Study Of High Harmonic Generation In Hexagonal Boron Nitride Based On Quantum Trajectories

In recent years,researchers have observed the high-order harmonic generation(HHG),induced by the interaction between ultrafast pulse laser and solid materials.Compared with gas phase system,solid system has more compact and periodic atomic configuration characteristics,and HHG in solids have become a new research direction in the field of strong field physics.Compared with bulk crystals,two-dimensional(2D)materials have the advantages of simple structure,high damage threshold and no propagation effect.Therefore,HHG in 2D materials are considered to be very valuable research content.At the same time,HHG in solids is a quantum process,and the wave-particle duality of electrons is the basic property of this process.This paper focuses on the generation mechanism of HH in 2D materials,starting from the quantum trajectory of electrons,and carries out the following researches:Firstly,the transition dipole moments and Berry connections which are continuous and satisfy the periodic boundary condition are obtained by using the parallel transport gauge(PT gauge)and the twisted parallel transport gauge(TPT gauge).The application of this gauge realizes the description of the physical quantities of the system and lays a foundation for the numerical simulation of the HHG process.Secondly,the high harmonics emission time in h-BN is studied.The results showed that there is a deviation of about 500 attoseconds between the harmonic emission time predicted by the semi-classical model and the numerical solution of the semiconductor Bloch equations(SBEs).In contrast to the quantum trajectory model,the semi-classical model ignores the wave properties of electrons.This results in a quantitative deviation in the predicted harmonic emission time.In addition,based on the quantum trajectory model,the interference minimization in the time-frequency analysis diagram of high harmonics polarized perpendicular to the laser polarization direction(LPD)is studied.It is found that the structure is caused by the phase relationship of harmonics contributed by the quantum trajectory ionized at the Dirac points(K and K~′).The interference of odd and even order harmonics polarized perpendicular to the LPD is studied.The results showed that the Berry phase of the system leads to destructive interference of odd order harmonics,constructive interference of the even order harmonics.Thirdly,the two-color field detection scheme provides a means to measure harmonics emission time.The modulation of even-order harmonic signal in h-BN with the relative phase of two-color field is studied.The results showed that the Berry phase of the system results in the difference of even-order harmonic signal modulation between symmetric crystal(graphene)and asymmetric crystal(h-BN).Through the quantum trajectory model,we find the multi-channel effect of solids harmonics,where different order harmonics are contributed by quantum trajectories ionized at different positions near the Dirac points.