Adiabatic quantum control hampered by entanglement

We study the defects in adiabatic control of a quantum system caused by the entanglement of the system with its environment. Such defects can be related to decoherence processes due to perturbative couplings between the system and the environment. We propose, for analysing these effects, a geometric approach, based on a field theory on the control manifold issuing from the higher gauge theory associated with the C*-geometric phases. We study a visualization method for analysing the defects of the adiabatic control, based on plotting the field strengths of the gauge theory. To illustrate the present methodology, we consider the example of 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.