Abstract
Understanding and manipulating the non-Hermitian optical property based on coherent atomic gases is of great importance and has attracted much theoretical and experimental attentions. Advancing this study to the nonlinear optics regime is highly desirable due to its importance in fundamental physics and potential applications. In this work, we propose to realize a tunable electromagnetically induced grating (EIG) with parity-time ($\mathcal{PT}$) symmetry in a cold gas of Rydberg atoms, where interatomic interactions between Rydberg states are mapped to strong and long-range optical interactions, and investigate nonlinear light diffractions in this system. We show that for far-field diffraction, laser beams incident upon the $\mathcal{PT}$-symmetric EIG display distinctive asymmetric diffraction fringes, which can be actively manipulated through tuning the gain-absorption coefficient of the EIG, the incident intensity of the laser beam, and the nonlocality provided by Rydberg atoms. For near-field diffraction, the nonlinear Talbot diffraction carpets emerge and can be modulated by $\mathcal{PT}$ symmetry in the presence of strong nonlocal interactions, allowing the realization of controllable optical self-imaging. The results are not only imperative for the study of non-Hermitian nonlinear optics but also useful for characterizing the interatomic interaction in Rydberg gases and for designing new optical devices useful in optical information processing and transmission.
Highlights
In the past decades, the study of light diffraction in optical media whose refractive indices can be engineered has attracted enormous attention due to its significant applications in optical science and technology [1,2]
We show that for far-field diffraction, laser beams incident upon the PT -symmetric electromagnetically induced grating (EIG) display distinctive asymmetric diffraction fringes, which can be actively manipulated through tuning the gain-absorption coefficient of the EIG, the incident intensity of the laser beam, and the nonlocality provided by Rydberg atoms
We show that the diffraction asymmetry degree can be controlled by the gain-absorption coefficient of the EIG, the incident intensity of the laser beam, and the nonlocality provided by Rydberg atoms, which might be used to characterize the interatomic interaction property of the Rydberg gas
Summary
The study of light diffraction in optical media whose refractive indices can be engineered has attracted enormous attention due to its significant applications in optical science and technology [1,2]. In the presence of relatively weak optical Kerr nonlinearity, the formation of vector dipole solitons [20] and photonic topological insulators [21] has been predicted with EIGs. More importantly, through laser coupling of multilevel atoms, the optical refractive index with gain and absorption can be realized and tuned simultaneously, giving rise to optical media with parity-time (PT ) symmetry [22,23,24,25,26,27]. We investigate nonlinear light diffractions from EIGs with PT symmetry and strong, long-range optical interactions in a cold gas of Rydberg atoms. We show that the diffraction asymmetry degree can be controlled by the gain-absorption coefficient of the EIG, the incident intensity of the laser beam, and the nonlocality provided by Rydberg atoms, which might be used to characterize the interatomic interaction property of the Rydberg gas. V we summarize the main results obtained in this work
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