Simple theory of the measured current through quantum dots

TL;DR

This paper presents a straightforward theoretical framework for analyzing the measured current in quantum dot charge qubits, enabling exact calculations of current fluctuations and confirming known quantum Zeno effects.

Contribution

It introduces a simple, transparent theory based on continuous measurement for quantum dots, allowing precise fluctuation spectrum calculations and validation of quantum Zeno phenomena.

Findings

Confirmed quantum Zeno effect with increasing measurement strength

Calculated exact fluctuation spectrum showing Lorentzian peak near Rabi frequency

Demonstrated the formalism's ability to analyze current noise in quantum dots

Abstract

A simple theory of the detected current I(t) flowing through charge qubits -- quantum dots -- is proposed in terms of standard continuous measurement theory. Applied to a double dot, our formalism easily confirms previous results on quantum Zeno effect, driven by growing ammeter performance gamma. Due to the transparent formalism, we can calculate the exact fluctuation spectrum S(omega) of the detected current, containing a significant Lorentzian peak near the Rabi frequency of the double dot.