JPAdroid

Use your phone for evaluating the time evolution of an ideal JPA. -IMS 2017

This educational app uses a circuit model of an ideal Josephson parametric amplifier (JPA) for modelling of the dynamical behavior. It basically consists of three sections. In the first section, one can choose the parameters for evaluating the dynamics of the system. The results are displayed as line graphs in another section. The third section consists of a comprehensive documentation for the problem of parametric amplification. Here, the governing equations are derived by formulating the Lagrangian of the system. From this, the classical Hamilton function is obtained by Legendere transform. Canonical quantization with a certain commutator relation is then used to obtain the quantum mechanical description of the The quantum Hamiltonian is then written in terms of creation- and annihilation operators, in second quantization. We then derive expressions for the time evolution of the creation- and annihilation operators and their second order combinations. The system energy is given by the time evolution of the photon number operator. The app uses numerical solvers for calculating a solution to a system of 14 coupled differential equations. One can choose between a classical and a quantum mechanical description and numerical evaluation.