with said correlation functions will be studied through an Exact diagonalization algorithm in conjunction with an Arnoldi-Lanczos time propagator. The parameter space considered is comprised of the electron-electron repulsion energy, U, and peak electric field strength. Additionally, the study is not restricted to half-filling, and results for doped materials will be presented. We find that the high U-induced energy gap in the Fermi-Hubbard model plays the same role as the valence-conduction bandgap in models like for instance the Semiconductor Bloch Equations when it comes to generating high harmonic radiation through multiphoton processes. The central part of this thesis aims at providing insight to and making further contributions to an article published in Nature Photonics in March 2018. [1]

•Jun 23, 2018•0 citations

Intensity dependence of the phase of harmonics in one- and two-frequency laser fields

W.-C. Liu, Charles W. Clark

The phase relationship between an induced atomic dipole moment and a driving laser field is an essential aspect of high harmonic generation (HHG) in a dense medium. A ``phase-matching'' criterion must be fulfilled to obtain coherent amplification of harmonic radiation, which is critical for practical HHG. We have performed numerical calculations on model atoms to survey the intensity dependence of the phase in the case of strong one- or two-frequency laser fields. The calculations show that multiphoton resonances significantly affect the yield of harmonic generation and that in the ``plateau'' regime, the phases exhibit only weak dependence upon the intensity of the driving field. \textcopyright{}1996 The American Physical Society.

Physical Review A•May 1, 1996•5 citations

Noninteger high-order harmonic generation from extended correlated systems

Christian Saugbjerg Lange, Thomas Hansen, Lars Bojer Madsen

The spectra produced by high-order 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.

arXiv:2403.08327•Physical Review A•Jun 3, 2024•11 citations

High-harmonic generation in systems with chiral Bloch states: application to rhombohedral graphene

Jessica O. de Almeida, Wilton J. M. Kort-Kamp, Mathias S. Scheurer

Nonlinear light-matter interaction and, in particular, high-harmonic generation (HHG) are fundamentally interesting and frequently discussed as versatile probes of quantum materials with potential for optical information processing applications. Meanwhile, there has also been significant progress in graphene-based multilayer systems to engineer interesting band structures and boost correlation effects. Motivated by the successful demonstration of HHG in graphene, we here study this effect in rhombohedral stacks of $n$ layers of graphene, a recent very prominent representative of correlated multilayer graphene systems. We show how the chiral Bloch states of the valleys of this system crucially affect the HHG. The "winding" of the Bloch states scales linearly with $n$, just like the dominant harmonic order. The location of the strongest quantum geometry in momentum space on a ring of finite radius is shown to be imprinted on the time-dependent momentum distribution at the beginning of the strong laser pulse. We further demonstrate that the presence of an interaction-induced splitting of the two valleys leads to a complex interplay of the opposite chiralities of the two valleys, directly visible in the $n$ dependence of the circular dichroism. We also analyze the impact of doping and identify a quantity that tracks the net chirality of the occupied states. Our findings show that rhombohedral graphene constitutes a promising platform for exploring rich nonlinear optical phenomena.

