Analytical View on Non-invasive Measurement of Moving Charge by Various Topologies of Wannier Qubit

Detection of moving charge in free space is presented in the framework of single electron CMOS devices. It opens the perspective for construction of new type detectors for beam diagnostic in accelerators. General phenomenological model of noise acting on position based qubit implemented in semiconductor quantum dots is given in the framework of simplistic tight-binding model. At first linear position-based qubit also known as Wannier qubit is considered with the situation of being excited by external movement of charged particle in its proximity. Analytical formulas describing the change of qubit state are derived analytically. In the next steps the roton semiconductor qubit representing closed loop of coupled quantum dots is given and the effect of external moving charge on the change of qubit state is determined by analytical formulas. Roton qubit physical state can be controlled by external magnetic and electric field what is the extension of controlling mechanism in comparison with linear Wannier qubit, when we have N quantum dots aligned.