Monitored quantum transport through a disordered one-dimensional conductor

TL;DR

This paper develops a quantum master equation model for electron transport in a disordered 1D conductor, revealing how monitoring affects localization and coherence length.

Contribution

It introduces a novel quantum master equation approach that combines disorder scattering with time-resolved measurements to study transport properties.

Findings

Monitoring suppresses phase coherence and localization effects.

The coherence length depends logarithmically on measurement frequency.

Transition from exponential to Ohmic decay occurs at length scale ~____.

Abstract

We formulate a quantum master equation for the many-particle density matrix of electrons propagating through a single-mode conductor, combining elastic scattering by disorder with time-resolved projective measurements that monitor the outcome of scattering events. The full counting statistics of transmitted electrons has a binomial distribution function, whose mean ${\cal T}$ and variance ${\cal T}(1-{\cal T})$ determine the conductance and shot noise power, respectively. Monitoring suppresses the phase coherence responsible for one-dimensional localization: The decay with conductor length $L$ of the typical transmission probability crosses over at $L\simeq \ell_\phi$ from the exponential $e^{-L/\xi}$ (with localization length $\xi$) to the Ohmic $1/L$ decay. Numerical solution of the master equation gives, for weak monitoring, a logarithmic dependence $\ell_\phi\simeq \xi\ln(v_{\rm F}\tau_\phi/\xi)$ of the coherence length $\ell_\phi$ on the mean time $\tau_\phi$ between measurements.