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The response of high harmonics of a laser field to the change of Fermi surface topology in graphene-like nanostructures during the process of the high harmonic generation has been investigated. The microscopic nonlinear quantum theory of the interaction of intense coherent electromagnetic radiation with such systems near the critical Fermi level is used. The Liouville–von Neumann equation for the density matrix in the multiphoton excitation regime is solved numerically. The obtained results show that high harmonics are sensitive to the change of the topology of the Fermi surface which can be used for the determination of the Fermi energy in such systems.

The generation of high-order harmonics in quasi-one-dimensional graphene nanoribbons (GNRs) initiated by intense coherent radiation is investigated. A microscopic theory describing the extreme nonlinear optical response of GNRs is developed. The closed set of differential equations for the single-particle density matrix at the GNR-strong laser field multiphoton interaction is solved numerically. The obtained solutions indicate the significance of the bandgap width and Fermi energy level on the high-order harmonic generation process in GNRs., 13 pages, 5 figures

The high-order wave mixing by two-color multiphoton excitation in nonlinear regime along with the harmonics generation in two-dimensional (2D) nanostructures such as graphene, silicene, germanene, and stanene is investigated. We consider the coherent part of the spectra corresponding to high harmonic generation by two-color intense laser pulses. The developed theory of interaction of free carriers with the driving effective field of two-color waves covers the full Brillouin zone of 2D hexagonal nanostructures. We also consider the case when one of the driving waves is in one-photon resonance with the van Hove singularity at the $M$ point of the Brillouin zone. Obtained results show that novel 2D nanostructures can serve as an effective medium for high-order wave mixing and harmonic generation at the two-color multiphoton excitation with strong laser pulses.

The collective decay of excitons from initial Bose-Einstein condensate state is investigated theoretically. As practically more interesting case we consider excitons of the yellow series in the semiconductor cuprous oxide where we have collective photon and phonon assisted decay of excitons. It is shown that because of intrinsic instability of recoilless two-boson decay of Bose-Einstein condensate, the spontaneously emitted bosonic pairs are amplified leading to an exponential buildup of a macroscopic population into the certain modes. The collective decay rate has a nonlinear dependence on the excitonic density being comparable or larger than Auger recombination loss rate up to the high densities, which makes obtainable its observation. The considering phenomenon can also be applied for the realization of phonon laser., Comment: 12 pages, 1 figure

We consider harmonics generation and wave mixing by two-color multiphoton resonant excitation of three-level atoms and molecules in strong laser fields. The coherent part of the spectra corresponding to multicolor harmonics generation is investigated. The obtained analytical results on the basis of a generalized rotating wave approximation are in a good agreement with numerical calculations. The results applied to the hydrogen atoms and homonuclear diatomic molecular ions show that one can achieve efficient generation of moderately high multicolor harmonics via multiphoton resonant excitation by appropriate laser pulses.

Multiphoton interaction of coherent electromagnetic radiation with 2D metallic carriers confined on the surface of the 3D topological insulator is considered. A microscopic theory describing the nonlinear interaction of a strong wave and metallic carriers with many-body Coulomb interaction is developed. The set of integrodifferential equations for the interband polarization and carrier occupation distribution is solved numerically. Multiphoton excitation of Fermi-Dirac sea of 2D massless carriers is considered for a THz pump wave. It is shown that in the moderately strong pump wave field along with multiphoton interband/intraband transitions the intense radiation of high harmonics takes place., 13 pages, 7 figures

A scheme is presented for generation of powerful coherent terahertz radiation by multiphoton resonant excitation of three-level hydrogenlike atoms and homonuclear diatomic molecules or molecular ions with strong laser pulses. The results of analytical and numerical investigations of the problem show that with the proposed mechanism one can achieve the implementation of widely tunable powerful terahertz sources, which may open new perspectives for terahertz science and its applications.

The coherent scattering spectrum of a three-level atom driven by an intense laser field with multiphoton resonant excitation is considered. The spectrum corresponding to harmonic generation is investigated both analytically and numerically for different initial atomic states. The analytical calculations are based on the generalized rotating wave approximation, which allows one to explain obtained spectra containing in general both even and odd harmonics. The results applied to the hydrogen atom show that one can achieve efficient generation of moderately high harmonics using multiphoton resonant excitation by appropriate laser pulses.

Coherent light scattering by a three-level atom due to multiphoton resonant excitation by laser radiation is studied towards the coherent shortwave radiation generation. The spectrum corresponding to harmonics generation is investigated both analytically and numerically.

The multiphoton resonant excitation of three-level atoms by the two laser fields of different frequencies is investigated. The time evolution of the system and analytical solutions expressing Rabi oscillations of the probability amplitudes at the two-color multiphoton resonant excitation are found using a nonperturbative resonant approach. The specific examples for experimental implementation of two-color multiphoton resonant excitation of hydrogen atoms are considered.

The theory of coherent radiation emission in two-level quantum systems with permanent dipole moments at the multiphoton resonant excitation by moderately strong laser fields is presented. A simple analytic formula for the expectation value of a dipole moment operator is obtained. The spectrum corresponding to harmonic generation and low-frequency radiation on the generalized Rabi frequency is investigated both analytically and numerically. The effect of dynamic Stark shift on a dipole spectrum under direct multiphoton resonant excitation is considered.