Left handness in a four-level atomic system

A scheme is proposed for realizing simultaneous negative permittivity and negative permeability based on quantum coherence in a four-level dense atomic system here.Under some parametric conditions the system shows that simultaneous negative permittivity and negative permeability(i.e.Left handness) can be achieved in a wider frequency band because of quantum coherence.And the novelty properties of gain and dispersion near the resonance frequency may have some potential applications.