  This study focuses on generating and manipulating squeezed states with two
external oscillators coupled by an InP HEMT transistor operating at cryogenic
temperatures. First, the small-signal nonlinear model of the transistor at high
frequency at 5 K is analyzed using quantum theory, and the related Lagrangian
is theoretically derived. Subsequently, the total quantum Hamiltonian of the
system is derived using Legendre transformation. The Hamiltonian of the system
includes linear and nonlinear terms, by which the effects on the time evolution
of the states are studied. The main result shows that the squeezed state can be
generated owing to the nonlinearity of the transistor, and more importantly, it
can be manipulated by some specific terms introduced in the nonlinear
Hamiltonian. In fact, the nonlinearity of the transistors induces some effects
such as capacitance, inductance, and second-order transconductance, by which
the properties of the external oscillators are changed. These changes may lead
to squeezing or manipulation of the parameters related to squeezing in the
oscillators. In addition, it is theoretically derived that the circuit can
generate two-mode squeezing. Finally, second-order correlation (photon counting
statistics) is studied as a complementary task, and the results demonstrate
that the designed circuit exhibits antibunching, where the quadrature operator
shows squeezing behavior.
