Potentials from Symmetric and Asymmetric Ion-Atom Scattering

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.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.

Physical Review AApr 24, 201919 citations

Time delays in anisotropic systems

Ulf Saalmann, Jan Michael Rost

Scattering properties and time delays for general (nonsymmetric) potentials in terms of the respective S-matrices are discussed paradigmatically in one dimension and in comparison to symmetric potentials. Only for the latter the Wigner and Smith time delays coincide. Considering asymmetric potentials also reveals that only one version of S-matrices used in the literature (the one with reflection coefficients on the diagonal) generalizes to the asymmetric case. Finally, we give a criterion how to identify a potential with intrinsic symmetry that behaves like an asymmetric one if it is merely offset from the scattering center.Scattering properties and time delays for general (nonsymmetric) potentials in terms of the respective S-matrices are discussed paradigmatically in one dimension and in comparison to symmetric potentials. Only for the latter the Wigner and Smith time delays coincide. Considering asymmetric potentials also reveals that only one version of S-matrices used in the literature (the one with reflection coefficients on the diagonal) generalizes to the asymmetric case. Finally, we give a criterion how to identify a potential with intrinsic symmetry that behaves like an asymmetric one if it is merely offset from the scattering center.

arXiv:2309.02059Canadian Journal of PhysicsFeb 9, 20242 citations

Scattering of Particles by Potentials

Springer eBooksApr 16, 20070 citations

Scattering from Complex Potentials

WORLD SCIENTIFIC eBooksNov 8, 20120 citations

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.