The High-Order Harmonics From An Initial Atomic Superposition States Irradiated By Chirped Pulses

The interaction of intense laser pulses with atoms, molecules, cluster, and solids can lead to high-order harmonics generation (HHG) of the incident laser frequency, as a consequence of highly nonlinear dynamics. Currently HHG is a potential way to generate radiations in x-ray and XUV regions. The unremitting pursuit in HHG studies is to simultaneously widen and heighten the HHG plateau on a large scale. The cutoff frequency is predicted byω_cutoff = I_p + 3.2U_p, (where I_p is the ionization potential and U_p is the pondermotive energy in pulse, it equals toe² F₀² /(4 mω² ), F₀ is the maximum of the pulse intensity).From the cutoff law, we notice that for a single atom model, taking the ion with larger ionization potential as target is one of the most direct way in extending the harmonic plateau. In fact, the generation of high-density ions with large ionization is very difficult. Another direct way is to increase ponderomotive energy. To realize the aim, it is necessary to raise the intensity of the laser pulse when laser wavelength is kept constant. However, an atom will be depleted completely when the laser intensity rises up to a certain threshold amount, so that the corresponding harmonic emission process also terminates.In this paper, positive chirped pulse was used for interacting with an atom initially prepared in an equally weighted superposition of ground and the 1st-excited state. It is found that the HHG plateau is extended on a large scale by varying the chirp. The idea of preparing the initial state as a coherent state is that the HHG is stimulated; the conversion frequency is determined by the considerable populations of continuum and the ground state. We use this initial state not only to guarantee the high rate of ionization in a certain time but also to maintain the considerable population of ground state.The purpose of this paper is to rationally explain the reason why the HHG plateau is extended on a large scale with the increase of the chirp of pulse. The numerical calculations of HHG contain two parts at least: firstly, we need to calculate the single atom responding under the field in terms of seeking the average value of dipole moment or induced dipole moment, and then getting the spectra via Fourier Transforms; Secondly, we study the propagation effects in macroscopical medium. We only pay attention to the first one. A simple semiclassical argument which is proposed by Corkum et al. is used. As the atom is perturbed, it ionizes and can be seen as a source of electrons that are'born', with zero initial velocity, in the laser field. The means of ionization depend sensitively on the intensity of the field, it can be multiphoton ionization, tunnel ionization or over the barrier ionization. The electron trajectories depend on the phase of the field at the time of their birth;Some may ionize and others will return to recollide with the nucleus. HHG occurs when some electrons recombine with the parent ion by emitting high energy photons.The above law is used by analyzing the reason for the widen HHG. We can get the time of recombination and the recombined energy from pulse which corresponds to each time of ionization by Newtonian equation. It is found that the bigger chirp rate of the laser pulse, the larger kinetic energy the electrons get from the field. The physical reason is that the instantaneous frequency which is in the first half of pulse duration is smaller than 0.057, and the"three-step"processes for HHG entirely occur in this time under the case of an atom initially prepared in an equally weighted superposition of ground and the 1st-excited state, so the electron obtains more effective from laser pulse during this time domain, then the cutoff frequency will extend to shortwave. The time of primary ionization will occur in the time domain with lower frequency with the increase of chirp. So the HHG plateau was widened largely. The cutoff frequency is predicted by the cutoff law E_cutoff = I_p + E_k. We find that the results are consistent with the ones predicted by SMT except chirp 10. So we clarify the matter.The primary ionizations just occur at the time when the electron gets the most recombined kinetic energy from the field except the case of chirp 10. So the quantum results are consistent with that of semi-classical"three-step"model. For the case of chirp 10, the primary ionizations don't occur at the time when the electron gets the most recombined kinetic energy from the field predicted by SMT. Then its cutoff frequency must be predicted by its practical kinetic energy. With this operation, we get the exact cutoff frequency which is consistent with the quantum result under the condition of the initial state prepared on an equally weighted superposition of the ground state and the 1st-excited state.How to get its harmonic spectra in terms of the most recombined kinetic energy gotten from"three-step"model? It is found that the time of ionization occurs earlier than the one with initial state as a coherent superposition of the ground state and the 1st-excited state. So we prepare the initial state as a coherent superposition of ground state and the 2nd-excited state. It is guaranteed not only the main ionization occurs near the time of ionization when the electrons get the most recombined kinetic energy from the field , but also the populations of ground state and continuous state have considerable magnitude. We just get the cutoff frequency which is anticipated under this model. In conclusion, by preparing the initial state on the superposition of the ground state and different excited state equally, we can control the primary time of ionization and broaden the HHG plateau irradiated by chirped pulses.