Efficient generation of heralded narrowband color-entangled states

We show that narrowband two-color entangled single Stokes photons can be generated in a ultra-cold atoms sample via selective excitation of two spontaneous four-wave mixing (SFWM) processes. Under certain circumstances, the generation, heralded by the respective common anti-Stokes photon, is robust against losses and phase-mismatching and is remarkably efficient owing to balanced resonant enhancement of the two four-wave mixing processes in a regime of combined induced transparency. Maximally color-entangled states can be easily attained by adjusting the detunings of the external couplings and driving fields, even when these are quite weak.