Weak measurements of quantum effects in electronic nano-devices

测量过程是实际控制和操纵纳米尺寸固体系统的关键方面。在固态纳米器件中，通常需要对这种超出标准投影假设的过程进行描述。然后，测量可以被描述为探测器连续获取信息，同时逐渐修改系统状态，允许具有参数化小反作用的弱状态。在量子条件测量中出现了一个显著的结果，弱测量的结果与随后的强测量（后选择）有条件，导致所谓的弱值（WV）。wv与标准wv有很大的不同，而且由于两种测量之间的量子相关性，wv可能是负的，而标准结果是正的。WVs在光学系统中已经被实验观察到。它们已用于解决量子力学中的基本问题，并用于光学中的精密测量和经典信号放大。对于固态系统也有相关的建议。然而，弱测量和wv在不干扰量子过程的情况下检测量子过程的潜力尚未被利用来深入了解标准强测量失败的系统。这一建议旨在推动弱测量的概念朝这个方向发展。它将专注于电子纳米器件，尽管对实验实现的要求更高，但自然呈现出相干量子动力学和多体效应，而不是通过强测量直接检测到（而不是破坏它们）。在这里，弱值及其软的反向作用可能会独特地提供新的物理见解。该提案将讨论具体的案例，这可能会引发该领域的实验。作为第一步，我们将考虑“虚拟”共隧电子的弱检测，并使用WV协议来定义共隧时间。沿着同样的路线，我们还将考虑量子绝热过程的弱探测和驱动量子系统。在后一种情况下，wv可以提供一种可行的方式来定义量子水平上的功，也适用于与环境接触的系统。除此之外，作为项目的进一步可能的步骤，我们计划考虑到一维超导导线中马约拉纳端态的具体情况，可能将弱测量的概念推进到拓扑激励的检测及其编织。

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.