Optimal state transfer of a single dissipative two-level system

Optimal state transfer of a single two-level system (TLS) coupled to an Ohmic boson bath via off-diagonal TLS-bath coupling is studied by using optimal control theory. In the weak system-bath coupling regime where the time-dependent Bloch-Redfield formalism is applicable, we obtain the Bloch equation to probe the evolution of the dissipative TLS in the presence of a time-dependent external control field. By using the automatic differentiation technique to compute the gradient for the cost functional, we calculate the optimal transfer integral profile that can achieve an ideal transfer within a dimer system in the Fenna-Matthews-Olson (FMO) model. The robustness of the control profile against temperature variation is also analyzed.