Optimization of high-order harmonic generation by genetic algorithm and wavelet time-frequency analysis of quantum dipole emission

We present an ab initio three-dimensional quantum study of the coherent control of high-order harmonic generation ~HHG! processes in intense pulsed laser fields by means of the genetic algorithm optimization of the laser-pulse amplitude and phase. Accurate time-dependent wavefunction and HHG power spectrum are ob- tained by the time-dependent generalized pseudospectral method and wavelet transform is used to obtain the dynamical phase associated with the dipole-emission time profile. It is shown that ''intra-atomic'' dynamical phase matching on the sub-optical cycle, attosecond, time scale can be achieved, leading to nearly perfect constructive interference between different returning electronic wave packets and marked improvement in both emission intensity and purity of a given harmonic order. The study of coherent control of atomic and molecular processes is a subject of much current interest in science and technology @1#. In particular, temporally shaped ultrashort laser pulses have been successfully used to design well- defined wave packets@2#, and to control multiphoton absorp- tion @3# and chemical reactions @4#, etc. In the area of the interaction of atoms with intense-laser-pulse, high-order har- monic generation ~HHG! of orders as high as 300 has been observed @5,6#, with photon energies in excess of 500 eV. A novel concept of ''intra-atomic'' phase matching has been recently introduced, allowing the enhancement of the inten- sity of a specific high harmonic @7#. It is shown that by carefully tailoring the shape of the temporal profile of the driving laser pulse, one can control the time evolution of the electron response to the intense laser field on a sub-optical- cycle, attosecond time scale @7#. A semiclassical model @8,9# is used to interpret these results in terms of the constructive interference in the frequency domain between different elec- tron trajectories @10#, but the effect of atomic structure is not considered. In this Rapid Communication, we present a fully ab initio quantum treatment of the coherent control and enhancement of high-harmonic emission by means of the genetic algo- rithm ~GA! optimization @11# of the laser-pulse shape and intra-atomic phase matching. We show that by combining the GA search algorithm and accurate quantum solution of the time-dependent Schrodinger equation, an optimal laser-pulse field can be identified, allowing the enhancement of a given high-harmonic intensity by at least one order of magnitude. Moreover, the study provides physical insights regarding the role of the quantum dynamical phaseof the dipole-emission time profile for the coherent control of intra-atomic phase matching, taking into account the effect of atomic structure. We consider the optimization of the HHG intensity of atomic H driven by intense linearly polarized ~LP! ultrashort laser pulsed fields. We first outline the procedure for the numerical solution of the time-dependent Schrodinger equa- tion, i)/)tC(t)5H(t)C(t), where H(t)5H01V(t). H0 is the unperturbed Hamiltonian and V(t) is the coupling of the electron with the laser pulse: V(t)52Re@e(t)#z, where e(t) is the electric field. The time-dependent Schrodinger equa- tion is solved accurately and efficiently by the time- dependent generalized pseudospectral~TDGPS! method re- cently developed @12#. The radial coordinate is discretized by the generalized pseudospectral technique @13#, allowing non- uniform spatial grid spacing: a denser mesh near the origin and a sparser mesh for the outer regime. The time propaga- tion of the wave function is achieved by the second-order split-operator method in the energy representation @12# .A s demonstrated in our recent studies of both strong-field HHG processes of atomic H @12,14#, rare-gas atoms @15#, and H2 @16#, as well as Rydberg-atom high-resolution spectroscopy @17#, the TDGPS procedure is capable of providing a high- precision time-dependent wave function and is computation- ally more efficient than the conventional time-dependent techniques using equal-spacing grid discretization. The uni- tarity of the wave function is preserved in the TDGPS pro- cedure. The energy ~520.500 000 000 000 0 a.u.! and the norm of the field-free ground-state wave function is pre-