Coherent superposition of states in degenerate systems using zero-area pulses

The coherent superposition of states in degenerate quantum systems is investigated using detuned laser pulses in which the Rabi frequencies are time-dependent, and the pulse area is zero. In this study, a quantum system with an arbitrary number of degenerate states in the ground set as well as an arbitrary number of degenerate states in the exciting set is considered. We assume that all states in the ground set are coupled to the excited states using laser pulses such that the pulse area of Rabi frequency is zero, and all of them have the same time dependence. It is also assumed that all laser pulses are in a non-resonant condition with Bohr transitions, and all detunings are the same. We will show that by applying the appropriate temporal dependence for the pulses and the appropriate rate for the detunings, the population can be transferred from an arbitrary superposition from the ground states to a desired superposition from the excited states.