Efficient Split-Lanczos propagator for strong-field ionization of atoms

High angular momentum partial waves are indispensable in the numerical calculations of the time-dependent Schrodinger equation (TDSE) for the interaction between atoms and strong long-wavelength laser pulses. In these cases, the widely-applied Lanczos propagator, used to solve the TDSE, requires an extremely small time step to be convergent. By splitting out the centrifugal potential from the whole Hamiltonian, we demonstrate that the stiffness of the TDSE can be reduced and a rather large time step is allowed for the present Split-Lanczos propagator. Compared with the ordinary Lanczos propagator, the efficiency of the propagation can be improved by more than 100 times for large angular momentum in present tests.