Laser linewidth in a STIRAP process

[Malamala]

Hello! In a STIRAP process, for the right parameters (assuming a $\Lambda$-type transition), the lifetime of the excited state doesn't come into play, so one can achieve very narrow linewidths of the measured transition of interest, regardless of the linewidth of the intermediate, excited state. However, I am not sure I understand how does the laser linewidth come into play. I imagine that if the linewidth of the laser is bigger than the splitting between the 2 levels I am connecting (basically if the laser linewidths are bigger than the difference between the 2 laser frequencies) I won't be able to induce STIRAP (right?), so I can't have arbitrary large laser linewidths (unlike the case of the excited state, whose linewidth can in principle can be as large as possible, given that it is usually very far away from the 2 levels I am interested in). So how does the laser linewidth come into play? Is the transition linewidth actually limited by the laser linewdith? Or the laser linewidth doesn't matter as long as it is smaller than the splitting between the 2 levels? Thank you!

 

[Twigg]

So how does the laser linewidth come into play?

STIRAP is a form RAP (adiabatic passage). Adiabatic passage means that the quantum state needs to be preserved. If your laser linewidth is broader than the splitting between the bottom 2 states, then you will progress into a mixed state as the randomized fluctuation of the laser phase will scramble the phase of the atomic state.

Or the laser linewidth doesn't matter as long as it is smaller than the splitting between the 2 levels?

The broader the laser linewidth, the lower your population transfer efficiency will be with STIRAP. This is again because of loss as the excited state atoms are randomly shuffled back into the ground state by laser noise.

unlike the case of the excited state, whose linewidth can in principle can be as large as possible, given that it is usually very far away from the 2 levels I am interested in

This isn't inexactly true. The excited state linewidth has to be smaller than 1 over the pulse duration. Otherwise, you'd see spontaneous decay during your STIRAP pulses, and that has a similar effect of scrambling the coherent state during the adiabatic process. The result would also be atoms returning to the ground state.