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Register a new userHigh-order Harmonic Generation and its Unconventional Scaling Law in the Mott-insulating $rm{Ca_2RuO_4}$
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Competition and cooperation among orders is at the heart of many-body physics in strongly correlated materials and leads to their rich physical properties. It is crucial to investigate what impact many-body physics has on extreme nonlinear optical phenomena, with the possibility of controlling material properties by light. However, the effect of competing orders and electron-electron correlations on highly nonlinear optical phenomena has not yet been experimentally clarified. Here, we investigated high-order harmonic generation from the Mott-insulating phase of Ca2RuO4. Changing the gap energy in Ca2RuO4 as a function of temperature, we observed a strong enhancement of high order harmonic generation at 50 K, increasing up to several hundred times compared to room temperature. We discovered that this enhancement can be well-reproduced by an empirical scaling law that depends only on the material gap energy and photon emission energy. Such scaling law cannot be explained by a simple two-band model under the single electron approximation. Our results suggest that the highly nonlinear optical response of strongly correlated materials is deeply coupled to their electron-electron correlations and resultant many-body electronic structure.
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Using Floquet dynamical mean-field theory, we study the high-harmonic generation in the time-periodic steady states of wide-gap Mott insulators under AC driving. In the strong-field regime, the harmonic intensity exhibits multiple plateaus, whose cutoff energies $epsilon_{rm cut} = U + mE_0$ scale with the Coulomb interaction $U$ and the maximum field strength $E_0$. In this regime, the created doublons and holons are localized because of the strong field and the $m$-th plateau originates from the recombination of $m$-th nearest-neighbor doublon-holon pairs. In the weak-field regime, there is only a single plateau in the intensity, which originates from the recombination of itinerant doublons and holons. Here, $epsilon_{rm cut} = Delta_{rm gap} + alpha E_0$, with $Delta_{rm gap}$ the band gap and $alpha>1$. We demonstrate that the Mott insulator shows a stronger high-harmonic intensity than a semiconductor model with the same dispersion as the Mott insulator, even if the semiconductor bands are broadened by impurity scattering to mimic the incoherent scattering in the Mott insulator.
We study high-harmonic generation (HHG) in the one-dimensional Hubbard model in order to understand its relation to elementary excitations as well as the similarities and differences to semiconductors. The simulations are based on the infinite time-evolving block decimation (iTEBD) method and exact diagonalization. We clarify that the HHG originates from the doublon-holon recombination, and the scaling of the cutoff frequency is consistent with a linear dependence on the external field. We demonstrate that the subcycle features of the HHG can be reasonably described by a phenomenological three step model for a doublon-holon pair. We argue that the HHG in the one-dimensional Mott insulator is closely related to the dispersion of the doublon-holon pair with respect to its relative momentum, which is not necessarily captured by the single-particle spectrum due to the many-body nature of the elementary excitations. For the comparison to semiconductors, we introduce effective models obtained from the Schrieffer-Wolff transformation, i.e. a strong-coupling expansion, which allows us to disentangle the different processes involved in the Hubbard model: intraband dynamics of doublons and holons, interband dipole excitations, and spin exchanges. These demonstrate the formal similarity of the Mott system to the semiconductor models in the dipole gauge, and reveal that the spin dynamics, which does not directly affect the charge dynamics, can reduce the HHG intensity. We also show that the long-range component of the intraband dipole moment has a substantial effect on the HHG intensity, while the correlated hopping terms for the doublons and holons essentially determine the shape of the HHG spectrum. A new numerical method to evaluate single-particle spectra within the iTEBD method is also introduced.
With a combination of numerical methods, including quantum Monte Carlo, exact diagonalization, and a simplified dynamical mean-field model, we consider the attosecond charge dynamics of electrons induced by strong-field laser pulses in two-dimensional Mott insulators. The necessity to go beyond single-particle approaches in these strongly correlated systems has made the simulation of two-dimensional extended materials challenging, and we contrast their resulting high-harmonic emission with more widely studied one-dimensional analogues. As well as considering the photo-induced breakdown of the Mott insulating state and magnetic order, we also resolve the time and ultra-high frequency domains of emission, which are used to characterize both the photo-transition, and the sub-cycle structure of the electron dynamics. This extends simulation capabilities and understanding of the photo-melting of these Mott insulators in two-dimensions, at the frontier of attosecond non-equilibrium science of correlated materials.
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.
High harmonic generation (HHG) has unleashed the power of strong laser physics in solids. Here we investigate HHG from a large system, solid C$_{60}$, with 240 valence electrons engaging harmonic generation at each crystal momentum, the first of this kind. We employ the density functional theory and the time-dependent Liouville equation of the density matrix to compute HHG signals. We find that under a moderately strong laser pulse, HHG signals reach 15th order, consistent with the experimental results from C$_{60}$ plasma. The helicity dependence in solid C$_{60}$ is weak, due to the high symmetry. In contrast to the general belief, HHG is unsuitable for band structure mapping in C$_{60}$. However, we find a window of opportunity using a long wavelength, where harmonics are generated through multiple-photon excitation. In particular, the 5th order harmonic energies closely follow the transition energy dispersion between the valence and conduction bands. This finding is expected to motivate future experimental investigations.
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