Reverse engineering control of the relative phase and populations of two-level quantum systems
Felipe Silveira Fagundes, Emanuel F. de Lima · Physical Review A · 2024
We consider the simultaneous control of the relative phase and populations of two-level quantum systems by an external field. We apply a reverse engineering approach, obtaining an analytical expression for the control field depending upon two user-defined functions that dictate the population and the relative phase dynamics. We show that, in general, the prescribed functions for the dynamics cannot be chosen arbitrarily, but still there is plenty of room for choice. We illustrate the reverse engineering technique for several target states using different kinds of functions to specify the system dynamics. We show that by adjusting these dynamical functions, we produce different kinds of control fields. These controls can be easily built, needing, apart from the dynamical function themselves, only their first derivatives. The methodology presented here will certainly find many applications that go beyond simple two-level systems.