  The optical response of an electronic two-level system (TLS) coupled to an
incident continuous wave (cw) electromagnetic (EM) field is simulated
explicitly in one dimension by the following five approaches: (i) the coupled
Maxwell-Bloch equations, (ii) the optical Bloch equation (OBE), (iii) Ehrenfest
dynamics, (iv) the Ehrenfest+R approach and (v) classical dielectric theory
(CDT). Our findings are as follows: (i) standard Ehrenfest dynamics predict the
correct optical signals only in the linear response regime where vacuum
fluctuations are not important; (ii) both the coupled Maxwell-Bloch equations
and CDT predict incorrect features for the optical signals in the linear
response regime due to a double-counting of self-interaction; (iii) by exactly
balancing the effects of self-interaction versus the effects of quantum
fluctuations (and insisting on energy conservation), the Ehrenfest+R approach
generates the correct optical signals in the linear regime and slightly beyond,
yielding, e.g., the correct ratio between the coherent and incoherent
scattering EM fields. As such, Ehrenfest+R dynamics agree with dynamics from
the quantum OBE, but whereas the latter is easily applicable only for a single
TLS in vacuum, the former should be applicable to large systems in environments
with arbitrary dielectrics. Thus, this benchmark study suggests that the
Ehrenfest+R approach may be very advantageous for simulating light-matter
interactions semiclassically.
