  We explore the coherent dynamics of a three-level V-system interacting with a
thermal bath in the regime where thermal excitation occurs much faster than
spontaneous decay. We present analytic solutions of the Bloch-Redfield quantum
master equations, which show that strong incoherent pumping can generate
long-lived quantum coherences among the excited states of the V-system in the
overdamped regime defined by the condition $\Delta/(\bar{n}\gamma)<f(p)$, where
$\Delta$ is the excited-state level splitting, $\gamma$ is the spontaneous
decay rate, $\bar{n}\gg 1$ is the effective photon occupation number
proportional to the pumping intensity, and $f(p)$ is a universal function of
the transition dipole alignment parameter $p$. In the limit of nearly parallel
transition dipoles ($p\to 1$) the coherence lifetime $\tau_c = 1.34
(\bar{n}/\gamma) (\Delta/\gamma)^{-2}$ scales linearly with $\bar{n}$ and is
enhanced by the factor $0.67 \bar{n}$ with respect to the weak-pumping limit
[Phys. Rev. Lett. 113, 113601 (2014); J. Chem. Phys. 144, 244108 (2016)]. We
also establish the existence of long-lived quasistationary states, which occur
in the overdamped regime and affect the process of thermalization of the
V-system with the bath, slowing down the approach to thermal equilibrium. In
the case of nonparallel transition dipole moments ($p<1$), no quasistationary
states are formed and the coherence lifetime decreases sharply. Our results
reveal new regimes of long-lived quantum coherent dynamics, which could be
observed in thermally driven atomic and molecular systems.
