Nondecaying state in a three-level system driven by a single field: Effect of relaxations

We discuss the condition under which a pair of closely lying levels, when coupled to a fourth level via a single-laser field, exhibit population trapping without decay to a lower level. In the discussion, the decay between the pair and the fourth level is taken into account. When the fourth level is lower than the pair, the condition for population trapping in the pair can be satisfied under arbitrary laser intensity by adjusting the laser detuning. When the fourth level is above the pair, population trapping in the pair is impossible when the decay from the fourth level to the pair is included. The influence of the decay between the pair and the fourth level on the spontaneous spectrum from the pair to the lower level is also studied.