We numerically implement a Mach-Zehnder interferometer, where the coherence and oscillatory properties of Bose-Einstein condensates are explored and the system is modeled by the Gross-Pitaevskii equation. Several time-dependent external trapping potentials were engineered seeking the adiabatic regime which is quantified using fidelity measurements with respect to the actual ground-state of the trap. The dynamics of both conjugate variables, namely density and phase of the matter-wave function, are shown. Moreover, the density and fidelity profiles of the system are presented when the phase-shifter is switching-on and -off, being found in the presented profiles that the system exhibits three different regimes during the recombination stage among them even an orthogonal BEC to the original one is obtained. We achieve the numerical solution through an adequate implementation of the finite-difference method for the spatial discretization and a Runge-Kutta method for the time evolution.

No abstract

More than two decades ago a new state of matter called Bose-Einstein Condensation was proved experimentally although predicted long before in 1924-25. At extremely low temperatures and controlled densities, this exotic state can be achieved where all atoms share the same energy and linear momentum similarly as the light behaves in a laser. Therefore, it is interesting to analyze the matterwave counterparts for the nowadays well-known optical devices. Here, we present a numerical implementation of a Mach-Zehnder interferometer which we engineered by means of time-dependent external trapping potentials. We use an appropriate implementation of the finite-difference method for the spatial discretization and the Runge-Kutta technique for the time evolution. The dynamics of both conjugate variables, namely density and phase of the matter-wave functions are shown. Our aim is also to show that this kind of problems and techniques can be addressed in standard courses of Quantum Mechanics and Computational Physics.