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Physical Review Letters

Chaos in an Electromagnetically Induced Transparent Medium Inside an Optical Cavity

Wenge Yang, Amitabh Joshi, Min Xiao

Published Aug 25, 2005• 20 citations
Publisher

Abstract

We theoretically predict and experimentally demonstrate chaotic behaviors in a system comprising of three-level atoms inside an optical ring cavity. This electromagnetically induced transparency (EIT) system is driven to chaos through period-doubling route by reducing the frequency detuning of the coupling laser beam. The chaos occurs in a different parametric regime as previously predicted and is believed to be caused by the enhanced dispersion and nonlinearity due to induced atomic coherence in such EIT system.

DOI
10.1103/physrevlett.95.093902

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We theoretically predict and experimentally demonstrate chaotic behaviors in a system comprising of three-level atoms inside an optical ring cavity. This electromagnetically induced transparency (EIT) system is driven to chaos through period-doubling route by reducing the frequency detuning of the coupling laser beam. The chaos occurs in a different parametric regime as previously predicted and is believed to be caused by the enhanced dispersion and nonlinearity due to induced atomic coherence in such EIT system.
Dynamic instability and chaos are experimentally observed in the output field of an optical cavity consisting of three-level atoms near the condition of electromagnetically induced transparency (EIT). The observed dynamic instability and route to chaos can be well controlled by the coupling laser field, and are greatly enhanced by the modified absorption, dispersion, and nonlinearity due to induced atomic coherence in the three-level atomic EIT system. A theoretical model is developed to quantitatively explain the observed results.
Summary form only given. The reduced absorption and enhanced nonlinearity in a three-level electromagnetically induced transparency (EIT) system are very important in achieving an effective all-optical switching action. The Kerr-nonlinear index of refraction of a three-level EIT medium can be greatly enhanced near resonance due to atomic coherence induced in such a system in comparison with a two-level atomic system, as we have shown by using an optical ring cavity. Both the magnitude and sign of the Kerr-nonlinear index change dramatically for different frequency detunings of the controlling (or coupling) or cavity (or probe) field. Bistability and dynamic instability occur when such a three-level /spl Lambda/-type EIT system is placed inside an optical ring cavity and the controlling and cavity input intensities to exceed certain threshold values. In this paper, we present a recent experimental demonstration of controlling the cavity output intensity by modulating the frequency detuning of the controlling beam.
We have experimentally studied the optical bistable behavior in an optical ring cavity filled with a collection of three-level $\ensuremath{\Lambda}$-type rubidium atoms, interacting with two collinearly propagating laser beams. The bistability so observed is very sensitive to the induced atomic coherence in this electromagnetically induced transparency system or consequently to the altered nonlinearity in the system and, thus, can easily be controlled by changing the intensity and the frequency detuning of the coupling field.
Steady-state dynamics of a \ensuremath{\Lambda} atom in a ring cavity driven by two coherent fields are studied for arbitrary detunings, arbitrary incoherent pumping, and coherent driving intensities. Effects of both cavity and effective atom number on electromagnetically induced transparency (EIT) are pointed out. New physical pictures for cavity EIT are given in terms of collective cooperative coefficients and dispersion experienced by the probe. In the regime of smaller collective cooperative coefficients, an absorption-gain profile is reduced to that of a general EIT estimated by the imaginary part of a corresponding dipole moment, and its transparency window is directly proportional to power broadening, if the total Rabi frequency is large enough. But in the region of larger collective cooperative coefficients which means a dense atomic medium, longer optical path, or high-Q cavity, EIT is determined not only by the imaginary part but also by the real part of the corresponding dipole moment, which results in the possibility of observing an EIT central peak with a subnatural width, while there may be nearly no power broadening.
Summary form only given. Nonlinear optical properties of an atomic medium can be modified by coherence and quantum interference that utilizes electromagnetically induced transparency (EIT). Because of the vanishing linear absorption and large enhancement of nonlinearities in an EIT medium, nonlinear optics may be studied at low light levels. We report studies of light absorption and parametric amplification based on the EIT enhanced third-order nonlinearity in a four-level atomic system. We have observed the enhanced nonlinear absorption when two coupling lasers and one probe laser are present. We are in the process of preparing the experiments for the double EIT demonstration and observation of the efficient parametric amplification in the four-level system. Because the experimental system is essentially free of Doppler broadening, quantitative comparisons between the experimental measurements and the theoretical calculations can readily be achieved.