Crossover between strong and weak measurement in interacting many-body systems

Abstract

Measurements with variable system-detector interaction strength, ranging from weak to strong, have been recently reported in a number of electronic nanosystems. In several such instances many-body effects play a significant role. Here we consider the weak-to-strong crossover for a setup consisting of an electronic Mach-Zehnder interferometer, where a second interferometer is employed as a detector. In the context of a conditional which-path protocol, we define a generalized conditional value (GCV), and determine its full crossover between the regimes of weak and strong (projective) measurement. We find that the GCV has an oscillatory dependence on the system-detector interaction strength. These oscillations are a genuine many-body effect, and can be experimentally observed through the voltage dependence of cross current correlations.

How to extract weak values from a mesoscopic electronic system

“…Shpitalnik et al [21] have implemented, in principle, a WV protocol in this setup, and have shown that the outcome of such measurement may produce a complete tomography of the WV measured in the system's MZI. An exhaustive analysis of the correlated signal in this system has been reported in the single particle regime [6], and the many body effects on the weak to strong measurement crossover have been classified [8]. The fact that such a protocol is amenable to experimental verification [25] has been undermined by the lack of a concrete manual on how to implement it.…”

Detection of Quantum Interference without an Interference Pattern

“…The observation of interference and of the collapse of the coherent wavefunction to a state that does not exhibit an interference pattern (following which-path detection) are a manifestation of the quantum nature of the phenomenon. Such combined measurements have been demonstrated in studies of average currents of electronic interferometers [5][6][7][8][9], and analyzed theoretically for single-electron [10,11] and manybody [12,13] protocols. The question addressed here is of fundamental nature: can one detect particle interference avoiding the need to vary an external parameter, and verify that the interference signal is inherently of a quantum nature?…”