Coherence Induced by Incoherent Pumping Field and Decay Process in Three-level $\Lambda$ Type Atomic System

Following the method of Victor V. Kozlov et al.[PhysRevA. 74. 063829],we inspect the coherence induced by incoherent pump and spontaneous decay process in $\Lambda$ type three-level atomic system with degenerated lower duplicate levels. The system shows a coherent population trapping state and multi-steady states characteristic in different conditions. Interestingly, two kinds of steady states generated by the system in different sets of pumping and decaying parameters, the "singlet" state and the "triplet" state, exhibit stable or unstable characteristics under the action of pumping field and vacuum reservoir, which promise fruitful applications to atomic coherence and interference in quantum optics.