Investigation Of The Generation Of High-order Harmonics Through Bohmian Mechanics Method

In classical quantum mechanics, the probability interpretation of wave function isconsistent with the experimental results, which inspires people to explore themicrocosmic universe confidently by using the quantum theory. Bohmian mechanicsis an another explanation of quantum mechanics which was first proposed by deBroglie and further developed by David Bohm. The calculation results obtained fromBohmian mechanics are exactly the same as that of the classical quantum mechanics,and the Bohmian scheme does not require people to abandon the concept of classicalorbits and its interpretation of physical problems are closer to the classical mechanics,for which it was widely used.Trajectories of Bohmian particles represents the possible trajectories of theelectrons, and the density of trajectories is proportional to the probability density ofthe electron at that point. The motions of Bohmian particles are guided by the wavefunction and they follow the Newton-Bohm equation which has a more term thanNewton’s equation, i.e. quantum force. When the electron moves close to the nuclearzone, the quantum force play a major role, quantum effects become significantly, andthe monition of electron follows the Newton-Bohm equation; When the electronmoves far away from the nuclear zone, the quantum force decays rapidly and themotion of the electron only determined by the classic force, i.e. the motion of electronfollows Newton’s law.Using these features of Bohmian particles, this dissertation adopts the Bohmianmechanics scheme to investigate a typical phenomenon in the strong field physics—high harmonic generation(HHG). There have been many theoretical methods for HHG,however, they all share imperfections: Accurate results can be obtained bynumerically solving the time-dependent schrodinger equation (TDSE), but physicalpicture is not clearly revealed and it is of great difficulty to deal with many-electron system. Classical trajectory method has advantage in fast calculation speed andpresenting the clear physical picture, however, the quantum effect is not involvedmaking it impossible to obtain accurate harmonic spectrum. In order to solve theabove problems, we use Bohmian trajectories scheme to investigate the HHG process.The specific research work mainly includes the following four parts:First, we investigat the HHG process of atoms in an intense laser field. In thebeginning, we get the steady state wave function by numerically solving the TDSE,and then the initial position of Bohmian particles can be obtained according to theprobability density of steady state wave function. Based on these initial positions andcombined with the time-depentent wave function, we can obtained trajectories,acceleration, energy and other classic information of Bohmian particles at anymoment. The time-dependent dipole moment can be obtained through thesetrajectories, therefore the HHG spectrum can be calculated. It is found that the HHGspectra calculated from Bohmian trajectories are consistent with that by numericallysolving the TDSE, and the more the Bohmian particles, the closer to each other theresults will be. By analyzing the dynamical behaviors of the typical Bohmian particles,we find the Bohmian particle is fist ionized in the laser field, accelerated in the laserelectric field, then returns to the parent ion after the laser electric field reverses, andfinally oscillates in high frequency in the nuclear zone after it recombines with theparent ion, intuitively presenting the HHG process. In addition, we arrive at theconclusion that the coherence of Bohmian particles plays a major role in harmonicemission.Secondly, based on the Bohmian mechanics scheme, we study the factors thatinfluence the efficiency of light emission by the recombination of ionized electronswith its parent ion.It is found that the intensity and frequency of light emission areproportional to the amplitude and oscillation frequency of the Coulomb acceleration,respectively.When the kinetic energy of the recombined electron (that of the incidentBohmian particle) is larger, the amplitude of Coulomb acceleration of all Bohmianparticles is generally reduced, and the oscillation frequency of Coulomb particlesgenerally increases.When the potential well of the nucleus is deeper, the amplitude ofCoulomb acceleration of Bohmian particles in the vicinity of the nuclear zonebecomes larger, as a result, the intensity of the light emission is larger. When theproduct of the population of the continuum-state wave packet and that of theground-state wave packet is larger, the amplitude of Coulomb acceleration of Bohmian particles generally increases, making intensity of the light emission larger.Thirdly, we study HHG of diatomic molecules in the strong laser pulse byBohmian mechanical scheme.We chose a Bohmian particle from each center of thetwo nuclear zone, analyze their independent light-emission behavior of these twoparticles and find that the minimum value structure dose not appear on their ownharmonic spectra, which is inconsistent with the overall harmonic spectrum ofmolecule by the TDSE, indicating that the light-emission behavior can not bedescribed accurately by only one Bohmian trajectory. Whereas, a clear minimumvalue structure can be clear seen on the harmonic spectrum generated by the twotrajectories together, which is identical to that calculated by numerical solving TDSE.Through the detail analysis of the position and acceleration of the two Bohmiantrajectories, we find the accelerations of the two Bohmian particles oscillate in phasein some time zone, while they are out of phase at other time zone. And the in-phasezone corresponds to the high intensity, while the out-of-phase zone corresponds to thelow intensity which is corresponding to the minimum in harmonic spectra. Only suchtwo Bohmian trajectories can be used to reproduce structure of the harmonic spectrumof the molecule qualitatively, due to the fact both the Bohmian particles locate in thevicinity of the two nuclear zone, therefore they can receive and store the wholeinformation from all of the other recolliding trajectories.Finally, we investigate HHG of two-electron atoms by time-dependent quantumMonte Carlo method which based on Bohmian mechanics. We first obtain the atomicground state wave function in the field free case by numerically solving aone-dimensional schrodinger equation of two electrons, then sample from theprobability density function by the rejection method, and obtain the initial positions ofthe Bohmian particles which is identical to the density distribution of ground stateelectron. Then we use the time-dependent wave function of two electron to calculatethe velocity and position of Bohmian particles, and in this calculation, the correlationeffect of two electrons is included. Through this algorithm, the harmonic emissionspectrum we get is more accurate and efficient than that obtained by solving thetime-dependent Hartree-fock method. On this basis, we also analyze the dynamicalprocess of HHG of multi-electron. By comparing the results obtained by accuratelysolving the TDSE and TDHF, we found that the correlation effect between theelectrons will reduce the intensity of the harmonic.