Numerical implementation of a matter-wave Mach-Zehnder interferometer

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.