High-harmonic generation (HHG) in inversion-symmetric systems is typically restricted to odd harmonics by symmetry. Here, we show that this selection rule can be broken without modifying the underlying Hamiltonian. We investigate a boundary-driven Su-Schrieffer-Heeger (SSH) chain coupled to source and sink reservoirs and demonstrate that dissipative dynamics generates a nonequilibrium steady state carrying a finite DC current. While the SSH Hamiltonian retains inversion symmetry, the current-carrying steady-state density matrix does not, leading to the emergence of even harmonics in the emitted spectrum. Using a correlation-matrix approach based on the Lindblad master equation, we obtain the steady state and calculate the resulting HHG response. We find that the intensity of the even harmonics is directly controlled by the transport current, establishing a link between nonequilibrium charge transport and HHG selection rules. Our results uncover a mechanism for even-harmonic generation that relies solely on nonequilibrium steady-state symmetry breaking and provide a route to probing transport currents through ultrafast nonlinear spectroscopy in centrosymmetric quantum systems.
High harmonic generation (HHG) has emerged as a powerful probe of ultrafast electron dynamics in solids. However, in strongly correlated materials, where electronic excitations arise from many-body interactions rather than single-particle band dispersion, the field remains in its infancy. Here, we report HHG up to the 23
rd order in the prototypical Mott insulator La
2CuO
4. We observe a robust 4 eV cutoff that is independent of driving field strength, revealing an intrinsic energy scale defined by the Hubbard bands. Using time-resolved high harmonic spectroscopy, we disentangle the distinct contributions of carrier creation, intraband acceleration, and interband recombination to the nonequilibrium radiation spectrum. We demonstrate that photo-doping triggers a fundamental reorganization of the many-body manifolds above a critical excitation density, a process that renormalizes the band curvature and suppresses nonlinear intraband currents, thereby directly imprinting the signature of many-body band reconstruction onto the harmonic emission. These results establish HHG as a sensitive probe of subtle correlation-driven electronic reconstructions and highlight that many-body interactions enable extreme nonlinear optical responses that are highly tunable in nonequilibrium states.
In the realm of open quantum systems, steady states and high-harmonic generation (HHG) existing far from equilibrium have become core pillars of ultrafast science. Most solid-state research explores charge HHG with limited investigations into spin degrees of freedom. In this study, we theoretically address spin HHG in the steady state resulting from the terahertz laser-driven spin-phonon coupling in a dissipative dimerized spin-1/2 chain. Instead of directly driving spins using time-dependent magnetic fields, we employ the magnetophononic mechanism, where the laser first drives the lattice, and then the excited lattice subsequently drives the spins. We investigate the role of various model parameters for optimizing HHG. Increasing the laser amplitude amplifies spin HHG beyond the perturbative regime, enhancing both harmonic amplitudes and orders. We find that configuring the drive frequency far below the spin band yields the highest harmonic order. Additionally, we provide a theory matching the numerical results under weak spin-phonon coupling and propose an experimental procedure to probe the emission spectrum of spin HHG.
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.
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.
We investigate the non-equilibrium topology of the steady state of a periodically driven, dissipative Su-Schrieffer-Heeger (SSH) chain using the ensemble geometric phase (EGP)
φEGP, a generalisation of the Zak phase to mixed states. The coupling to thermal reservoirs is treated microscopically within Floquet-Born-Markov theory without the rotating-wave approximation. We classify the steady state rather than the generator of the dynamics, using its purity spectrum as the analogue of a band structure. We show that, within the EGP framework, the
Z×Z structure of isolated chiral-symmetric Floquet SSH systems generally does not carry over to the steady state. Instead, the steady state carries a single invariant whose type is set by an underlying symmetry. When this symmetry holds, the invariant is
Z2-valued, with quantised
φEGP=±π/2 at all times and finite temperatures. The EGP can switch within a driving period, tracking the presence of edge modes in the open-boundary purity spectrum and thereby establishing a bulk-boundary correspondence. The fraction of each period spent in the nontrivial regime varies continuously with the driving frequency, and the switching disappears if the dependence of the dissipator on the drive is neglected. When the symmetry is broken,
φEGP is no longer quantised, but its winding over a drive period
T defines an invariant
νT∈Z, with no purity-spectrum bulk-boundary correspondence. We propose that its changes signal temperature- and frequency-driven topological phase transitions. Our formalism extends to general quadratic fermionic systems with linear bath couplings.