  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.
