Transition time in the stimulated Raman adiabatic passage technique

The technique of stimulated Raman adiabatic passage (STIRAP) is an efficient and robust technique for population transfer in three-state chain-wise connected quantum systems, 1-2-3. Here we analyze the transition time in STIRAP, that is the time it takes for the population to be transferred from state 1 to state 3. We derive a very simple formula for this transition time, which shows that it is inversely proportional to the nonadiabatic coupling (t(c)), estimated at the time tc when the pump and Stokes couplings have the same value. Explicit formulas for several pulse shapes of the pump and Stokes fields are derived. Contrary to the naive expectation that the transition time might be proportional to the delay between the pump and Stokes pulses, or to the width of their overlap region, we find that the transition time is inversely proportional to the delay, i.e., larger delays produce faster transitions. We also calculate the transition time in two important variations of the STIRAP technique-bright-STIRAP and STIRAP in multistate systems-where similar features are found.