Figure 1.  (a) A quantum dots molecule is coupled to a cavity. The symbol V denotes an electrical voltage which is used to control the electron tunnel. (b) Schematic diagram of band structure and level configuration of a quantum dots molecule. The system of the quantum dots molecule consists of two dots with lateral couplings. The electron and hole are represented by the red circle and black circle, respectively

Figure 2.  The dynamics of the ${\text{LGI}}$ violation are plotted as a function of the tunnel strength ${T_e}$ when $g = 1$, $\Delta = 0$ and ${\omega _{21}} = 0$. The nonzero values of ${\text{VLGI}}$ demonstrate the presence of temporal quantum correlation

Figure 3.  The maximal ${\text{LGI}}$ violation varies with cavity frequency detuning. The parameters $g = 1$, ${T_e} = 0.5g$ and ${\omega _{21}} = 0$ are chosen

Figure 4.  The evolution of the spatial and temporal correlation is shown when the parameters $g = 1$, ${T_e} = 0.5g$, $\Delta = 0$ and ${\omega _{21}} = 0$ are chosen. The red dashed line denotes the spatial quantum correlation evaluated by ${l_1}$-norm quantum coherence. The black solid line describes the behavior of temporal correlation given by the ${\text{LGI}}$ violation

Figure 5.  The effects of environmental noise on the temporal correlation are considered when the parameters are $g = 1$, ${T_e} = 0.6g$, $\Delta = 0$ and ${\omega _{21}} = 0$. (a) The decreased oscillation of the ${\text{LGI}}$ violation is plotted when the spontaneous decay $\gamma = 0.02g$ and the cavity leakage $\kappa = 0.01g$; (b) The maximal ${\text{LGI}}$ violations are plotted as a function of the tunneling coupling for the different decaying parameters of $\gamma = 0.02g,\;0.01g$ which are represented by the red circles and black squares, respectively