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Register a new userFloquet-Theoretical Formulation and Analysis of High-Harmonic Generation in Solids
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By using the Floquet eigenstates, we derive a formula to calculate the high-harmonic components of the electric current (HHC) in the setup where a monochromatic laser field is turned on at some time. On the basis of this formulation, we study the HHC spectrum of electrons on a one-dimensional chain with the staggered potential to study the effect of multiple sites in the unit cell such as the systems with charge density wave (CDW) order. With the help of the solution for the Floquet eigenstates, we analytically show that two plateaus of different origins emerge in the HHC spectrum. The widths of these plateaus are both proportional to the field amplitude, but inversely proportional to the laser frequency and its square, respectively. We also show numerically that multi-step plateaus appear when both the field amplitude and the staggered potential are strong.
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We consider several aspects of high-order harmonic generation in solids: the effects of elastic and inelastic scattering; varying pulse characteristics; and inclusion of material-specific parameters through a realistic band structure. We reproduce many observed characteristics of high harmonic generation experiments in solids including the formation of only odd harmonics in inversion-symmetric materials, and the nonlinear formation of high harmonics with increasing field. We find that the harmonic spectra are fairly robust against elastic and inelastic scattering. Furthermore, we find that the pulse characteristics play an important role in determining the harmonic spectra.
We consider noninteracting electrons coupled to laser fields, and study perturbatively the effects of the lattice potential involving disorder on the harmonic components of the electric current, which are sources of high-order harmonic generation (HHG). By using the Floquet-Keldysh Green functions, we show that each harmonic component consists of the coherent and the incoherent parts, which arise respectively from the coherent and the incoherent scatterings by the local ion potentials. As the disorder increases, the coherent part decreases, the incoherent one increases, and the total harmonic component of the current first decreases rapidly and then approaches a nonzero value. Our results highlight the importance of the periodicity of crystals, which builds up the Bloch states extending over the solid. This is markedly different from the traditional HHG in atomic gases, where the positions of individual atoms are irrelevant.
Recent developments on intense laser sources is opening a new field of optical sciences. An intense coherent light beam strongly interacting with the matter causes a coherent motion of a particle, forming a strongly dressed excited particle. A photon emission from this dressed excited particle is a strong nonlinear process causing high-harmonic generation(HHG), where the perturbation analysis is broken down. In this work, we study a coherent photon emission from a strongly dressed excited atom in terms of complex spectral analysis in the extended Floquet-Hilbert-space. We have obtained the eigenstates of the total Hamiltonian with use of Feshbach-Brilloiun-Wigner projection method. In this extended space, the eigenstates of the total Hamiltonian consisting of the radiation field and the atom system have complex eigenvalues whose imaginary part represents the decay rate. Time evolution of the system is represented by the complex eigenvector expansion so that the correlation dynamics between the photon and the atom is fully taken into account. The HHG is interpreted as the irreversible spontaneous photon emission due to the resonance singularity in terms of the multiple Floquet states that are generated by periodic external field. We have found that the interference between the emitted photons over the different Floquet states causes spatial pulse emission correlated with the decay process of the excited atom.
We study the high harmonic generation (HHG) in Mott insulators using Floquet dynamical mean-field theory (DMFT). We show that the main origin of the HHG in Mott insulators is the doublon-holon recombination, and that the character of the HHG spectrum differs depending on the field strength. In the weaker-field regime, the HHG spectrum shows a single plateau as in the HHG from gases, and its cut-off energy $epsilon_{rm cut}$ scales linearly with the field strength $E_0$ as $epsilon_{rm cut}=Delta_{rm gap} + alpha E_0$, where $Delta_{rm gap}$ is the Mott gap. On the other hand, in the stronger-field regime, multiple plateaus emerge and the $m$-th cut-off scales as $epsilon_{rm cut,m}=U + m E_0$. We show that this difference originates from the different dynamics of the doublons and holons in the weak- and strong-field regimes. We also comment on the similarities and differences between HHG from Mott insulators and from semiconductors. This proceedings paper complements our recent work, Phys. Rev. Lett. 121, 057405 (2018), with additional results and analyses.
A three step model for high harmonic generation from impurities in solids is developed. The process is found to be similar to high harmonic generation in atomic and molecular gases with the main difference coming from the non-parabolic nature of the bands. This opens a new avenue for strong field atomic and molecular physics in the condensed matter phase. As a first application, our conceptual study demonstrates the feasibility of tomographic measurement of impurity orbitals.
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