Monotonic convergent quantum optimal control method with exact equality constraints on the optimized control fields

We present a monotonic convergent quantum optimal control method that can be utilized to optimize the control field while exactly enforcing multiple equality constraints for steering quantum systems from an initial state towards desired quantum states. For illustration, special consideration is given to finding optimal control fields with (i) exact zero area and (ii) exact zero area along with constant pulse fluence. The method combined with these two types of constraints is successfully employed to maximize the state-to-state transition probability in a model vibrating diatomic molecule.

Figure 1

(a) Pulse area, (b) fluence, and (c) control objective as a function of iteration for both the unconstrained and the single-constraint simulations. The result at the zeroth iteration arises from the pulse $\mathcal{E}(0,t)$. Both unconstrained and constrained optimizations were stopped at $P_{i\to f}=0.999$.

Figure 2

Final control field and the corresponding Fourier power spectrum for the (a) and (b) unconstrained and (c) and (d) ac field single-constraint simulations.

Figure 3

(a) Pulse area, (b) fluence, and (c) control objective as a function of iteration for both the unconstrained and the double-constraint simulations. Both unconstrained and constrained optimizations were stopped at $P_{i\to f}=0.999$.

Figure 4

(a) Optimal control field and (b) corresponding power spectrum for the double constraints of zero-area field and fixed fluence constrained simulations.