Numerical Study On Vortex Momentum Distortion Induced By Dynamic Stark Effect In Hydrogen

Studies on the interaction between light and matter have been one of the hot subjects in the field of physics.The invention of the laser in the 1960 s brought this study into a completely new era.With the continuous development of laser technology,the laser intensity is steadily increasing and has far exceeded the electric field intensity needed to ionize atoms and molecules.Meanwhile,laser pulse duration continues to shorten,realizing the rapid development from nanosecond,picosecond to femtosecond and to attosecond.Under the action of ultrashort and ultra-intense laser fields,atoms or molecules will be ionized or dissociated by absorbing photon energy,and the corresponding strong field process can be investigated by analyzing the photoelectron momentum spectrum or energy spectrum generated.Vortex-shaped photoelectron momentum distributions in inert atoms and molecules exposed to two elliptically or circularly polarized and time-delayed laser pulses have been extensively studied and experimentally verified.On the basis of other's pioneering work,we numerically simulate the photoelectron momentum distributions in hydrogen atoms ionized by two circularly polarized and time-delayed laser pulses utilizing the strong field approximation(SFA)theory,and find that the vortex momenta will be generated if the two laser pulses are oppositely polarized and the number of the vortex arms is related to laser pulse carrier frequencies.When the two laser pulses are polarized in the same direction,no vortex momentum is generated regardless of the carrier frequency and intensity of the laser pulses.We attribute the generation of the vortex momentum distributions to the interference between the photoelectron wave packets.In addition,the effects of pulse width,intensity and delay time of the laser pulses on the formation of the vortex momentum distributions are systematically discussed.Dynamic Stark effect is a ubiquitous phenomenon existing in almost all strong field processes.It has been shown that the dynamic Stark effect shifts the ground state energy level of an atom either up or down.In order to quantitatively interrogate the effect of the dynamic Stark effect on the vortex momentum distributions,we model the up-shift of the ground state level of the hydrogen atom caused by dynamic Stark effect by an equivalent lowering of its ionization potential.An additional Stark phase is also introduced to elucidate this effect in the ionization process.It is found that when the dynamic Stark effect is taken into account,the vortex-shaped momentum distributions distort and the distortions intensify as the dynamic Stark effect is increased.We decipher the distortions in the vortex momentum distributions in hydrogen atom from the aspects of peak intensity,polar angle and the total action phase change of the vortex arms.At last,we present our preliminary numerical results and discussion of the saddlepoint approximation method and Feynman path integral method corresponding to the quantum orbits in photoelectron momentum distributions in hydrogen.We anticipate that the saddle-point method can be deployed in our future studies on the photoelectron vortex momentum formation in bi-circularly polarized laser fields.