Effect of measurement backaction on adiabatic coherent electron transport

We study the backaction of a nearby measurement device on electrons undergoing coherent transfer via adiabatic passage (CTAP) in a triple-well system. The measurement is provided by a quantum point contact capacitively coupled to the middle well. We account for this continuous measurement by treating the whole {triple-well+detector} as a closed quantum system. This leads to a set of coupled differential equations for the density matrix of the enlarged system which we solve numerically. This approach allows us to study a single realization of the measurement process while keeping track of the detector output, which is especially relevant for experiments. In particular, we find the emergence of a new peak in the distribution of electrons inside the detector, accompanied by a drop in the fidelity of the protocol.