Peculiarities of the dynamics of quantum states of Josephson nanosystems during their interaction with a non-classical electromagnetic field

The dynamics of quantum states of a Josephson superconducting nanosystem under the action of various non-classical fields is studied. Such consideration is promising from the point of view of developing methods for controlling the properties of the systems under consideration and their use in nanoelectronics, as well as for the development of quantum logic protocols. Theoretical modeling of the operation of planar circuits based on Josephson superconducting nanostructures outside the linear regime is carried out, and methods for controlling quantum states of higher dimension in such systems are developed. As an example of a Josephson nanostructure, a qubit-transmon is considered, made on the basis of a nanoscale superconducting Josephson contact, whose eigenstates can be described within the framework of a quantum anharmonic oscillator model and analyzed in terms of bosonic ladder operators of creation and annihilation of excitation. The peculiarities of the excitation dynamics of such structures due to the Kerr nonlinearity of the Josephson subsystem are revealed. The formation of states with different properties arising in the process of dynamics due to the effects of nonlinear phase modulation is shown. The possibility of significant noise suppression in the system below the shot noise level has been demonstrated. The possibility of controlling the excitation of states of the Josephson subsystem by varying the parameters of nonlinearity and frequency detuning has been discovered. The effect of establishing an energy balance between subsystems due to the presence of Kerr nonlinearity is revealed.