Electromagnetically induced transparency (EIT) and Stimulated Raman adiabatic passage (STIRAP) What is the connection between Electromagnetically induced transparency (EIT) and Stimulated Raman adiabatic passage (STIRAP) in case of lambda system? can we achieve STIRAP with different shapes of input pulses?
 A: In general, Electromagnetic-Induced Transparency (EIT) refers to any phenomenon which involves the (quantum) interference between two (or more) transitions in a three (or more) level system - optical, optomechanical, electrical, etc. This is in opposition to something like the AC Stark shift where everything is usually far-off resonance and just driven by a strong intensity of the laser - i.e. a very intense laser may shift the absorption lines of the atoms (say) so that they are not resonant anymore with another beam, and hence become transparent. EIT, on the other hand, gets its transparency from $a + (-a) = 0$.
In theory, STIRAP is an example of EIT.
In pratice, though, STIRAP is an example of Coherent Population Transfer (CPT). That is, it is used to e.g. coherently move the atomic population from a state $|1\rangle$ to a state $|2\rangle$ by driving $|1\rangle \rightarrow |3\rangle$ and $|2\rangle\rightarrow |3\rangle$ transitions, that is by never actually coupling $|1\rangle$ and $|2\rangle$ directly by a single laser beam. Since you want to eliminate absorption and then spontaneous emission (which would not be coherent), you detune the two transitions, in a way that the resulting interference of the two beams gives you an effective ("dressed") dark state, i.e. one that does not actually absorb (and spontaneously emit) light.
This dark state in usually expressed as $|\text{dark}\rangle = \cos\theta |1\rangle - \sin\theta|2\rangle$, where $\tan\theta$ is the ratio of the strengths of the pump $\Omega_P$ and Stokes $\Omega_S$ beams. So, changing the powers of the beams (the "shape of the pulses" you are quoting) such that $\theta$ adiabatically goes $0$ to $\pi/2$ results in a coherent (never a spontaneous scattering event) and total (because adiabatic) population transfer. Does the exact shape of the input beams matter? Well yes, but you can compromise on the effect it has by taking care of how slow you vary them (because of adiabaticity).
Long story short, STIRAP focusses on the populations of the states, that is the diagonal elements of the density matrix
$\rho_{jj}$.
"Pure"-EIT focusses on the off-diagonal elements of the density matrix $\rho_{ij}$ with $i \neq j$. This affects the optical response of a material: for example, the (macroscopic) polarisation $P$ at the transition frequency $\omega_{12}$ is related to the (microscopic) coherence $\rho_{12}$.
