Adiabatic quantum control hampered by entanglement

We study defects in adiabatic control of a quantum system caused by the entanglement of the system with its environment. Such defects can be assimilated to decoherence processes due to perturbative couplings between the system and the environment. To analyse these effects, we propose a geometric approach based on a field theory on the control manifold issued from the higher gauge theory associated with the $C^*$-geometric phases. We study a visualization method to analyse the defects of adiabatic control based on the drawing of the field strengths of the gauge theory. To illustrate the present methodology we consider the example of the atomic STIRAP (stimulated Raman adiabatic passage) where the controlled atom is entangled with another atom. We study the robustness of the STIRAP effect when the controlled atom is entangled with another one.