Coherent feedback control in quantum transport

We discuss control of the quantum-transport properties of a mesoscopic device by connecting it in a coherent feedback loop with a quantum-mechanical controller. We work in a scattering approach and derive results for the combined scattering matrix of the device-controller system and determine the conditions under which the controller can exert ideal control on the output characteristics. As a concrete example we consider the use of feedback to optimize the conductance of a chaotic quantum dot and investigate the effects of controller dimension and decoherence. In both respects we find that the performance of the feedback geometry is well in excess of that offered by a simple series configuration.