Left-handedness in the balanced/unbalanced resonance conditions of a quantized composite right-left handed transmission line

Left-handedness signifies negative permittivity (${\epsilon }_r$) and permeability ((μ_r)) in the same frequency band. The ${\epsilon }_r$ and ${\mu }_r$ are evaluated in a quantized composite right-left handed transmission line (CRLH-TL), and the frequency band for left-handedness is also valuated in the balanced resonance ($L_r{C}_l=L_l{C}_r$) and unbalanced resonance($L_l{C}_r\mathrm{\ne }{L}_r{C}_l$) cases in the displaced squeezed Fock state. The results show that the balanced resonance plays an important role in bandwidth and achieving for left-handedness. These displays some quantum mechanical behaviors and proposes a new potential approach to wider frequency band left-handedness for the quantized CRLH-TL.