Weak measurements of quantum effects in electronic nano-devices

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The measurement process is a key aspect of the actual control and manipulation of nano-size solid state systems. A description of such a process beyond the standard projection postulate is generally needed in solid state nano-devices. The measurement can then be described as a continuous acquisition of information by the detector alongside a gradual modification of the system's state, allowing for a weak regime with parametrically small back-action. A remarkable consequence appears in the case of quantum conditional measurements where the outcome of a weak measurement, conditional to a subsequent strong one (postselection), leads to the so-called weak value (WV). WVs substantially differ from standard ones and, uniquely due to the quantum correlations between the two measurements, can be negative whereas the standard outcome is positive. WVs have been experimentally observed in optical systems. They have been used in addressing fundamental problems in quantum mechanics and employed for precision measurements and classical signal amplification in optics. Related proposals exist for solid state systems as well. The potential of weak measurements and WVs in detecting quantum processes without essentially disturbing them has however not yet been exploited to get insights into systems where standard strong measurements would fail.This proposal is aimed at advancing the concept of weak measurement in this direction. It will focus on electronic nano-devices which, despite being more demanding for experimental realizations, naturally present coherent quantum dynamics and many-body effects not directly detectable by strong measurements (which would instead destroy them). Here, weak values, with their soft back-action, might uniquely provide new physical insight. The proposal will address specific cases, which might trigger experiments in the field. As a first step we will consider the weak detection of ``virtual'' cotunneling electrons and use the WV protocol to define the cotunneling time. Along the same line we will also consider the weak detection of quantum adiabatic processes, and driven quantum systems. In the latter, WVs can offer a viable way to the definition of work at a quantum level, also for systems in contact with an environment. Beyond that, as a further possible step in the project, we plan to possibly advance the concept of weak measurement to the detection of topological excitations, and their braiding, considering the specific case of Majorana end-states in 1D superconducting wires.