Negative refraction without absorption via quantum coherence

Negative refraction of a probe field is studied in a dense gas consisting of cascade-type four-level atoms. By coupling the magnetic component of the probe field to a Lambda scheme with initially prepared coherence in the two lower levels, strong negative permeability with minimal absorption can be obtained. The permittivity of the gas to the electric component of the probe field can be made negative by taking into account the local field effect of the dense atoms. Strong negative refraction with zero absorption can be achieved in a wide range of parameters in our scheme. A possible experimental realization is also discussed.