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Optics Express

Parity-time symmetric Bragg structure in atomic vapor

Zhongjie Chen, Haidong Wang, Bin Luo, Hong Mei Guo

Published Oct 7, 2014• 7 citations
Publisher

Abstract

We propose an efficient scheme in helium or alkaline earth atomic vapor to achieve a parity-time symmetric Bragg structure using coherent lights. Unidirectional invisibility can be realized in this scheme, i.e., the atomic vapor shows total transparency for probe light incident from one particular direction, but exhibits enhanced Bragg reflection for probe from the opposite side. By changing the relative phase between the coherent lights, this direction can easily be manipulated, providing a convenient way for investigating special properties of 𝒫𝒯 -symmetric Bragg structures.

DOI
10.1364/oe.22.025120

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We propose an efficient scheme in helium or alkaline earth atomic vapor to achieve a parity-time symmetric Bragg structure using coherent lights. Unidirectional invisibility can be realized in this scheme, i.e., the atomic vapor shows total transparency for probe light incident from one particular direction, but exhibits enhanced Bragg reflection for probe from the opposite side. By changing the relative phase between the coherent lights, this direction can easily be manipulated, providing a convenient way for investigating special properties of 𝒫𝒯 -symmetric Bragg structures.
In optical parity-time symmetry, the electric permittivity of an electromagnetic structure should have a real part, which is an even function of spatial coordinates, and an imaginary part, which is an odd function of coordinates. Since a Vee- and a Lambda-configuration three-level atomic vapor can be driven by both control and probe beams, and can exhibit both frequency-sensitive and field-controlling optical responses, the dielectric “constants” of these two atomic vapors can be tuned by manipulating the applied external control fields. The requirement for realizing optical parity-time symmetry can be fulfilled in quantum-coherent multilevel atomic vapors. A design based on Vee- and Lambda-configuration three-level atomic vapors for achieving optical parity-time symmetric interface is suggested in this paper. Under certain parameter conditions, an optical parity-time symmetric interface can possibly be fabricated in the present scenario of quantum-coherent multilevel atomic vapors.
A unidirectionally invisible PT\mathcal{P}\mathcal{T}PT-symmetric complex crystal with arbitrary thickness
We introduce a new class of parity-time ( )-symmetric complex crystals which are almost transparent and one-way reflectionless over a broad frequency range around the Bragg frequency, i.e., unidirectionally invisible, regardless of the thickness L of the crystal. The -symmetric complex crystal is synthesized by a supersymmetric (SUSY) transformation of a Hermitian square well potential, and exact analytical expressions of transmission and reflection coefficients are given. As L is increased, the transmittance and reflectance from one side remain close to one and zero, respectively, whereas the reflectance from the other side secularly grows like owing to unidirectional Bragg scattering. This is a distinctive feature as compared to the previously studied case of the complex sinusoidal -symmetric potential at the symmetry breaking point, where transparency breaks down as .
Rb atomic system both experimentally and theoretically. Such an instantaneously reconfigurable anti-PT-symmetric photonic lattice is "written" by two one-dimensional coupling fields, which are arranged alternately along the x direction and can modulate the refractive index of the atomic vapor in a spatially periodical manner via controllable atomic coherence. By properly adjusting the relevant atomic parameters, the phase shift between two adjacent lattice channels occurs in the constructed non-Hermitian photonic system. Such a readily reconfigurable anti-PT-symmetric photonic lattice may open the door for demonstrating the discrete characteristics of the optical waves in periodic anti-PT-symmetric photonic systems.
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 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.