Negative refraction index of the mesoscopic left-handed transmission line in the thermal Fock state

Negative refractive index (NRI) of the quantized lossless mesoscopic left-handed transmission line (LHTL) is deduced numerically in thermal Fock state. Some specific quantum features of NRI dependent the temperature, frequency of the electromagnetic wave and photon numbers, and quantum fluctuations are shown in the lossless LHTL. The results are significant for the miniaturizing applications of LHTL and quantum circuits.