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Journal of the Physical Society of Japan

Lattice Solitons in Optical Lattice Controlled by Electromagnetically Induced Transparency

Wei Pang, Jianxiong Wu, Zhonghui Yuan, Yan Liu, Guihua Chen

Published Oct 24, 2011• 19 citations
Publisher

Abstract

An optical four-level atomic discrete system in a solid through optical induction is proposed. A theoretical scheme to produce lattice solitons (LSs) in the system is presented by means of the effects of enhanced self-phase modulation and the giant kerr effect in the electromagnetically induced transparency. The power density and the photon flux can be tuned to a very low level by the controlling field and the soliton can propagate with very slow group velocity. By changing the sign of the detuning Δ 1 , both in-phase and π out-of-phase LSs can be produced in this system.

DOI
10.1143/jpsj.80.113401

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arXiv:quant-ph/0204076•Journal of the Optical Society of America B•Sep 1, 2002•9 citations
An optical four-level atomic discrete system in a solid through optical induction is proposed. A theoretical scheme to produce lattice solitons (LSs) in the system is presented by means of the effects of enhanced self-phase modulation and the giant kerr effect in the electromagnetically induced transparency. The power density and the photon flux can be tuned to a very low level by the controlling field and the soliton can propagate with very slow group velocity. By changing the sign of the detuning Δ 1 , both in-phase and π out-of-phase LSs can be produced in this system.
An optical four-level atomic discrete system through optical induction is proposed. A theoretical scheme to produce nonclassical lattice solitons (NLS) in the system is presented with the use of the effects of enhanced self-phase modulation and the giant kerr effect in the electromagnetically induced transparency. The power density and the photon flux can be tuned to a very low level by the controlling field and the soliton can propagate with very slow group velocity. By changing the sign of the detuning Δ1Δ_{1}Δ1​, both in-phase and πππ out-of-phase NLSs can be produced in this system.
We consider an active-Raman-gain scheme for realizing giant Kerr nonlinearity and superluminal optical solitons in a four-state atomic system with a gain doublet. We show that this scheme, which is fundamentally different from those based on electromagnetically induced transparency (EIT), is capable of working at room temperature and eliminating nearly all attenuation and distortion.We demonstrate that, due to the appearance of a gain spectrum hole induced by the quantum interference effect induced by a signal field, a significant enhancement of Kerr nonlinearity of probe field can be realized effectively, which can be more than ten times larger than that arrived by the EIT-based scheme with the same energy-level configuration. Based on these important features, we obtain a giant cross-phase modulation effect and hence a stable long-distance propagation of optical solitons, which have superluminal propagating velocity and very low generating power.
We derive the properties of self-induced transparency (SIT) solitary waves in a one-dimensional periodic structure doped uniformly with resonance two-level atoms. In our model, the electromagnetic field is treated classically and the dopant atoms are described quantum mechanically. The resulting solitary waves take the form of ultrashort (picosecond) laser pulses which propagate near the band edge of the nonlinear photonic band gap (PBG) material doped with rare-earth atoms such as erbium. Solitary wave formation involves the combined effects of group velocity dispersion (GVD), nonresonant Kerr nonlinearity, and resonant interaction with dopant atoms. We derive the general Maxwell-Bloch equations for a nonlinear PBG system and then demonstrate the existence of elementary solitary wave solutions for frequencies far outside the gap where GVD effects are negligible and for frequencies near the photonic band edge where GVD effects are crucial. We find two distinct new types of propagating SIT solitary wave pulses. Far from Bragg resonance, we recapture the usual McCall-Hahn soliton with hyperbolic secant profile when the nonlinear Kerr coefficient ${\ensuremath{\chi}}^{(3)}=0.$ However, when the host nonresonant Kerr coefficient is nonzero, we obtain the first new type of soliton. In this case, the optical soliton envelope function deviates from the hyperbolic secant profile and pulse propagation requires nontrivial phase modulation (chirping). We derive the dependence of the solitary wave structure on the Kerr coefficient ${\ensuremath{\chi}}^{(3)},$ the resonance impurity atom density, and the detuning of the average laser frequency from the atomic transition. When the laser frequency and the atomic transition frequencies are near the photonic band edge we obtain the second type of soliton. To illustrate the second type of soliton we consider two special cases. In the first case, GVD facilitates the propagation of an unchirped SIT-gap soliton moving at a velocity fixed by the material's parameters. The soliton structure changes dramatically as the laser frequency is tuned through the atomic resonance. In the second illustrative case we set the Kerr coefficient ${\ensuremath{\chi}}^{(3)}=0.$ In this case, the solution is a chirped pulse which arises from the balance between GVD and the resonance interaction with the dopant atoms. Finally, we show that under certain circumstances, these solitary wave solutions may persist even in the presence of (subpicosecond) dipolar dephasing of the dopant atoms and absorption losses of the host PBG material, provided that the system is incoherently pumped. These results may be relevant to the application of PBG materials as optical devices in fiber-optic networks.
Photonic crystals doped with resonant atoms allow for uniquely advantageous nonlinear modes of optical propagation. The first type of mode is self-induced transparency (SIT) solitons and multidimensional localized “bullets” propagating at photonic-bandgap frequencies. Such modes can exist even at ultraweak intensities (few photons) and therefore differ substantially either from solitons in Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. The second type of mode is cross coupling between pulses exhibiting electromagnetically induced transparency and SIT gap solitons. We show that extremely strong correlations (giant cross-phase modulation) can be formed between the two pulses. These features may find applications in high-fidelity classical and quantum optical communications.