Coherence preservation of Markovian open quantum systems in N-level Ξ configuration

Coherence preservation of Ξ-type N-level atoms is investigated. The coherence is embodied by the coherence functions that are defined in an N-dimension Hilbert space. The objective is to design external control field that maintains the coherence functions at a constant value. For this purpose, the number of components of the field should be the same as the number of coherence functions. We demonstrate that it is possible to keep multi-coherence functions constant for an finite time by applying designed field that each component addresses a particular coherence function. In addition, the applied field has singular character that makes the field effective within an interval time, and its practical significance is discussed in this circumstance.