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 q...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-Stückelberg 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.展开更多
In this paper,the equivalent circuit of the non-autonomous Josephson junction(JJ)is presented and the effect of the proper frequency on the phaseφis studied.We also study nonlinear resonance phenomena in the oscillat...In this paper,the equivalent circuit of the non-autonomous Josephson junction(JJ)is presented and the effect of the proper frequency on the phaseφis studied.We also study nonlinear resonance phenomena in the oscillations of a modified Josephson junction(MJJ).These oscillations are probed through a system of nonlinear differential equations and the multiple time scale method is employed to investigate all different types of resonance that occur.The results of primary,superharmonic and subharmonic resonances are obtained analytically.We show that the system exhibits hardening and softening behaviors,as well as hysteresis and amplitude hopping phenomena in primary and superharmonic resonances,and only the hysteresis phenomenon in subharmonic resonance.In addition,the stabilities and the steady state solutions in each type of resonances are kindly evaluated.The number of equilibrium points that evolve with time and their stabilities are also studied.Finally,the equations of motion are numerically integrated to check the correctness of analytical calculations.We further show that the dynamics of the MJJ is strongly influenced by its parameters.展开更多
文摘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-Stückelberg 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.
文摘In this paper,the equivalent circuit of the non-autonomous Josephson junction(JJ)is presented and the effect of the proper frequency on the phaseφis studied.We also study nonlinear resonance phenomena in the oscillations of a modified Josephson junction(MJJ).These oscillations are probed through a system of nonlinear differential equations and the multiple time scale method is employed to investigate all different types of resonance that occur.The results of primary,superharmonic and subharmonic resonances are obtained analytically.We show that the system exhibits hardening and softening behaviors,as well as hysteresis and amplitude hopping phenomena in primary and superharmonic resonances,and only the hysteresis phenomenon in subharmonic resonance.In addition,the stabilities and the steady state solutions in each type of resonances are kindly evaluated.The number of equilibrium points that evolve with time and their stabilities are also studied.Finally,the equations of motion are numerically integrated to check the correctness of analytical calculations.We further show that the dynamics of the MJJ is strongly influenced by its parameters.