cond-mat.mes-hallCross-listedarXiv:2604.11984•Apr 15, 2026
High-harmonic spectroscopy in solids gives insight into the inner workings of solids, such as reconstructing band structures or probing the topological phase of materials. High-harmonic generation (HHG) is a highly non-linear phenomena and simulations guide interpretation of experimental results. These simulations often rely on the electric dipole approximation, even though the driving fields enter regimes that challenge its accuracy. Here, we investigate effects of including nondipole terms in the light-matter coupling in simulations of HHG in materials with both topologically trivial and non-trivial phases. We show how the inclusion of nondipole terms breaks dipole selection rules, allowing for new polarizations of the generated light. Specifically we find that helicity, completely absent in the dipole approximation, is induced by the nondipole extension, and that this helicity is dependent on the topological phase of the material.
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-harmonic generation (HHG) provides a powerful platform for exploring the interaction between intense laser fields and matter on ultrafast timescales. Beyond its conventional description in terms of emitted radiation and electron dynamics, a fully quantum treatment of HHG reveals that the nonlinear light-matter interaction can modify the quantum state of the driving field itself, establishing correlations between the fundamental and harmonic modes. This perspective opens new possibilities for using HHG as a tool to engineer and control nonclassical states of light. In this work, we investigate the geometric properties of optical Schroedinger cat states generated in HHG via conditioning and post-selection. By analyzing the coherent-state displacements induced by different structured driving fields, we characterize the resulting phase-space evolution and the associated geometric phases of the generated quantum states. Particular emphasis is placed on how the polarization and spatial-mode structure of the driving light influence the geometry and evolution of displaced coherent states. Our results demonstrate that structured light offers a versatile means of controlling the geometric dynamics of HHG-generated cat states across the parameter space. Furthermore, we discuss the prospects for realizing genuinely topological optical cat states by exploiting more complex structured light configurations.
In recent years, the study of phenomena pertaining to non-linear properties of materials has seen a major upswing - especially in the context of High Harmonic Generation (HHG). In this thesis, an account of the current state of research in this area will be given. In addition, we seek to combine two seemingly disparate areas of research, both of which have been the subject of numerous years of intense research - namely those of HHG in solid state materials, and the optical response of strongly correlated quantum systems. To this end we will rely on solving the Fermi-Hubbard model coupled to an electromagnetic field under time propagation. With the aid of both numerical work and simple energy level analyses, we are able to explain most of the characteristics of our calculated spectra. High field strength will induce a Mott insulator to metal phase transition whose imprints will be established through time resolved high harmonic emission and doublon and spin correlation functions. The various HHG spectra, together with said correlation functions will be studied through an Exact diagonalization algorithm in conjunction with an Arnoldi-Lanczos time propagator. The parameter space considered is comprised of the electron-electron repulsion energy, U, and peak electric field strength. Additionally, the study is not restricted to half-filling, and results for doped materials will be presented. We find that the high U-induced energy gap in the Fermi-Hubbard model plays the same role as the valence-conduction bandgap in models like for instance the Semiconductor Bloch Equations when it comes to generating high harmonic radiation through multiphoton processes. The central part of this thesis aims at providing insight to and making further contributions to an article published in Nature Photonics in March 2018. [1]
The phase relationship between an induced atomic dipole moment and a driving laser field is an essential aspect of high harmonic generation (HHG) in a dense medium. A ``phase-matching'' criterion must be fulfilled to obtain coherent amplification of harmonic radiation, which is critical for practical HHG. We have performed numerical calculations on model atoms to survey the intensity dependence of the phase in the case of strong one- or two-frequency laser fields. The calculations show that multiphoton resonances significantly affect the yield of harmonic generation and that in the ``plateau'' regime, the phases exhibit only weak dependence upon the intensity of the driving field. \textcopyright{}1996 The American Physical Society.
The spectra produced by high-order 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.
Nonlinear light-matter interaction and, in particular, high-harmonic generation (HHG) are fundamentally interesting and frequently discussed as versatile probes of quantum materials with potential for optical information processing applications. Meanwhile, there has also been significant progress in graphene-based multilayer systems to engineer interesting band structures and boost correlation effects. Motivated by the successful demonstration of HHG in graphene, we here study this effect in rhombohedral stacks of nnn layers of graphene, a recent very prominent representative of correlated multilayer graphene systems. We show how the chiral Bloch states of the valleys of this system crucially affect the HHG. The "winding" of the Bloch states scales linearly with nnn, just like the dominant harmonic order. The location of the strongest quantum geometry in momentum space on a ring of finite radius is shown to be imprinted on the time-dependent momentum distribution at the beginning of the strong laser pulse. We further demonstrate that the presence of an interaction-induced splitting of the two valleys leads to a complex interplay of the opposite chiralities of the two valleys, directly visible in the nnn dependence of the circular dichroism. We also analyze the impact of doping and identify a quantity that tracks the net chirality of the occupied states. Our findings show that rhombohedral graphene constitutes a promising platform for exploring rich nonlinear optical phenomena.