Long-lived quasi-stationary coherences in V-type system driven by incoherent light

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.