Observation of non-Hermitian topology with non-unitary dynamics of solid-state spins

Non-Hermitian topological phases exhibit a number of exotic features that have no Hermitian counterparts, including the skin effect and breakdown of the conventional bulk-boundary correspondence. Recently, they have attracted tremendous attentions and experimental observations of the non-Hermitian skin effect have been reported in mechanical metamaterials, non-reciprocal topolectric circuits, and photonic systems. Here, we implement the non-Hermitian Su-Schrieffer-Heeger (SSH) hamiltonian, which is a prototypical model for studying non-Hermitian topological phases, with a solid-state quantum simulator consisting of an electron spin and a 13C nuclear spin in a nitrogen-vacancy center in a diamond. By employing a dilation method, we realize the desired non-unitary dynamics for the electron spin and map out its spin texture in the momentum space, from which the corresponding topological invariant can be obtained directly. Our result paves the way for further exploiting and understanding the intriguing properties of non-Hermitian topological phases with solid-state spins or other quantum simulation platforms.