Two-level Systems Coupled to Graphene plasmons: A Lindblad equation approach

In this paper we review the theory of open quantum systems and macroscopic quantum electrodynamics, providing a self-contained account of many aspects of these two theories. The former is presented in the context of a qubit coupled to a electromagnetic thermal bath, the latter is presented in the context of a quantization scheme for surface-plasmon polaritons (SPPs) in graphene based on Langevin noise currents. This includes a calculation of the dyadic Green's function (in the electrostatic limit) for a Graphene sheet between two semi-infinite linear dieletric media, and its subsequent application to the construction of SPP creation and annihilation operators. We then bring the two fields together and discuss the entanglement of two qubits in the vicinity of a graphene sheet which supports SPPs. The two qubits communicate with each other via the emission and absorption of SPPs. We find that a Sch\"odinger cat state involving the two qubits can be partially protected from decoherence by taking advantage of the dissipative dynamics in graphene. A comparison is also drawn between the dynamics at zero temperature, obtained via Schrodinger's equation, and at finite temperature, obtained using the Lindblad equation.