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Physical Review A

Talbot effects induced by gain-loss modulated optical lattices in a coherent atomic medium

Jingliang Feng, Zhaoyang Zhang, Min Xiao

Published Jun 21, 2021• 12 citations
Publisher

Abstract

We investigate the electromagnetically induced Talbot effects resulting from the gain-loss modulated optical lattices constructed in a coherent four-level $N$-type atomic system. Both integer and fractional Talbot effects are studied in a parity-time ($\mathcal{PT}$) symmetric optical lattice, quasi-$\mathcal{PT}$-symmetric optical lattices, and a conventional electromagnetically induced transparency (EIT) optical lattice. Additionally, the visibilities of Talbot images from a $\mathcal{PT}$-symmetric optical lattice, quasi-$\mathcal{PT}$-symmetric optical lattices, and a conventional EIT optical lattice are examined. This study provides insights for understanding the Talbot effects in experiments based on coherent atomic systems with gain and loss properties.

DOI
10.1103/physreva.103.063516

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We investigate the electromagnetically induced Talbot effects resulting from the gain-loss modulated optical lattices constructed in a coherent four-level NNN-type atomic system. Both integer and fractional Talbot effects are studied in a parity-time (PT\mathcal{PT}PT) symmetric optical lattice, quasi-PT\mathcal{PT}PT-symmetric optical lattices, and a conventional electromagnetically induced transparency (EIT) optical lattice. Additionally, the visibilities of Talbot images from a PT\mathcal{PT}PT-symmetric optical lattice, quasi-PT\mathcal{PT}PT-symmetric optical lattices, and a conventional EIT optical lattice are examined. This study provides insights for understanding the Talbot effects in experiments based on coherent atomic systems with gain and loss properties.
We experimentally demonstrate PT-symmetric optical lattices with periodical gain and loss profiles in a coherently prepared four-level N-type atomic system. By appropriately tuning the pertinent atomic parameters, the onset of PT-symmetry breaking is observed through measuring an abrupt phase-shift jump between adjacent gain and loss waveguides. The experimental realization of such a readily reconfigurable and effectively controllable PT-symmetric waveguide array structure sets a new stage for further exploiting and better understanding the peculiar physical properties of these non-Hermitian systems in atomic settings.
The nonlinear Talbot effect means formation of self-imaging of the periodic structure by utilizing the harmonic wave instead of the fundamental one. Electromagnetically induced optical lattices established in atomic ensembles by optical induction technique have received great attention in recent years. Here, we experimentally demonstrate the nonlinear four wave mixing (FWM) Talbot effect in the Rubidium medium, where the third-order susceptibility χ(3) has periodic distribution due to the modulation from the incident pump light. Two kinds of periodic structure, the square lattice and hexagonal lattice, are employed to investigate the nonlinear FWM Talbot effect. The integer and fractional Talbot images produced by the FWM field are all obtained. The experimental results are qualitatively consistent with theoretical simulations. Different from the self-imaging of the refractive index in the linear optics, the FWM Talbot effect is the self-imaging of the periodic χ(3). The results may offer a high-resolution lensless way for imaging various optical periodic structures.
ladder-type system. By launching a probe laser into a periodically modulated lattice constructed by two crossed coupling fields with a small angle inside the rubidium vapor, a high-resolution diffraction pattern is obtained. The diffraction pattern is reproduced completely at detection positions of an integer multiple of twice the Talbot lengths. Meanwhile, the fractional Talbot effect, presented as complicated subimages at special positions, is also clearly observed. Furthermore, the theoretical simulations are conducted and agree well with the experimental results. These results pave the way for studying the control of light dynamics based on the periodically modulated medium.
The electromagnetically induced Talbot effect (EITE) resulting from the repeated self-reconstruction of a spatially intensity-modulated probe field is experimentally demonstrated in a three-level atomic configuration. The probe beam is launched into an optically induced lattice (established by the interference of two coupling fields) inside a rubidium vapor cell and is diffracted by the electromagnetically induced grating that was formed. The diffraction pattern repeats itself at the planes of integer multiple Talbot lengths. In addition, a fractional EITE is also investigated. The experimental observations agree well with the theoretical predictions. This investigation may potentially pave the way for studying the nonlinear and quantum dynamical features that have been predicted for established periodic optical systems.
In this study, we report on the fractional Talbot effect of nonparaxial self-accelerating beams in a multilevel electromagnetically induced transparency (EIT) atomic configuration, which, to the best of our knowledge, is the first study on this subject. The Talbot effect originates from superposed eigenmodes of the Helmholtz equation and forms in the EIT window in the presence of both linear and cubic susceptibilities. The Talbot effect can be realized by appropriately selecting the coefficients of the beam components. Our results indicate that the larger the radial difference between beam components, the stronger the interference between them, the smaller the Talbot angle is. The results of this study can be useful when studying optical imaging, optical measurements, and optical computing.
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.