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A semiconductor quantum dot (QD) embedded within an optical microcavity is asystem of fundamental importance within quantum information processing. Theoptimization of quantum coherence is crucial in such applications, requiring anin-depth understanding of the relevant decoherence mechanisms. We provideherein a critical review of prevalent theoretical treatments of the QD-cavitysystem coupled to longitudinal acoustic phonons, comparing predictions againsta recently obtained exact solution. Within this review we consider a range oftemperatures and exciton-cavity coupling strengths. Predictions of the polaronNakajima-Zwanzig (NZ) and time-convolutionless (TCL) master equations, as wellas a variation of the former adapted for adiabatic continuous wave excitation(CWE), are compared against an asymptotically exact solution based uponTrotter's decomposition (TD) theorem. The NZ and TCL implementations, whichapply a polaron transformation to the Hamiltonian and subsequently treat theexciton-cavity coupling to second order, do not offer a significant improvementaccuracy relative to the polaron transformation alone. The CWE adaptationprovides a marked improvement, capturing the broadband features of theabsorption spectrum (not present in NZ and TCL implementations). We attributethis difference to the effect of the Markov approximation, and particularly itsunsuitability in pulsed excitation regime. Even the CWE adaptation, however,breaks down in the regime of high temperature ($50K$) and strong exciton-cavitycoupling ($g \gtrsim 0.2$ meV). The TD solution is of comparable computationalcomplexity to the above-mentioned master equation approaches, yet remainsaccurate at higher temperatures and across a broad range of exciton-cavitycoupling strengths (at least up to $g=1.5$ meV).

Phonon-induced dephasing in quantum dot-cavity QED: Limitations of the polaron master equation