Projective versus weak measurement of charge in a mesoscopic conductor

Abstract

We study the charge dynamics of a quantum dot as measured by a nearby quantum point contact probing the dot via individual single-particle wave packets. We contrast the two limiting cases of weak and strong system--detector coupling exerting vanishing and strong back-action on the system and analyze the resulting differences in the charge-charge correlator. Extending the study to multiple projective measurements modelling a continuous strong measurement, we identify a transition from a charge dynamics dominated by the system's properties to a universal dynamics governed by the measurement

Short-time dynamics of molecular junctions after projective measurement

“…Discussions on quantum measurement in electronic transport systems involve both the von Neumann projecton postulate and detector's backaction on the system 52,53 . In Refs.…”

“…In Refs. [52] and [53], the quantum point contact (QPC) detector is capacitively coupled to the central scattering region and the current through QPC detector serves as a readout for the charge in the scattering region. When the coupling strength t c between the detector and scattering region is larger than hΓ which is related to the QPC tunneling time scale 1/Γ, strong backaction of the detector on the system leads to the strong projective measurement.…”

Time correlators from deferred measurements

“…2 and Ref. 13 for a recent discussion of this system. Here, we want to characterize the dot's dynamics by its two-time charge correlator.…”

“…The measurement with a weakly coupled detector can be treated perturbatively, with the von Neumann projection excerted on the detector and no back action on the system 1 . In a strong measurement with a large system-detector coupling, the projection formally can be applied directly to the system, therefore producing a maximal back action 13 .…”

“…11, leads to symmetrized (RS(τ 1 , τ 2 )) and antisymmetrized (IS(τ 1 , τ 2 )) correlators weighted with different detector response functions 2,12 , while a strong measurement produces a projected correlator S P (τ 1 , τ 2 ). These different forms of measured correlators can be derived 13 by invoking the von Neumann projection postulate 14 , telling how to restart the system after the first measurement at τ 1 (or after previous measurements at times τ j < τ n in a n-th order correlator). The measurement with a weakly coupled detector can be treated perturbatively, with the von Neumann projection excerted on the detector and no back action on the system 1 .…”