Phase Dependent Parity Time Symmetry in a quantum dot nanostructure

We present a diamond configuration quantum dots nanostructure trapped in two-dimensional (2D) optical lattices for the investigation of parity time (PT ) symmetry. We trap quantum dots in a Gaussian density distribution to examine the PT, non-PT, and anti-PT symmetry in periodic 2D optical lattices. The variation in the relative phase of the optical beams in the quantum dots spectrum indicates either PT, anti-PT, or non-PT symmetry, resulting in an intriguing modulation of imaginary and real refractive index (RI) components. Controlling the appropriate modulation of the RI leads in PT symmetry being controlled by a single parameter, the relative phase of the optical fields. Using detuning and the coupling field of Rabi frequencies, we may determine the state of PT symmetry as well as the direction of field propagation. Coherent control of PT symmetry in 2D quantum dot nanostructure trapped in optical lattices may also have applications in 2D optical devices such as diodes, modulators and photonic transistors.