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Optics Letters

Asymmetric light diffraction of an atomic grating with PT symmetry

Yi-Mou Liu, Feng Gao, Chu-Hui Fan, Jin‐Hui Wu

Published Oct 16, 2017• 62 citations
Publisher

Abstract

Cold atoms trapped in one-dimensional optical lattices and driven to the four-level N configuration are exploited for achieving an electromagnetically induced grating with parity-time-symmetry. This nontrivial grating exhibits unidirectional diffraction patterns, e.g., with incident probe photons diffracted into either negative or positive angles, depending on the sign relation between spatially modulated absorption and dispersion coefficients. Such asymmetric light diffraction is a result of the out-of-phase interplay of amplitude and phase modulations of transmission function and can be easily tuned via optical depth, probe detuning, pump Rabi frequencies, etc.

DOI
10.1364/ol.42.004283

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Cold atoms trapped in one-dimensional optical lattices and driven to the four-level N configuration are exploited for achieving an electromagnetically induced grating with parity-time-symmetry. This nontrivial grating exhibits unidirectional diffraction patterns, e.g., with incident probe photons diffracted into either negative or positive angles, depending on the sign relation between spatially modulated absorption and dispersion coefficients. Such asymmetric light diffraction is a result of the out-of-phase interplay of amplitude and phase modulations of transmission function and can be easily tuned via optical depth, probe detuning, pump Rabi frequencies, etc.
An asymmetric double semiconductor quantum well is proposed to realize two-dimensional parity-time (PT) symmetry and an electromagnetically induced grating. In such a nontrivial grating with PT symmetry, the incident probe photons can be diffracted to selected angles depending on the spatial relationship of the real and imaginary parts of the refractive index. Such results are due to the interference mechanism between the amplitude and phase of the grating and can be manipulated by the probe detuning, modulation amplitudes of the standing wave fields, and interaction length of the medium. Such a system may lead to new approaches of observing PT-symmetry-related phenomena and has potential applications in photoelectric devices requiring asymmetric light transport using semiconductor quantum wells.
Two-dimensional (2D) optical lattices of driven cold atoms can provide a useful platform to construct 2D electromagnetically induced grating (EIG) with parity-time (PT) antisymmetry. This atomic grating is achieved by the spatial modulations of the atomic density and frequency detunings in the four-level double-Λ atomic system. Gain-assisted PT antisymmetry allows us to realize lop-sided Raman-Nath diffraction with high diffraction efficiency at the exception point. It is shown that the nontrivial phenomenon originates from non-Hermitian degeneracy of PT antisymmetry. Our scheme may provide the possibility for active all-optical control and conversion of the spatial beam in optics.
Rb) atomic ensemble with a non-Hermitian optical structure, in which a lopsided optical diffraction grating can be realized just with the combination of single spatially periodic modulation and loop-phase. Parity-time (PT) symmetric and parity-time antisymmetric (APT) modulation can be switched by adjusting different relative phases of the applied beams. Both PT symmetry and PT antisymmetry in our system are robust to the amplitudes of coupling fields, which allows optical response to be modulated precisely without symmetry breaking. Our scheme shows some nontrivial optical properties, such as lopsided diffraction, single-order diffraction, asymmetric Dammam-like diffraction, etc. Our work will benefit the development of versatile non-Hermitian/asymmetric optical devices.
We propose and analyze an efficient scheme for the lopsided Raman-Nath diffraction of one-dimensional (1D1\mathrm{D}1D) and two-dimensional (2D2\mathrm{D}2D) atomic gratings with periodic parity-time (PT\mathcal{PT}PT)-symmetric refractive index. The atomic grating is constructed by the cold-atomic vapor with two isotopes of rubidium, which is driven by weak probe field and space-dependent control field. Using experimentally achievable parameters, we identify the conditions under which PT\mathcal{PT}PT-symmetric refractive index allows us to observe the lopsided Raman-Nath diffraction phenomenon and improve the diffraction efficiencies beyond what is achievable in a conventional atomic grating. The nontrivial atomic grating is a superposition of an amplitude grating and a phase grating. It is found that the lopsided Raman-Nath diffraction at the exceptional point (EP) of PT\mathcal{PT}PT-symmetric grating originates from constructive and destructive interferences between the amplitude and phase gratings. Furthermore, we show that the PT\mathcal{PT}PT-phase transition from unbroken to broken PT\mathcal{PT}PT-symmetric regimes can modify the asymmetric distribution of the diffraction spectrum and that the diffraction efficiencies in the non-negative diffraction orders can be significantly enhanced when the atomic grating is pushed into a broken PT\mathcal{PT}PT-symmetric phase. In addition, we also analyze the influence of the grating thickness on the diffraction spectrum. Our scheme may provide the possibility to design a gain-beam splitter with tunable splitting ratio and other optical components in integrated optics.
Abstract In this paper, we investigate two-dimensional parity-time (PT) symmetry and electromagnetically induced grating (EIG) in four-level asymmetric triple quantum wells (QWs). Here, PT-symmetry and EIG are realized by appropriately varying the detuning value of the probe, and the modulation amplitudes of a coupling field and standing wave (SW) pump. By virtue of its PT symmetry, the EIG asymmetrically diffracts the probe beam. The angular switching of the diffracted beam can be achieved either by varying the probe or the coupling and SW pump fields. The intensity distribution of the diffracted beam over higher-order diffraction peaks depends on the interaction length in the QW. For small interaction lengths, most of the energy is distributed close to the central diffraction peak. With an increase in the interaction length, energy is gradually transferred to higher order diffraction peaks.
Due to its myriad applications in many fields of science and technology, novel light diffraction from specially designed optical gratings is a subject of great interest. Here, we propose a scheme to realize the linear and nonlinear Bragg diffractions from an electromagnetically induced grating (EIG) with parity-time (PT)(\mathcal{PT})(PT) symmetry in a cold Rydberg atomic gas, where the Rydberg-Rydberg interaction between atoms are mapped to strong and long-range interaction between photons, characterized by a giant nonlocal Kerr nonlinearity. We show that a probe laser beam with very low light intensity incident upon the PT\mathcal{PT}PT-symmetric EIG can display distinctive asymmetric diffraction patterns, which can be actively manipulated through tuning the gain-absorption coefficient of the EIG and the input power of the laser beam. We also show that the intensity distribution among different diffraction orders depends significantly on the PT\mathcal{PT}PT-symmetry property of the EIG and on the magnitude and nonlocality degree of the Kerr nonlinearity. In addition, we demonstrate that such Bragg diffraction patterns can be controlled by an external gradient magnetic field, which provides a different way of diffraction control. The research results reported here are not only useful for understanding the unique properties of linear and nonlinear Bragg diffractions by PT\mathcal{PT}PT-symmetric gratings but may also be promising for designing optical devices applicable in optical information processing and transmission.