Quantum control of high harmonic generation in anharmonic potential

In this work, we first aim to realize the high harmonic generation(HHG) spectrum in a classical and quantum treatment, and then to achieve the quantum control of the HHG spectrum. Here, we consider the HHG from the Duffing oscillator well-known as a typical anharmonic system. The HHG induced by the intense laser is a nonlinear optical process, where a molecular system absorbs n photons with energy ω and emits one high energy photon with energy nω. The light generated by HHG is a promising light source with an attosecond ultrashort pulse, which could be used to analyze the electronic structure and motion in molecule. First, we perform a classical simulation to explain the structure of the HHG spectrum. Then, we investigate quantum-mechanically the mechanism of HHG, and compare the classical and quantum result. In quantum treatment, we apply the Fourier Grid Method (FGM) to obtain the eigenvalues and wavefuntion of the Duffing oscillator and use the Split Operator Method (SOM) to solve the time-dependent Schr¨odinger equation. Here we study the laser intensity dependence of the HHG with a single laser pulse, and then from the interference point of view, we focus on the role of the relative phase of two laser pulses and simulate to find out the phase dependence of the HHG. Finally we investigate the laser control of the HHG by changing the initial quantum state, which is a kind of a wave packet due to the superimposition of few eigenstates