Non-Markovian dynamics of a nanomechanical resonator measured by a quantum point contact

TL;DR

This paper develops a non-Markovian quantum master equation for a nanomechanical resonator measured by a quantum point contact, revealing significant differences from Markovian models and identifying a transient current signature of non-Markovian dynamics.

Contribution

It derives a second-order non-Markovian master equation without common approximations, highlighting differences from Markovian models and identifying a measurable current signature.

Findings

Non-Markovian dynamics differ significantly from Markovian predictions.

An extra transient current term is identified as a signature of non-Markovian behavior.

The transient current can serve as an experimental witness of non-Markovian effects.

Abstract

We study the dynamics of a nanomechanical resonator (NMR) subject to a measurement by a low transparency quantum point contact (QPC) or tunnel junction in the non-Markovian domain. We derive the non-Markovian number-resolved (conditional) and unconditional master equations valid to second order in the tunneling Hamiltonian without making the rotating-wave approximation and the Markovian approximation, generally made for systems in quantum optics. Our non-Markovian master equation reduces, in appropriate limits, to various Markovian versions of master equations in the literature. We find considerable difference in dynamics between the non-Markovian cases and its Markovian counterparts. We also calculate the time-dependent transport current through the QPC which contains information about the measured NMR system. We find an extra transient current term proportional to the expectation value of the symmetrized product of the position and momentum operators of the NMR. This extra current term, with a coefficient coming from the combination of the imaginary parts of the QPC reservoir correlation functions, has a substantial contribution to the total transient current in the non-Markovian case, but was generally ignored in the studies of the same problem in the literature. Considering the contribution of this extra term, we show that a significantly qualitative and quantitative difference in the total transient current between the non-Markovian and the Markovian wide-band-limit cases can be observed. Thus, it may serve as a witness or signature of the non-Markovian features in the coupled NMR-QPC system.