Cross-correlation spectra in interacting quantum dot systems

TL;DR

This paper develops a modified semiclassical method to analyze spin cross-correlation spectra in interacting quantum dot systems, revealing how inter-dot interactions influence the low-frequency noise spectra and can be characterized by external magnetic fields.

Contribution

It introduces a quaternion-based semiclassical approach that incorporates nuclear quadrupolar interactions and randomness, enabling mapping of complex quantum dot interactions onto an effective two-dot model.

Findings

The method accurately models spin noise spectra considering nuclear and g-factor effects.

Inter-dot interaction length scales influence the low-frequency cross-correlation spectra.

External magnetic fields help extract interaction strength distributions from the spectra.

Abstract

Two-color spin-noise spectroscopy of interacting electron spins in singly charged semiconductor quantum dots provides information on the inter quantum dot interactions. We investigate the spin cross-correlation function in a quantum dot ensemble using a modified semiclassical approach. Spin-correlation functions are calculated using a Hamilton quaternion approach maintaining local quantum mechanical properties of the spins. This method takes into account the effects of the nuclear-electric quadrupolar interactions, the randomness of the coupling constants, and the electron g factor on the spin-noise power-spectra. We demonstrate that the quantum dot ensemble can be mapped on an effective two-quantum dot problem and discuss how the characteristic length scale of the inter-dot interaction modifies the low-frequency cross-correlation spectrum. We argue that details on the interaction strength distribution can be extracted from the cross-correlation spectrum when applying a longitudinal or a transversal external magnetic field.