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Supersymmetry in quantum optics and in spin-orbit coupled systems

Light-matter interaction is naturally described by coupled bosonic and fermionic subsystems. This suggests that a certain Bose-Fermi duality is naturally present in the fundamental quantum mechanical description of photons interacting with atoms. We reveal submanifolds in parameter space of a basic light-matter interacting system where this duality is promoted to a supersymmetry (SUSY) which remains unbroken. We show that SUSY is robust with respect to decoherence and dissipation. In particular, a stationary density matrix at the supersymmetric lines in the parameter space has a degenerate subspace. A dimension of this subspace is given by the Witten index and thus topologically protected. As a consequence of this SUSY, dissipative dynamics at the supersymmetric lines is constrained by an additional conserved quantity which translates some part of information about an initial state into the stationary state subspace. We also demonstrate a robustness of this additional conserved quantity away from the supersymmetric lines. In addition, we demonstrate that the same SUSY structures are present in condensed matter systems with spin-orbit couplings of Rashba and Dresselhaus types, and therefore spin-orbit coupled systems at the SUSY lines should be robust with respect to various types of disorder and decoherences. Our findings suggest that optical and condensed matter systems at the SUSY points can be used for quantum information technology and can open an avenue for quantum simulation of the SUSY field theories.