Quantum Interferometry for Different Energy Landscapes in a Tuneable Josephson Junction Circuit

This paper presents a simple Josephson-junction circuit with two parameters (inductance and capacitance) which can be tuned to represent different energy landscapes with different physical properties. By tuning this quantum circuit through external accessible elements we can move from two to three and more energy levels depending on the parameter setting. The inductance, the capacitance as well as the external voltage (driving terms) condition the number of relevant energy levels as well as the model to be used. We show that the quantized circuit represents a multi-state system with tunneling induced by the Landau-Zener and Landau-Zener-Stuckelberg transition. The special cases of single crossing and multi-crossing models are thoroughly studied and the transition probability is obtained in each case. It is proven that, the crossing time as well as the relaxation time affect drastically the transition probability; the system mimics a single passage for short relaxation and a multiple passage problem for large relaxation. The nonlinearity of energy levels modifies the transition probability and the derived adiabatic parameters help to redefine the Landau-Zener probability. The observed constructive and destructive interferences are parametrically conditioned by the initial condition set by the inductive branch. Moreover, the total population transfers as well as the complete blockage of the system are obtained in a permissible range of parameters only by changing the values of the inductance. Therefore, the system models a controllable level-crossing where the additional branches (inductive and capacitive) help in designing the number of states, the type of interferometry as well as the control of states occupation.