Coherent Radiation Of Atoms In Ultrashort Laser Field

Coherent photon emission of atoms in ultrashort laser pulses with variant frequency and intensity are simulated. Fine structures in the emission spectrum except the high-order harmonic lines, which have been studied well by many researchers, are discussed, in particular for the hyper-Raman lines and terahertz emissions. The whole research work is composed of four parts as follows.The first part is an introduction of the fundamental theories and design of the numerical scheme. The methods for solving the field-free eigenfunctions are represented. Then the detailed procedure for calculating the time-dependent Schrodinger equation with and without the dipole approximation is introduced by means of the symmetrized split-operator method in order to discribe the response of atom to an intense laser field. When the smoothing parameter in the soft Coulomb potential is chosen to be small enough, the so-called hard Coulomb potential can be obtained. The eigenfunctions and eigenstates are calculated for the soft Coulomb potential and the hard Coulomb potential in order to find the relationship between these two kinds of potentials. Combining with the high-order harmonic spectrum, we can get the conclusion that the choice of one-dimensional soft Coulomb potential can get the creditable results with much fewer calculations.The second part is about the enhancement of the hyper-Raman lines. This section is composed of two parts according to the choice of the laser field. The first part is to choose the infrared laser field with the initial state prepared as a coherent superposition between the ground and first excited states. When the energy difference of the two states is small we choose proper laser pulse such that the electron can be excited only to other bound states instead of being ionized. We show that only the hyper-Raman lines are observable instead of the harmonics. The similar results can be obtained by using a combination of two laser pulses with different frequencies interacting with the atom initially at the ground state. Then the intense high-frequency laser pulse is chosen. The conditions for the enhancement of the hyper-Raman lines can be satisfied automatically when stabilization happens. Regular fine structures appear in the two sides of both the odd and even times of photon energy of the laser field besides the ordinary odd harmonic peaks. It is proved that the splits of the fine structures are hyper-Raman lines and the space around the odd harmonic line is equal to the energy difference of the eigenstates with the same parity of the time averaged Krameters-Henneberger (KH) potential. By analyzing the features of the fine structures, we also verify that the so-called even order harmonics in the stabilization condition are indeed hyper-Raman lines caused by the transitions between the dressed atomic states with different parity.The third part concerns the terahertz (THz) emission of an isolated atom in an intense ultrashort laser field is simulated by solving the time-dependent Schrodinger equation. From numerical calculations with one- and three-dimensional models of hydrogen atom and a short-range shallow potential model, we get the conclusions that continuum THz emissions are caused much more effectively by the transitions between the intermediate states lying within the continuum ionization states of the atom than the intermediate states well below the ionization threshold of the atom. Line shape THz transitions are also found between the high lying Rydberg states. Enhanced terahertz emissions by superposing a second order harmonic laser field or a spatially constant electric field on the fundamental one are described well by the present models and the dependence of the THz field strength on the intensities of the fundamental laser field and the superposed field is obtained in accordance with the experiments. Strong field approximation is also used to prove the general features of the THz emission caused by the continuum free-free transitions of an electron in strong two-color laser fields. The result is helpful for people to understand the THz emission processes intuitively. The dependence of the THz strength on the phase difference between the fundamental and the second order harmonic laser fields is investigated by solving the time-dependent Schrodinger equation with the help of the short-range shallow potential model. It is proved that the dependence of the THz strength on the phase difference between the two incident laser fields will deviate from the cosine expression with larger absorbtion of the laser fields or in other words, the energy loss when the coefficient of the imaginary unit of the three-order nonlinear tensor is not zero. The deviation angle depends on the velocity of the excited electron before emitting the THz photon linearly when the proportion of the photon energy between the fundamental laser field and the ionization energy ranges from 0.5 to 1.0. These researches on the dependence of the THz strength on the phase difference between the two incident laser fields can provide valid information on the coherent control of THz radiation in two-color laser field.In the final part, we solve the fully relativistic time-dependent Dirac equation by means of the symmetrized split-operator method and get the corresponding radiation spectrum. The spectrum is compared to those calculated from the time-dependent Schrodinger equation with and without the dipole approximation in order to investigate the relativistic effects on the conherent radiation of atoms. Besides, the intrinsic phenomenon of the Dirac equation which is defined as Zitterbewegung and the corresponding emission lines in the calculated spectrum are introduced.