Excitation of squeezed States in a Transmission by a Josephson Degenerate Parametric Amplifier

Squeezed states of the radiation field can be used in several ways to increase the sensitivity of precision quantum radar measurements 1 . It is well known, that s queezed state s 2 can be genera ted by a DC pumped degenerate Josephson parametric amplifier , (DCPJPA) 3 4 4 . The DCPJPA consists of a Josephson Junction in series with a DC voltage source, and LC parallel circuit coupled to a long lossless transmission line 5 . A sufficiently long transmission line acts also as an ohmic resistor with a real impedance equal to the wave impedance of the transmission line. A DC voltage applied to a Josephson junction excites in the Josephson an AC current with a frequency proporti onal to the applied Voltage ( f 0 » 483,6 GHz/mV). Applying a DC voltage corresponding to twice the r esonant frequency f r of the LC circuit allows to generate squeezed photon states at f r . The problem has to be treated quantum mechanically under quantization of the LC circuit as well as the transmission line. Pulsed operation of the DCPJPA as well as thermal excitation of the transmission line has to be considered. A transmission line initia lly thermally excited and of length sufficiently large that the signal propagation time along the transmission line exceeds the modeling time interval models an infinitely long transmission line. For finite excitation pulse length the spectral width of the pulsed signal of the DCPJPA excites numerous longitudinal transmission line modes. The statistics of the excited transmission line wave has to be investigated