  The longitudinal ($\Gamma_1$) and transverse ($\Gamma_2$) decay rates of a
two-level quantum system have profound influence on its evolution. Atomic
systems with $\Gamma_2=\tfrac{1}{2}\Gamma_1$ have been studied extensively, but
with the rise of solid-state quantum devices it is also important to consider
the effect of stronger transverse relaxation due to interactions with the solid
environment. Here we study the quantum dynamics of a single organic dye
molecule driven by a laser. We measure the variation of $\Gamma_2$ with
temperature and determine the activation energy for thermal dephasing of the
optical dipole. Then we measure the second-order correlation function
$g^{(2)}(\tau)$ of the light emitted by the molecule for various ratios
$\Gamma_2/\Gamma_1$ and saturation parameters $S$. We show that the general
solution to the optical Bloch equations accurately describes the observed
quantum dynamics over a wide range of these parameters, and we discuss the
limitations of the various approximate expressions for $g^{(2)}(\tau)$ that
appear in the literature.
