Application of the Space-Time Method to Stimulated Raman Adiabatic Passage on the Simple Harmonic Oscillator

The space-time method is applied to a model system-the Simple Harmonic Oscillator in a laser field to simulate the Stimulated Raman Adiabatic Passage (STIRAP) process. The Space-Time method is a computational theory first introduced by Weatherford et. al. to solve Time-Dependent Systems with one boundary value and applied to electron spin system with invariant Hamiltonian [Journal of Molecular Structure {\bf 592} 47]. The implementation in the present work provides an efficient and general way to solve the Time-Dependent Schr{\"o}dinger Equation and can be applied to multi-state systems. The algorithm for simulating the Simple Harmonic Oscillator STIRAP can be applied to solve STIRAP problems for complex systems.