Controllable PT phase transition and asymmetric soliton scattering in atomic gases with linear and nonlinear potentials

We propose a physical scheme to realize combined linear and nonlinear optical potentials with parity-time ($\mathcal{PT}$) symmetry and investigate the scattering property of optical solitons in a coherent atomic gas. We show that the combined linear and nonlinear $\mathcal{PT}$-symmetric potentials can be created through the spatial modulation of the control laser field and the inclusion of the Kerr nonlinearity of the signal laser field. We demonstrate that the imaginary part of the nonlinear $\mathcal{PT}$ potential plays a crucial role for the occurrence of the $\mathcal{PT}$ phase transition and the change of the $\mathcal{PT}$ phase diagram, which can be actively manipulated in our system. We demonstrate also that the system supports stable optical solitons, which can be managed via tuning the combined linear and nonlinear $\mathcal{PT}$ potentials; furthermore, by taking the combined linear and nonlinear $\mathcal{PT}$ potentials as a defect, the scattering of the optical solitons by the defect displays evident asymmetric behavior, controlled by the imaginary parts of the combined linear and nonlinear $\mathcal{PT}$ potentials. The results reported here may have potential applications in optical information processing and transmission.