Tunable spectral singularities: Coherent perfect absorber and laser in an atomic medium

We propose a scheme for a coherent perfect absorber (CPA) and a laser in an atomic medium with gain and loss, obeying simultaneously a spectral singularity and a time-reversed spectral singularity, both occurring at different wavevectors (or frequencies). We term this system a CPA-and-laser and investigate its features allowing to obtain asymmetric lasing and absorbing properties, switches, etc. We show that the CPA-and-laser can be obtained by modifying characteristics of a CPA-laser of an initial -symmetric configuration, provided there are at least three tunable parameters. The physical mechanism of emergence of a CPA-and-laser in this way, is based on splitting of a self-dual spectral singularity of the -symmetric CPA-laser into the spectral singularity and time-reversed spectral singularity. After the discussion of a particular example of a bilayer consisting of one active and one passive slabs, we suggest a realistic physical system for implementing a CPA-and-laser. It consists of two adjacent atomic cells filled with isotopes of Λ-type three-level rubidium atoms interacting with probe and control fields, allowing for the required number of tunable parameters.