  The standard weak-coupling approximations associated to open quantum systems
have been extensively used in the description of a two-level quantum system,
qubit, subjected to relatively weak dissipation compared with the qubit
frequency. However, recent progress in the experimental implementations of
controlled quantum systems with increased levels of on-demand engineered
dissipation has motivated precision studies in parameter regimes that question
the validity of the approximations, especially in the presence of
time-dependent drive fields. In this paper, we address the precision of
weak-coupling approximations by studying a driven qubit through the numerically
exact and non-perturbative method known as the stochastic Liouville-von Neumann
equation with dissipation. By considering weak drive fields and a cold Ohmic
environment with a high cutoff frequency, we use the Markovian Lindblad master
equation as a point of comparison for the SLED method and study the influence
of the bath-induced energy shift on the qubit dynamics. We also propose a
metric that may be used in experiments to map the regime of validity of the
Lindblad equation in predicting the steady state of the driven qubit. In
addition, we study signatures of the well-known Mollow triplet and observe its
meltdown owing to dissipation in an experimentally feasible parameter regime of
circuit electrodynamics. Besides shedding light on the practical limitations of
the Lindblad equation, we expect our results to inspire future experimental
research on engineered open quantum systems, the accurate modeling of which may
benefit from non-perturbative methods.
