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 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) symmetry via electromagnetically induced transparency (EIT). The system we consider is an ensemble of cold four-level atoms with an EIT core. We show that the cross-phase modulation contributed by an assisted field, the optical lattice potential provided by a far-detuned laser field, and the optical gain resulted from an incoherent pumping can be used to construct a PT-symmetric complex optical potential for probe field propagation in a controllable way. Comparing with previous study, the present scheme uses only a single atomic species and hence is easy for the physical realization of PT-symmetric Hamiltonian via atomic coherence.
We propose a scheme to realize parity-time (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 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 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 symmetry and giant nonlocal optical nonlinearity.
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)-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-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.
We propose a physical scheme to realize combined linear and nonlinear optical potentials with parity-time (PT) symmetry and investigate the scattering property of optical solitons in a coherent atomic gas. We show that the combined linear and nonlinear 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 potential plays a crucial role for the occurrence of the PT phase transition and the change of the 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 potentials; furthermore, by taking the combined linear and nonlinear 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 potentials. The results reported here may have potential applications in optical information processing and transmission.
We propose a scheme to realize an optical Bessel potential with parity-time (PT) 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-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-symmetric potentials, but also for promising applications in optical information processing and transmission.
Inspired by the discovery of real energy spectra of non-Hermitian Hamiltonians obeying parity-time (PT) symmetry, many proposals and relevant experiments have been suggested and implemented for the realization of PT-symmetric Hamiltonians in various physical systems. Among them PT-symmetric atomic gases are of great interest as they possess many unique advantages, including: (i) the possession of active PT symmetry with balanced optical gain and loss, (ii) the ability to be extended to high-dimensional ones, and (iii) the feasibility to acquire enhanced Kerr nonlinearity based on the resonance character between light and atoms. Here, we review the new progresses made on the study of PT symmetry in coherent atomic gases since our last review paper [Advances in Physics: X, 2, 737–783 (2017)]. Particularly, we focus on the newly emerged research topics in this direction, including nonlocal nonlinear effect, non-Hermitian quantum effect, exceptional point and associated phenomenon, and non-Hermitian skin effect with PT symmetry. Perspectives and potential applications of the subject are also discussed.