Semiclassical calculation of the diffusion constant for the Λ system momentum

We present a one-dimensional, semiclassical calculation of the momentum diffusion constant for a stationary Λ atom. We show that if the difference detuning between the driving fields is zero, the diffusion vanishes, and we interpret this behavior in terms of the atom-field eigenstates. We present explicit solutions to the equations of motion in the special case where one of the driving fields vanishes and compare them to the case of a two-level atom at a field node. Finally, we examine the correspondence between the semiclassical and quantum-mechanical analyses at zero difference detuning and we show a correspondence between the semiclassical and quantum-mechanical dark states when the driving fields are superpositions of plane waves with the same magnitude of wave vector.