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Physical Review E

Formation and propagation of matched and coupled ultraslow optical soliton pairs in a four-level double- Λ system

L. Deng, M. G. Payne, Guoxiang Huang, E. W. Hagley

Published Nov 17, 2005• 48 citations
Publisher

Abstract

We investigate the simultaneous formation and stable propagation of ultraslow optical soliton pairs in a lifetime broadened four-state atomic system under double-Lambda excitation with large one- and two-photon detunings. We show that detrimental probe field distortions due to strong dispersion effects under weak driving conditions can be well balanced by self- and cross-phase modulation effects, leading to a pair of temporal, group velocity, and amplitude matched ultraslow optical solitons of different frequencies.

DOI
10.1103/physreve.72.055601

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In this article, a theoretical scheme is proposed to investigate the formation and propagation of three-wave coupled vector optical solitons with ultraslow group velocities in a lifetime-broadened seven-state triple-$\ensuremath{\Lambda}$ atomic system under Raman excitation. We show that in the presence of a weak applied magnetic field that removes the degeneracy of the corresponding sublevels of the atomic medium, three continuous-wave control fields with circularly left or right polarized fields induce a quantum interference effect which can largely suppress the absorption of the three low-intensity pulsed fields, that is, the circularly ${\ensuremath{\sigma}}^{\ensuremath{-}}$ (right), the linearly $\ensuremath{\pi}$, and the circularly ${\ensuremath{\sigma}}^{+}$ (left) polarized fields converted from one weak linear-polarized probe field. By means of the standard method of multiple scales, we solve the equations of motion of atomic response and probe-control electromagnetic fields and derive three-coupled nonlinear Schr\"odinger equations that govern the nonlinear evolution of the envelopes of the probe fields in this scheme. We then demonstrate that because of the nonlinear coupling to one another, the three probe fields can evolve into three-wave temporal, group velocity, and amplitude-matched optical solitons under appropriate conditions, which are produced from the delicate balance of the dispersion effects and the self- and cross-phase modulation effects. This scheme may thus pave the way to generate ultraslow vector optical solitons composed of three field components in a highly resonant atomic medium and result in a substantial impact on this field of nonlinear optics.
We analyze a lifetime-broadened four-state, ladder-type four-wave mixing (FWM) scheme in the context of optical soliton formation. We show that a pulsed probe field and a pulsed FWM field of considerably different frequency can evolve into a pair of matched solitons with the same temporal shape and ultraslow group velocity $({V}_{g}∕c\ensuremath{\sim}{10}^{\ensuremath{-}3})$, i.e., two-color ultraslow optical solitons. In addition, we show regimes where two-color superluminal (Vg∕c<0)({V}_{g}∕c<0)(Vg​∕c<0) optical soliton propagation may occur.
We study nonlinear excitations in a lifetime-broadened Λ-type three-level atomic system with a configuration of electromagnetically induced transparency. Different from previous works, we show that a significant depletion of the control field may occur during the formation and propagation of ultraslow optical solitons for the probe field. We demonstrate that ultraslow optical solitons predicted in previous works correspond to the limits of weak dispersion and weak nonlinearity, adiabatons correspond to the limits of stronger dispersion and stronger nonlinearity, and simultons correspond to the limits of strong dispersion and strong nonlinearity. Between these different limits the system also yields solitonlike nonlinear excitations with different levels of depletion of the control field. The results provided here are useful not only for a deep understanding of the interrelation between ultraslow optical solitons, adiabatons, and simultons, but also for potential applications in optical information processing and transmission.
We theoretically investigate the simultaneous formation and stable propagation of slow optical soliton pairs in semiconductor quantum dots with a four-level biexciton-exciton cascade configuration. Owing to the destructive interference set up by two continuous wave control fields that couple to a biexciton state, the linear as well as nonlinear dispersion can be dramatically enhanced simultaneously with the absorptions of two weak probe fields being almost suppressed. These results reveal that the detrimental distortions of the two weak-pulsed probe fields due to dispersion effects can be well balanced by the self-phase modulation effect under very low input light intensity, which leads to the slow temporal optical soliton pairs with matched group velocity and amplitude. We also show that the propagation of slow optical solitons can be strongly modified by the biexciton coherence.