Linear Optical Approach to Supersymmetric Dynamics

TL;DR

This paper proposes a linear optical scheme to simulate and observe supersymmetric quantum dynamics using photons, employing interferometry and Suzuki-Trotter expansion, and demonstrates its feasibility with current technology.

Contribution

It generalizes ultracold atom supersymmetry experiments to linear optics, introducing a universal, experimentally feasible optical setup for supersymmetric quantum simulations.

Findings

Scheme is universal and adaptable to current optical technologies.

Uses diffraction and phase plates to simulate kinetic and potential terms.

Proposes an interferometric method with amplitude alternator for non-unitary operators.

Abstract

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.