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