Electron spin tomography through counting statistics: a quantum trajectory approach

TL;DR

This paper applies quantum trajectory methods to electron spin qubits in quantum dots, demonstrating how counting statistics can enable quantum state tomography and estimate decoherence times, bridging quantum optics techniques with condensed matter physics.

Contribution

It introduces a quantum trajectory approach to analyze electron spin qubits, enabling state tomography and decoherence measurement through counting statistics in condensed matter systems.

Findings

Quantum trajectories successfully simulate stochastic tunneling events.

Counting statistics combined with ESR enables qubit state tomography.

Decoherence and relaxation times can be estimated from time-domain data.

Abstract

We investigate the dynamics of electron spin qubits in quantum dots. Measurement of the qubit state is realized by a charge current through the dot. The dynamics is described in the framework of the quantum trajectory approach, widely used in quantum optics, and we show that it can be applied successfully to problems in condensed matter physics. The relevant master equation dynamics is unravelled to simulate stochastic tunneling events of the current through the dot.Quantum trajectories are then used to extract the counting statistics of the current. We show how, in combination with an electron spin resonance (ESR) field, counting statistics can be employed for quantum state tomography of the qubit state. Further, it is shown how decoherence and relaxation time scales can be estimated with the help of counting statistics, in the time domain. Finally, we discuss a setup for single shot measurement of the qubit state without the need for spin-polarized leads.