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Nonlinear Optics

Numerical implementation of a Mach-Zehnder interferometer for Bose-Einstein condensates

Gustavo Marín-Alvarado, Karen Rodríguez

Published Jan 1, 2017• 0 citations
Publisher

Abstract

We numerically implement a Mach-Zehnder interferometer for Bose-Einstein condensates using time-dependent potentials. We analyze density and phase dynamics, the fidelity of the engineered potentials and the acquired phase-difference as function of the phase-shifter depth.
DOI
10.1364/nlo.2017.nw4a.11

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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.
We construct a Mach-Zehnder interferometer using Bose-Einstein condensed rubidium atoms and optical Bragg diffraction. In contrast to interferometers based on normal diffraction, where only a small percentage of the atoms contribute to the signal, our Bragg diffraction interferometer uses all the condensate atoms. The condensate coherence properties and high phase-space density result in an interference pattern of nearly 100% contrast. The two arms of the interferometer may be completely separated in space, making it an ideal tool that can be used to detect vortices or other topological condensate phases.