Nonlinear quantum logic with colliding graphene plasmons

Graphene has emerged as a promising platform to bring nonlinear quantum optics to the nanoscale, where a large intrinsic optical nonlinearity enables long-lived and actively tunable plasmon polaritons to strongly interact. Here we theoretically study the collision between two counter-propagating plasmons in a graphene nanoribbon, where transversal subwavelength confinement endows propagating plasmons with %large effective masses a flat band dispersion that enhances their interaction. This scenario presents interesting possibilities towards the implementation of multi-mode polaritonic gates that circumvent limitations imposed by the Shapiro no-go theorem for photonic gates in nonlinear optical fibers. As a paradigmatic example we demonstrate the feasibility of a high fidelity conditional Pi phase shift (CZ), where the gate performance is fundamentally limited only by the single-plasmon lifetime. These results open new exciting avenues towards quantum information and many-body applications with strongly-interacting polaritons.