Two-color Photonic Band Gaps Via Balanced Four-wave Mixing In One-dimensional Atomic Lattices

We have investigated the steady-state optical responses of ultracold atomstrapped in the1D optical lattices and driven into a four-level double-Lambdaconfiguration. We find that dynamically tunable two-color photonic bandgaps(PBGs) can be achieved in this atomic system via balanced four-wave mixing(FWM) and periodic density distribution. As is well known, photonic crystals(PCs) are composed of different dielectric materials arranged into some specialperiodic patterns, and are difficult to be modified in their structure such that thepositions, the widths, and other characteristics of PBGs cannot be changed ondemand. To avoid these difficulties or shortcomings of traditional PCs, here weconsider a novel periodic atomic structure by assuming that: I) vast cold atoms areloaded with a Gaussian distribution into the1D lattices of dipole traps; II) atomicabsorption and dispersion properties can be coherently modulated by atraveling-wave coupling laser. In this case, our numerical results show that a pairof well-developed PBG structures can be found on both probe transitions ascharacterized by high reflectivity platforms and low photonic densities. Inparticular, a narrow PBG is found inside the resonant EIT window with probeabsorption being well suppressed by quantum destructive interference, and a widePBG is located far from the probe resonance with probe absorption beinginherently negligible. It is worth stressing that both near-resonant narrow PBGand far-detuned wide PBG are two-color correlated PBGs in fact. The reason isthat one probe field can be converted into the other probe field and vice versa witha very high efficiency via coherent FWM in a closed loop interaction until thenonlinear balanced coupling is established. Our two-color correlated PBGs can be easily manipulated by changing the coupling field Rabi frequency, the geometricBragg detuning, the atomic density distribution, etc.Based on our work, it is easy to obtain other multi-color tunable PBGs byextending the present double-Lambda configuration into those configurations withsimilar symmetries of lattice atoms. Then it’s viable to manipulate weak lightsignals at network nodes via nonlinear effects at the single-photon level, e.g. toachieve optical switching, light routing, and photonic diodes.