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

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