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International review of physics

Optical Parity-Time Symmetric Structure with Vee- and Lambda-Configuration Atomic Vapors

Frost Mengmeng Xu, Hao Song, Jian Xu, Jian Qi Shen

Published Jun 30, 2017• 0 citations
Publisher

Abstract

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.

DOI
10.15866/irephy.v11i3.12279

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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.
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 an all-optical-control scheme to simultaneously realize parity-time (𝒫𝒯)-symmetric and 𝒫𝒯-antisymmetric susceptibilities along the propagation direction of light by applying an external magnetic field. Through the light-atom interaction within a double-Λ configuration, the resulting position-dependent susceptibilities for the interacting fields can be manipulated through the relative phase between them. In particular, for the probe field, one can switch its refractive index from the 𝒫𝒯-symmetry to 𝒫𝒯-antisymmetry by just varying the phase. Based on the quantum interference among transition channels in a closed loop, analytical formulas are also derived to illustrate the conditions for 𝒫𝒯-symmetry and 𝒫𝒯-antisymmetry.
A periodic layered medium, with unit cells consisting of a dielectric and an electromagnetically-induced transparency (EIT)-based atomic vapor, is designed for light propagation manipulation.Considering that a destructive quantum interference relevant to a two-photon resonance emerges in EIT-based atoms interacting with both control and probe fields, an EIT-based periodic layered medium exhibits a flexible frequency-sensitive optical response, where a very small variation in the probe frequency can lead to a drastic variation in reflectance and transmittance.The present EIT-based periodic layered structure can result in controllable optical processes that depend sensitively on the external control field.The tunable and sensitive optical response induced by the quantum interference of a multi-level atomic system can be applied in the fabrication of new photonic and quantum optical devices.This material will also open a good perspective for the application of such designs in several new fields, including photonic microcircuits or integrated optical circuits.
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.
The author of this thesis concentrates his attention on quantum optical properties of some artificial electromagnetic media, such as quantum coherent atomic vapors (various multilevel electromagnetically induced transparency vapors) and negative refractive index materials, and suggests some possible ways to manipulate wave propagations inside the artificial electromagnetic materials based on quantum coherence and quantum vacuum effects. In Chapters 1 and 2, the author reviews the previous papers on quantum coherence as well as the relevant work such as electromagnetically induced transparency (EIT), atomic population trapping and their various applications. The basic concepts of quantum coherence (atomic phase coherence, quantum interferences within atomic energy levels) and quantum vacuum are introduced, and the theoretical formulations for treating wave propagations in quantum coherent media are presented. In Chapter 3, the author considers three topics on the manipulation of light propagations via quantum coherence and quantum interferences: i) the evolutional optical behaviors (turn-on dynamics) of a four-level N-configuration atomic system is studied and the tunable optical behavior that depends on the intensity ratio of the signal field to the control field is considered. Some typical photonic logic gates (e.g. NOT and NOR gates) are designed based on the tunable four-level optical responses of the N-configuration atomic system; ii) the destructive and constructive quantum interferences between two control transitions (driven by the control fields) in a tripod-type four-level system is suggested. The double-control quantum interferences can be utilized to realize some photonic devices such as the logic-gate devices, e.g., NOT, OR, NOR and EXNOR gates; iii) some new quantum coherent schemes (using EIT and dressed-state mixed-parity transitions) for realizing negative refractive indices are proposed. The most remarkable characteristic (and advantage) of the present scenarios is such that the isotropic left-handed media (with microscopic structure units at the atomic level) in the optical frequency band can be achieved. Quantum vacuum (the ground state of quantized fields) can exhibit many interesting effects. In Chapter 4, we investigate two quantum-vacuum effects in artificial materials: i) the anisotropic distribution of quantum-vacuum momentum density in a moving electromagnetic medium; ii) the angular momentum transfer between quantum vacuum and anisotropic medium. Such quantum-vacuum macroscopic mechanical effects could be detected by current technology, e.g., the so-called fiber optical sensor that can measure motion with nanoscale sensitivity. We expect that these vacuum effects could be utilized to develop sensitive sensor techniques or to design new quantum optical and photonic devices.In Chapter 5, the author suggests some interesting effects due to the combination of quantum coherence and quantum vacuum, i.e., the quantum coherent effects, in which the quantum-vacuum fluctuation field is involved. Two topics are addressed: i) spontaneous emission inhibition due to quantum interference in a three-level system; ii) quantum light-induced guiding potentials for coherent manipulation of atomic matter waves (containing multilevel atoms). These quantum guiding potentials could be utilized to cool and trap atoms, and may be used for the development of new techniques of atom fibers and atom chips, where the coherent manipulation of atomic matter waves is needed.In Chapter 6, we conclude this thesis with some remarks, briefly discuss new work that deserves further consideration in the future, and present a guide to the previously published papers by us.
Phase-dependent PT\boldsymbol{\mathcal{PT}}PT -, non-PT\boldsymbol{\mathcal{PT}}PT -, and anti-PT\boldsymbol{\mathcal{PT}}PT -symmetry
We propose a scheme to realize -, non- -, and anti- -symmetry in an ensemble of four-level double-lambda configuration. We find that the ensemble of atoms exhibits either symmetry, non-symmetry and antisymmetry of parity-time in terms of the refractive index modulation. Such fascinating modulation of real and imaginary parts of refractive index is attained via the relative phase ( ϕ ) of the optical fields. The control of spatial modulations of refractive index then leads to the control of -, non- -, and anti- -symmetry via the relative phase of the optical fields. Such interesting and controllable system via relative phase may open a new way in observing -, non- -, and anti- -symmetry with gain-loss contrast in atomic systems.