Fig. 1: Atomic energy levels, linear bandgap structure, and edge states. | Nature Communications

Fig. 1: Atomic energy levels, linear bandgap structure, and edge states.

From: Observation of edge solitons in photonic graphene

Fig. 1

a The driven 85Rb atomic transitions involve two hyperfine states \(F = 2\) (level \(|1\rangle\)) and \(F = 3\) (\(|2\rangle\)) of the ground state \(5{\mathrm{S}}_{1/2}\) and one excited state \(5{\mathrm{P}}_{1/2}\) (\(|3\rangle\)). \({\mathbf{E}}_1\) and \({\mathbf{E}}_2\) are the probe and the coupling fields, respectively. b The transmission spectrum for the probe beam. c Calculated nonlinear coefficient \(n_2\) versus probe detuning \(\Delta _1\). d Band structure of the photonic graphene in an EIT window calculated for \(\Delta _1 = 135\,{\mathrm{MHz}}\) and \(\Delta _2 = 100\,{\mathrm{MHz}}\).\(\beta\) is the propagation constant, and \(k\) is the Bloch momentum normalized to the width \({\mit{K}}\) of the first Brillouin zone. e Simulated honeycomb lattice with zigzag-bearded edges in the \(y\) direction. The structure is periodic in the x direction, and we show six periods of the structure. f Simulated unconventional edge state located on the bearded edge corresponding to the red circle in (d). g Simulated edge state on the zigzag edge corresponding to the green circle in (d).

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