The Interaction Of Intense Laser With One-dimensional H Atom And The Enhancement Of High-order Harmonic

In recent years, with the rapid development of laser technologies, especially the progress in femto-second laser pulses, the peak intensity of laser pulses has reached and even exceeded that of the Coulomb field in a hydrogen atom. Under the action of such strong pulses, a series of phenomena which can no longer be interpreted by the conventional perturbation theory occurs. That is to say, the traditional perturbation theory in the quantum mechanics is invalid for the laser-atom interaction. Time-dependent Schr?dinger equation (TDSE) implies all the physical messages about the atom, the laser field and the laser-atom interaction, so solving numerically TDSE is one of the popular and reasonable methods for the research about the laser-atom interaction in the present theoretical research. In the laser-atom interaction, the electronic influence in the direction along the polarization of the laser field is greater than that of other directions, so the one-dimensional model atom is chosen to research for the laser-atom interaction and makes the problem simpler.Quantum system is an infinite-dimensional Hamiltonian system. The time-evolution of the wave function of the system is unitary, which is equivalent to the properties of symplectic product conservation and the norm conservation of the wave function. So TDSE is discretized into a finite dimensional canonical equation whose norm of the wave function is a conservation quantity, and it should be solved by the symplectic scheme which keeps the norm conservation. The Split-Operator-FFT method could preserve unitary product conservation, so it is effective and reasonable to solve TDSE.In general, time-independent Schr?dinger equation is one of the basic equations of quantum mechanics. But most time-independent Schr?dinger equations have no analytical solution. Therefore, numerical solving time-independent Schr?dinger equation appears to be particularly important and meaningful. In this work, we introduced improved symplectic scheme-shooting method (ISSSM) and the correlation function-spectral method (CFSM) to solve the one-dimensional time-independent Schr?dinger equation. The results show that our methods are effective. We have also introduced the imaginary time evolution method (ITEM). The ITEM is accurate and reliable but it is only efficient for the determination of the lowest-lying states. A basis set expansion approach can solve the continuum states. Each basis function contains two parts. Two parts will be presented about how to choose the basis function here: 1). the discrete Eigen-function by the ISSSM; 2). the sine and cosine functions are members of a truncated Fourier series. The linear combination of the two parts is the maturity basis function. The advantage of this basis function is that it can describe both the discrete states and the continuum states of the atom commendably.In the paper the enhancement of efficiency of HHG has been found when 1D H atom has been subjected to the two-color laser field. To analyze the mechanism of the enhancement the ionization, the average distance, the population of the first excited sate has been calculated. The greatly enhancement has been found with mixing the 4-th harmonic by mixing the different order harmonic. Finally, the mechanism of the enhancement with mixing 4-th harmonic has been analyzed. The energy of single-photon of the 4-th harmonic is equal to ionization energy of the first excited state. Then the channels of the transition from the bound states to the odd parity and even parity continuum are unobstructed, and the efficiency of HHG can be greatly enhanced. The qualitative analysis is given by the average distance.