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Abstract : 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.
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