Nonetheless, this does not spell the end for mixed quantum-classical approaches. Although we will wish to treat the cavity mode quantum mechanically, there is probably no need to treat the entire system in this way. For instance, it is yet to be verified in future work whether the continuous dissipative bath modes can be treated classically. Finally, we must also consider the error inherent to the Ehrenfest meanfield approximation, which is well known to have a poor description of detailed balance. In previous studies, this approximation has been found to be significantly less accurate than alternative mixed quantum-classical methods such as spin mapping and the mapping approach to surface hopping. Therefore, in future work, we will investigate the possibility of combining HEOM with these more reliable approximations, which may overcome some of the errors observed with the Ehrenfest approximation in this work.