Formation and propagation of ultraslow three-wave-vector optical solitons in a cold seven-level triple-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>Λ</mml:mi></mml:mrow></mml:math>atomic system under Raman excitation

Abstract

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.