Carrier-envelope Phase Dependence Of Nonsequential Double Ionization Of Ar In Few-cycle Laser Pulses

The interaction of the ultra-intense pulse with matters has become one of the most important fields in the frontier research of physics with the development of the high power laser facilities.Especially,the development of few-cycle laser pulse technology provides a powerful means to understand and control electron dynamics on attosecond time scale.For few-cycle laser pulse,the shape of the electric field depends strongly on the carrier-envelope phase(CEP).By changing the CEP,we can control the electric field of the few-cycle laser pulse and direct the ultra-fast electron dynamics.In 2001,Paulus et al.first observed the effect of CEP on photoelectron emission.After that,researchers use CEP stabilized few-cycle laser pulses to study the strong field ultrafast atomic physics phenomena such as high-order harmonic generation(HHG),high-order above-threshold ionization(HATI)and nonsequential double ionization(NSDI).The NSDI of atoms in intense laser fields has attracted more and more attention due to the basic physical problem of electron correlation.The NSDI is a rescattering process induced by strong laser field,which can be attributed to inelastic scattering of the returning electron by the parent ion,including recollision direct ionization(RDI)and recollision excitation with subsequent ionization(RESI).In 2004,Liu et al.reported differential measurements of Ar2+ ion momentum distributions from NSDI in phase-stabilized few-cycle laser pulses by using cold target recoil ion momentum spectroscopy(COLTRIMS).It was found that the tunneling time,ionization probability and return energy can be controlled by changing CEP in a few-cycle laser field,which leads to the strong dependence of Ar2+ parallel momentum distributions on CEP.However,the numerical results obtained by Liu et al.using the classical model are quite different from the experimental results.So far,the experimental results have not been further studied.Recently,Quan et al.also investigated the evolution of Ne2+ ion momentum distributions from NSDI in few-cycle laser pulses with respect to the CEP both experimentally and theoretically.It was found that the distributions depend strongly on the CEP and exhibit an asymmetric double-hump structure at some CEPs.While the main feature has been well reproduced by the semiclassical model,the double-hump structure in the simulated results deviates from the experiment.In this paper,we simulate the CMD for NSDI of Ar by near-single-cycle laser pluses with a wavelength of 760 nm at an intensity of214? W/cm103.5.The correlated two-electron momentum distributions are calculated by using quantitative rescattering(QRS)model,in which the lowering of the threshold energy due to the presence of an electric field at the instant of recollision is taken into account.In the framework of the QRS model,the correlated two-electron momentum distributions in NSDI can be factorized as a product of the returning-electron wave packet(RWP)and the field-free differential cross section(DCS).The RWPs,which describe the momentum distribution of the returning electrons,are obtained within the strong-field approximation.The DCSs for electron impact excitation of Ar+ are calculated using the state-of-the-art many-electron R-matrix theory,and the tunneling ionization rates for electrons in the excited states are evaluated by solving the time-dependent Schr?dinger equation.In addition,the triple differential cross sections for electron impact ionization of Ar+ are calculated within the distorted wave Born approximation which have further been calibrated by the Lotz formula.Finally,we get the parallel momentum spectrum of Ar2+ under different CEPs.Direct comparisons of the simulated results with the experimental data show that QRS theory can reproduce the experimental results quantitatively.With the accurate cross sections obtained from fully quantum mechanical calculations for both electron impact excitation and electron impact ionization of Ar+,we unambiguously identify the contributions from RDI and RESI to the parallel momentum spectrum of Ar2+.It is found that under the experimental conditions,the main contribution of the parallel momentum spectrum of Ar2+ comes from RESI,while RDI leads to the asymmetric double-hump structure.