The emission spectrum of semiconductor quantum dots (QDs) is affected by the phonon environment, in particular through the appearance of the phonon sideband (PSB). However, the standard quantum-optical method of calculating the emission spectrum using the quantum regression theorem fails to correctly capture the PSB unless the polaron master equation is employed.  

In this work I present a new method of modelling the PSB relying on the recently developed ‘sensor theory'. The method introduces an additional ‘sensor' to the description of the system. This allows for a simple calculation of correlation functions of the frequency-filtered emitted light. However, previous studies utilising the senor theory have not considered the influence of the phonon environment. 

I will demonstrate an extension of the sensor theory and show that it successfully captures the PSB even when using a simplistic weak-coupling master equation for the phonon environment. Extensions to higher-order frequency-filtered correlations will also be discussed.