New analytic solutions to the problem of a three-state system driven simultaneously by resonant optical pulses of different shapes are presented. The solutions are useful for prescribing the conditions for complete population transfer from one state to another or for complete population return.
This paper presents an analytic study of the properties of a three-state system coupled to two external laser fields on two-photon resonance. The intermediate state is generally off single-photon resonance and can decay irreversibly out of the system. The two fields are assumed to have the same pulse-shaped time dependence but may have different strengths. Various general properties for arbitrary pulse shapes, detunings and decay rates are derived and illustrated with an exactly solvable analytic model. They include the conditions for complete population transfer and depletion, complete population loss or no loss, various limitations on the values of the populations, the effect of overdamping at large decay rates and others.
We use a three-state model for an atom or molecule in which two transitions are simultaneously driven by the oscillating electric fields of two laser beams. The amplitudes and detunings of the applied oscillating fields vary during the optical pulse, which can cause transitions from one state to another. For some special cases not previously known, the transition probabilities and probabilities of no transition are obtained analytically. We give conditions for complete transfer of the atomic population from one state to another, and for complete return to the initial state.
We demonstrate that various properties of population transfer by delayed pulses in three-level systems on two-photon resonance can be deduced analytically and for general pulse shapes. We use the fact that the three-level system reduces to effective two-level problems at large intermediate-level detuning \ensuremath{\Delta}, on resonance (\ensuremath{\Delta}=0) and for completely overlapping pulses. Special attention is paid to the effect of the pulse order on the population transfer efficiency. We show that on resonance the transfer efficiency depends substantially on the pulse order, while at large \ensuremath{\Delta} it does not. We also find that under some natural restrictions on the symmetry of the problem, the population of the initial level does not depend on the pulse order at any \ensuremath{\Delta}. Furthermore, we demonstrate that the population transfer in the three-level system can be viewed as a level-crossing problem in an equivalent two-level system not only at large \ensuremath{\Delta} (which is known) but also on resonance, \ensuremath{\Delta}=0. The effective on-resonance two-level problem is interesting by itself as it shows that a level crossing and adiabatic evolution do not necessarily lead to complete population inversion. As examples throughout the paper, we present several analytically solvable models.