Analytic Solution of Nondegenerate Quantum Control Problem

2 ANALYTIC SOLUTION OF NONDEGENERATE QUANTUM CONTROL PROBLEM 

The system evolution is described by the wave function l F(O) — - Below, the vector c(t) denotes the ck(t) coefficients . 1) 

In order to solve for c(7) we consider the dynamics in the rotating-wave approxima J tion. One convenient way to do this is to write the Hamiltonian directly in this J approximation, and neglect off-resonance terms. This corresponds to a molecule-  

the time-dependent Rabi frequencies, are given by 

Inserting P(t) into the time-dependent Schrodinger equation and using Eq. (9.f gives 

---