Optimal population inversion of a single dissipative two-level system

Optimal population inversion 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 Bloch-Redfield formalism is applicable, we derive the Bloch equation for describing 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 energy difference profile that can achieve an ideal inversion. Further we examine the robustness of driving-induced tunneling oscillations (DITO) in presence of dissipation.