  The concept of supersymmetry developed in particle physics has been applied
to various fields of modern physics. In quantum mechanics, the supersymmetric
systems refer to the systems involving two supersymmetric partner Hamiltonians,
whose energy levels are degeneracy except one of the systems has an extra
ground state possibly, and the eigenstates of the partner systems can be mapped
onto each other. Recently, an interferometric scheme has been proposed to show
this relationship in ultracold atoms [Phys. Rev.A 96, 043624 (2017)]. Here this
approach is generalized to linear optics for observing the supersymmetric
dynamics with photons. The time evolution operator is simulated approximately
via Suzuki-Trotter expansion with considering the realization of the kinetic
and potential terms separately. The former is realized through the diffraction
nature of light and the later is implemented using phase plate. Additionally,
we propose an interferometric approach which can be implemented perfectly using
amplitude alternator to realize the non-unitary operator. The numerical results
show that our scheme is universal and can be realized with current
technologies.
