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Physical Review A

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

Lu Qin, Chao Hang, Guoxiang Huang

Published Apr 24, 2019• 19 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.99.043832

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We propose a physical scheme to realize combined linear and nonlinear optical potentials with parity-time (PT\mathcal{PT}PT) symmetry and investigate the scattering property of optical solitons in a coherent atomic gas. We show that the combined linear and nonlinear PT\mathcal{PT}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 PT\mathcal{PT}PT potential plays a crucial role for the occurrence of the PT\mathcal{PT}PT phase transition and the change of the PT\mathcal{PT}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 PT\mathcal{PT}PT potentials; furthermore, by taking the combined linear and nonlinear PT\mathcal{PT}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 PT\mathcal{PT}PT potentials. The results reported here may have potential applications in optical information processing and transmission.
We propose a realistic physical scheme to realize linear Gaussian optical potential with parity-time (PT) symmetry and two dimensional (2D) spacial solitons in a coherent atomic gas. It is shown that the PT-symmetric potential can be created through the spatial modulation of the control and relevant atomic parameters. We find that the Gaussian PT potential parameters, the imaginary part and the width and the position, play crucial roles in the occurrence of the PT phase transition. We demonstrate that the system supports stable 2D dipole solitons and vortex solitons, which can be managed via tuning PT potential. Furthermore, the dynamic characteristics of the symmetric scatter and collision of solitons are shown.
We propose a scheme to realize a parity-time (PT) symmetric nonlinear system in a coherent atomic gas via electromagnetically induced transparency. We show that it is possible to construct an optical potential with PT symmetry due to the interplay among the Kerr nonlinearity stemmed from the atom-photon interaction, the linear potential induced by a far-detuned Stark laser field, and the optical gain originated from an incoherent pumping. Since the real part of the PT-symmetric potential depends only on the intensity of the probe field, the potential is nonlinear and its PT-symmetric properties are determined by the input laser intensity of the probe field. Moreover, we obtain the fundamental soliton solutions of the system and attain their stability region in the system parameter space. The dependence of the exceptional point (EP) location on the soliton maximum amplitude is also illustrated. The research results reported here open a new avenue for understanding the unique properties of PT symmetry of a nonlinear system. They are also promising for designing novel optical devices applicable in optical information processing and transmission.
We propose a scheme to realize parity-time (PT\mathcal{PT}PT) symmetry and nonlocal optical solitons in a cold Rydberg atomic system with electromagnetically induced transparency. We show that a two-dimensional (2D) periodic optical potential with PT\mathcal{PT}PT symmetry can be obtained for the propagation of probe laser field by using an incoherent population pumping between two low-lying levels and spatial modulations of control and assistant laser fields. We also show that, based on the giant nonlocal Kerr nonlinearity originated from the strong, long-range atom-atom interaction, the system supports 2D nonlocal gap solitons with very low light intensity. In particular, we find that the degree of the nonlocality of the Kerr nonlinearity, which can be actively tuned in our system, can be used to manipulate the phase transition of the PT\mathcal{PT}PT symmetry and the behavior of the nonlocal optical solitons. Our study opens a route for developing non-Hermitian nonlinear optics, especially for realizing and controlling high-dimensional weak-light optical solitons through adjustable PT\mathcal{PT}PT symmetry and giant nonlocal optical nonlinearity.
Realizing vector spatiotemporal solitons that are stable in high dimensions is a long-standing goal in the study of nonlinear optical physics. Here, a scheme is proposed to generate three-dimensional (3D) vector spatiotemporal solitons in a cold atomic system with linear and nonlinear parity-time (PT) potentials by utilizing electromagnetically induced transparency (EIT). We investigate the existence and stability of these vector 3D semilunar solitons (SSs) and vortex solitons (VSs) supported by the linear and nonlinear PT potentials. The results show that these solitons have extremely low generation power and very slow propagation velocity and can stably propagate with constant total energy in this system. The frontal head-on collisions of two vector solitons feature quasi-elastic collisions. The dynamics characteristics of these solitons depend on the linear and nonlinear PT-symmetric potential parameters, in particular, the imaginary part of PT potentials. Our study provides a new route for manipulating high-dimensional nonlinear vector optical signals via the controlled optical linear and nonlinear potentials in cold atomic gases.
We propose a scheme to realize an optical Bessel potential with parity-time (PT\mathcal{P}TPT) symmetry and investigate the existence, propagation, and manipulation of multidimensional optical solitons through the interplay among diffraction, Kerr nonlinearity, and potential confinement in a cold atomic gas under the condition of electromagnetically induced transparency (EIT). We show that the system supports not only two-dimensional stationary optical solitons but also rotary ones; the stability of such solitons can be actively controlled by the gain-loss component (imaginary part), while the rotary motions can be tuned by the refractive-index component (real part) of the PT\mathcal{P}TPT-symmetric potential. Moreover, we demonstrate that the system allows the existence of stable three-dimensional spatiotemporal optical solitons, i.e., optical bullets, which have ultraslow propagation velocity and display helicoidal motions with controllable propagation trajectories. Due to the Kerr nonlinearity enhanced by the EIT effect, extremely low power is needed to create these multidimensional optical solitons. The results reported here are useful not only for the generation and manipulation of high-dimensional solitons via PT\mathcal{P}TPT-symmetric potentials, but also for promising applications in optical information processing and transmission.
We present a physical setup for realizing all-real-spectrum optical potentials with arbitrary gain-and-loss distributions in a coherent medium consisting of a cold three-level atomic gas driven by control and probe laser fields. We show that by the interference of Raman resonances and the Stark shift induced by a far-detuned laser field, tunable, non-parity-time (non-PT)\mathcal{PT})PT)-symmetric optical potentials with all-real spectra proposed recently by Nixon and Yang [Phys. Rev. A 93, 031802(R) (2016)] can be actualized physically. We also show that when the real parts of the non-PT\mathcal{PT}PT-symmetric optical potentials are tuned cross certain thresholds, phase transitions---where the eigenspectrum of the system changes from all real to complex---may occur and hence the stability of the probe-field propagation is altered. Our scheme can also be extended to high dimensions and to a nonlinear propagation regime, where stable optical solitons with power of the order of nano-Watts may be generated in the system.