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Physical Review A

Realization of two-dimensional Aubry-André localization of light waves via electromagnetically induced transparency

Hui‐jun Li, Jian-Peng Dou, Guoxiang Huang

Published Mar 24, 2014• 6 citations
Publisher

Abstract

We propose a scheme to construct a two-dimensional Aubry-Andr\'e (AA) model and realize two-dimensional AA localization of light waves via electromagnetically induced transparency (EIT). The system we suggest is a cold, resonant atomic gas with an $N$-type level configuration and interacting with probe, control, assisted, and far-detuned laser fields. We show that under EIT conditions the probe-field envelope obeys a modified nonlinear Schr\"odinger equation with a quasiperiodic potential, which becomes a two-dimensional nonlinear AA model when the system parameters are suitably chosen. The quasiperiodic potential is obtained by the cross-phase modulation of the assisted field and the Stark shift of the far-detuned laser field. In addition, the cubic nonlinearity term appearing in the model is contributed by the self-phase modulation of the probe field. We demonstrate that the system can be used to not only realize various two-dimensional AA localizations of light waves, but also to display nonlinearity and dimensionality effects on the AA localizations.

DOI
10.1103/physreva.89.033843

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We propose a scheme to realize a transition from delocalization to localization of light waves via electromagnetically induced transparency. The system we suggested is a resonant cold atomic ensemble having NNN configuration, with a control field consisting of two pairs of laser beams with different cross angles, which produce an electromagnetically induced quasiperiodic waveguide (EIQPW) for the propagation of a signal field. By appropriately tuning the incommensurate rate or relative modulation strength between the two pairs of control-field components, the signal field can exhibit the delocalization-localization transition as it transports inside the atomic ensemble. The delocalization-localization transition point is determined and the propagation property of the signal field is studied in detail. Our work provides a way of realizing wave localization via atomic coherence, which is quite different from the conventional, off-resonant mechanism-based Aubry-Andre model, and the great controllability of the EIQPW also allows an easy manipulation of the delocalization-localization transition.
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We propose a scheme to realize a (2+1)-dimensional vectorial Thirring model in a coherent atomic system via electromagnetically induced transparency (EIT). We show that under EIT conditions the probe field envelopes obey coupled nonlinear Schr\"odinger equations, which are reduced to a Thirring model when system parameters are suitably chosen. We present spatial soliton-pair solutions exhibiting many interesting features, including controllability (i.e., the soliton property of one component can be adjusted by the propagation constant of another component in which the soliton remains unchanged), diversity (i.e., many different types of soliton-pair solutions can be found, including bright-bright, dark-bright, dark-dark, darklike-dark, dark-dipole, darklike-multidark, and high-dimensional bright-bright, dark-darklike soliton pairs), and stability. Furthermore, we demonstrate that the stability of soliton pairs in the system can be strengthened by adjusting the propagation constant. Comparing with previous studies, in addition to supporting much more stable (1+1)-dimensional and (2+1)-dimensional spatial soliton-pair solutions, the present scheme needs only a single atomic species and hence is easy to realize experimentally.
We propose a scheme to generate and stabilize the high-dimensional spatial solitons via electromagnetically induced transparency (EIT). The system we consider is a resonant atomic ensemble having $\mathrm{\ensuremath{\Lambda}}$ configuration. We illustrate that under EIT conditions the equation satisfied by the probe field envelope is reduced to a saturable nonlinear Schr\"odinger equation with the trapping potential, provided by a far-detuned laser field and a random magnetic field. We present high-dimensional soliton solutions exhibiting many interesting characteristics, including diversity (i.e., many different types of soliton solutions can be found, including bright, ring multipole bright, ring multipole defect mode, multiring bright, multiring defect mode, and vortices solitons), the phase transition between bright soliton and higher-order defect modes (i.e., the phase transition can be realized by controlling the nonlinear coefficient or the intensity of the trapping potential), and stability (i.e., various solitons can be stabilized by the Gaussian potential provided by the far detuned laser field, or the random potential provided by the magnetic field). We also find that some solitons are the extension of the linear eigenmode, whereas others entirely derive from the role of nonlinearity. Compared with previous studies, we not only show the diverse soliton solutions in the same system but also find the boundary of the phase transition for the type of solitons. In addition, we present the possibility of using the random potential to stabilize various solitons and vortices.
We propose a scheme to demonstrate the existence of optical Peregrine rogue waves and Akhmediev and Kuznetsov-Ma breathers and realize their active control via electromagnetically induced transparency (EIT). The system we suggest is a cold, $\mathrm{\ensuremath{\Lambda}}$-type three-level atomic gas interacting with a probe and a control laser fields and working under EIT condition. We show that, based on EIT with an incoherent optical pumping, which can be used to cancel optical absorption, (1+1)-dimensional optical Peregrine rogue waves, Akhmediev breathers, and Kuznetsov-Ma breathers can be generated with very low light power. In addition, we demonstrate that the Akhmediev and Kuznetsov-Ma breathers in (2+1)-dimensions obtained can be actively manipulated by using an external magnetic field. As a result, these breathers can display trajectory deflections and bypass obstacles during propagation.
We propose a scheme to generate and control high-dimensional rogue waves in a coherent three-level Λ-type atomic system via electromagnetically induced transparency (EIT). Under EIT conditions, the probe field envelopes obey the non-integrable nonlinear Schrödinger equations (NLSE) with or without the external potential, which result from the stark (Zeeman) effect contributed by an electric (magnetic) field. By adjusting the amplitude and width of the initial pulse, we can generate the high-dimensional rogue waves and obtain the phase-transition curves of high-dimensional rogue waves. In the system, the far-detuned electric field, the random weak magnetic field, and the Gauss weak magnetic field are not conducive to the excitation of high-dimensional rogue waves. The results not only provide a theoretical basis for the experimental realization or prevention of the high-dimensional rogue waves, but also prove the possibility of generating and controlling the rogue waves in other high-dimensional non-integrable systems.