We investigate the Kerr and magneto-optical effects for a probe laser field with two orthogonally polarized components, propagating in a cold Rydberg atomic gas with an inverted-$\mathsf{Y}$-type level configuration via double electromagnetically induced transparency (EIT). Through an approach beyond both mean-field and ground-state approximations, we make detailed calculations on third-order nonlinear optical susceptibilities and show that the system possesses giant nonlocal self- and cross-Kerr nonlinearities contributed by Rydberg-Rydberg interaction. The theoretical result of the cross-Kerr nonlinearity obtained for ${}^{85}\mathrm{Rb}$ atomic gas is very close to the experimental one reported recently. Moreover, we demonstrate that the probe laser field can acquire a very large magneto-optical rotation via the double EIT, which may be used to design atomic magnetometers with high precision. The results presented here are promising not only for the development of nonlocal nonlinear magneto-optics but also for applications in precision measurement and optical information processing and transmission based on Rydberg atomic gases.

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.

By effectively controlling the dipole-dipole interaction, we investigate the characteristics of the ground state of bright solitons in a spin-orbit coupled dipolar Bose-Einstein condensate. The dipolar atoms are trapped within a double-lattice which consists of a linear and a nonlinear lattice. We derive the motion equations of the different spin components, taking the controlling mechanisms of the dipole-dipole interaction into account. An analytical expression of dipole-dipole interaction is derived. By adjusting the dipole polarization angle, the dipole interaction can be adjusted from attraction to repulsion. On this basis, we study the generation and manipulation of the bright solitons using both the analytical variational method and numerical imaginary time evolution. The stability of the bright solitons is also analyzed and we map out the stability phase diagram. By adjusting the long-range dipole-dipole interaction, one can achieve manipulation of bright solitons in all aspects, including the existence, width, nodes, and stability. Considering the complexity of our system, our results will have enormous potential applications in quantum simulation of complex systems.

Exceptional points (EPs) in non-Hermitian systems have attracted enormous attention and spawned intriguing prospects for the manipulation of waves. Despite many efforts focusing on the exotic behaviors about EPs, there are only a few studies of phase transitions involving multiple EPs. Here, by employing staggered couplings as well as two pairs of on-site gain/loss, we propose a one-dimensional parity-time (PT)-symmetric Lieb photonic lattice and demonstrate diverse phase transitions of such a multiband structure. Owing to the non-Hermitian chiral symmetry, symmetry-protected higher-order EPs are constructed, and the system exhibits PT symmetry breaking beyond a certain threshold. More importantly, both the relative couplings and the on-site gain/loss can be flexibly reconfigured on demand, which yields the degeneracy of different bands, i.e., the emergence of multiple EPs. We also unveil that the EPs will no longer exist in the presence of a non-Hermitian diagonal disorder. In contrast, the spectrum remains symmetric and the EPs, along with the flatband, are robust against the off diagonal disorder due to the preserved non-Hermitian particle-hole symmetry. Our work not only provides a controllable platform for studying EPs but also sheds light on the exciting non-Hermitian physics based on exceptional degeneracies.

We propose a physical scheme to study the formation of optical soliton molecules (SMs), consisting of two solitons bound together with a π-phase difference, and the scattering of SMs by a localized parity-time (PT)-symmetric potential. In order to stabilize SMs, we apply an additional space-dependent magnetic field to introduce a harmonic trapping potential for the two solitons and balance the repulse interaction induced by the π-phase difference between them. On the other hand, a localized complex optical potential obeying PT symmetry can be created through an incoherent pumping and spatial modulation of the control laser field. We investigate the scattering of optical SMs by the localized PT-symmetric potential, which exhibits evident asymmetric behavior and can be actively controlled by changing the incident velocity of SMs. Moreover, the PT symmetry of the localized potential, together with the interaction between two solitons of the SM, can also have a significant effect on the SM scattering behavior. The results presented here may be useful for understanding the unique properties of SMs and have potential applications in optical information processing and transmission.