Long-lifetime Polariton BEC in a Microcavity with an Embedded Quantum Well and Graphene

We study the propagation of a Bose-Einstein condensate (BEC) of long-lifetime exciton polaritons in a high-quality microcavity with an embedded semiconductor quantum well or a graphene layer using the Gross-Pitaevskii equation. It is shown that in these heterostructures the BEC of the long-lifetime polaritons can propagate over the distance up to 0.5 mm. The obtained results are consistent with the recent experimental observations for GaAs/AlGaAs microcavity. It is demonstrated that the BEC density in a polariton trace in a microcavity with embedded graphene at large distances from the excitation spot is higher for the microcavity with higher dielectric constant. It is also predicted that the propagation of a polariton BEC in a microcavity with graphene is dynamically tunable by changing the gap energy, that makes it potentially useful for applications in integrated optical circuits.