Photon circulation in photonic structures integrated with quantum dots - a consequence of multi-path geometry

The typical route to achieve circulation of photons is via artificial gauge fields. We show that even without any artificial gauge field, by using multiple path geometry such as, that of a triangle and the quantum nature of bosonic particles, the steady state photonic current can circulate in a photonic structure integrated with quantum dots. Our system is made up of three quantum dots which are connected in a triangular geometry, this geometry is embedded in photonic crystal and waveguide. The photon-exciton interaction limits the number of photons that can be transferred between the quantum dots, a phenomenon also called photon blockade. We use the Lindblad form of the quantum optical master equation to calculate the steady state currents with the maximal photon number per site set by the photon blockade. Our results show that the photon circulations have a non-trivial dependence not only on the internal system parameters such as the tunneling coefficient, or the effective photon-photon interaction but also on external parameters such as the system-reservoir coupling. This system can be tailored to function as a density independent local pump or memory device.