  This article mainly focuses on one of the important phenomena in the quantum
realm called entanglement. It is clear that entanglement created due to the
nonlinearity property has been arisen by some different methods. This study in
contrast uses a unique approach in which a cryogenic low noise amplifier is
designed and using the transistor nonlinearity effect (third-order
nonlinearity) entangled microwave photons are created. It is supposed that the
low noise amplifier contains two coupled oscillators resonating with different
frequencies. The mentioned oscillators are coupled to each other through the
gate-drain capacitor and nonlinear transconductance as an important factor by
which the entangled microwave photons are strongly manipulated. For
entanglement analysis, the Hamiltonian of the system is initially derived, then
using the dynamic equation of motion of the designed amplifier the oscillator's
number of photons and also the phase sensitive cross-correlation factor are
calculated in Fourier domain to calculate the entanglement metric. As a main
conclusion, the study shows that the designed low noise amplifier using
nonlinearity of the transistor has the ability to generate the entangled
microwave photons at very low intrinsic transconductance and more importantly
when the noise figure is strongly minimized. Additionally, a cryogenic low
noise amplifier is designed and simulated to verify that it is possible to
achieve an ultra-low noise figure by which the probability of the generation of
the entangled microwave photons is increased.
