  Supersymmetric systems derive their properties from conserved supercharges
which form a supersymmetric algebra. These systems naturally factorize into two
subsystems, which, when considered as individual systems, have essentially the
same eigenenergies, and their eigenstates can be mapped onto each other. We
first propose a one-dimensional ultracold atom setup to realize such a pair of
supersymmetric systems. We propose a Mach-Zehnder interference experiment which
we demonstrate for this system, and which can be realized with current
technology. In this interferometer, a single atom wave packet that evolves in a
superposition of the subsystems, gives an interference contrast that is sharply
peaked if the subsystems form a supersymmetric pair. Secondly, we propose a
two-dimensional setup that implements supersymmetric dynamics in a synthetic
gauge field.
