  We present a theoretical study of noise-induced quantum coherences in a model
three-level V-type system interacting with incoherent radiation, an important
prototype for a wide range of physical systems ranging from trapped ions to
biomolecules and quantum dots. By solving the quantum optical equations of
motion for the V-type system, we obtain analytical expressions for the
noise-induced coherences and show that they exhibit an oscillating behavior in
the limit of large excited level spacing $\Delta$ ($\Delta /\gamma \gg 1$,
where $\gamma$ is the radiative decay rate). Most remarkably, we find that in
the opposite limit of small level spacing $\Delta/\gamma \ll 1$, appropriate
for large molecules, (a) the coherences can survive for an arbitrarily long
time $\tau=(2/\gamma) (\Delta/\gamma)^{-2}$ before eventually decaying to zero,
and (b) coherences at short times can be substantial. We further show that the
long-lived coherences can be robust against environmental relaxation and
decoherence, and discuss implications to the design of quantum heat engines and
incoherent light excitation of biological systems.
