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Physical Review A

Weak-light solitons and their active control in a parity-time-symmetric atomic system

Chao Hang, Guoxiang Huang

Published Apr 22, 2015• 21 citations
Publisher

Abstract

We propose a realistic physical scheme to produce one-dimensional and two-dimensional weak-light solitons in an atomic system with $\mathcal{PT}$ symmetry. The system we suggest is a cold three-level atomic gas with two species and is driven by control and probe laser fields. We show that by the interference of two Raman resonances a highly adjustable probe-field refractive index with $\mathcal{PT}$ symmetry in one and two dimensions can be realized. We further show that it is possible to produce various light solitons when the weak nonlinearity of the probe field is taken into account. Due to the resonant character of the system, the light solitons obtained in one and two dimensions have extremely low light power (at the level of nanowatts). In addition, we demonstrate that the stability of these light solitons can be actively controlled via $\mathcal{PT}$ phase transition of the system.

DOI
10.1103/physreva.91.043833

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We propose a realistic physical scheme to produce one-dimensional and two-dimensional weak-light solitons in an atomic system with PT\mathcal{PT}PT symmetry. The system we suggest is a cold three-level atomic gas with two species and is driven by control and probe laser fields. We show that by the interference of two Raman resonances a highly adjustable probe-field refractive index with PT\mathcal{PT}PT symmetry in one and two dimensions can be realized. We further show that it is possible to produce various light solitons when the weak nonlinearity of the probe field is taken into account. Due to the resonant character of the system, the light solitons obtained in one and two dimensions have extremely low light power (at the level of nanowatts). In addition, we demonstrate that the stability of these light solitons can be actively controlled via PT\mathcal{PT}PT phase transition of the system.
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.
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.
We propose a physical setup to realize parity-time (PT) symmetric moiré optical lattices (ML) and nonlocal optical solitons in a cold Rydberg atomic system with electromagnetically induced transparency (EIT). We also show that based on the PT symmetry lattice strength and giant nonlocal Kerr nonlinearity originated from the strong, long-range atom–atom interaction, the system supports two-dimension (2D) nonlocal solitons with very low light intensity. By using numerical simulation method, we uncover the formation, properties, and dynamics of higher-order solitons and vortical ones. 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-symmetric moiré lattice parameters and giant nonlocal optical nonlinearity.
We propose a scheme to generate superluminal optical solitons in a four-level atomic system with two control fields via an active Raman gain. We derive a modified nonlinear Schrödinger equation with high-order corrections contributed from linear and differential absorption, nonlinear dispersion, and delay response of nonlinear refractive index of the system. We predict various optical solitons in different regimes of system parameters, and show that these optical solitons have superluminal propagating velocity and very low generation power.
We show that a vapor of multilevel atoms driven by far-off-resonant laser beams, with the possibility of interference of two Raman resonances, is highly efficient for creating parity-time symmetric profiles of the probe-field refractive index, whose real part is symmetric and imaginary part is antisymmetric in space. The spatial modulation of the probe-field susceptibility is achieved by a proper combination of standing-wave strong control fields and of Stark shifts induced by far-off-resonance laser fields. As particular examples we explore a mixture of isotopes of rubidium atoms and design a parity-time symmetric lattice and a parabolic refractive index with a linear imaginary part.
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.