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Modern Physics Letters B

ULTRASLOW SOLITONS VIA FOUR-WAVE MIXING IN A CRYSTAL OF MOLECULAR MAGNETS

Liu-Gang Si, Xin‐You Lü, Peijun Song, Ji-Bing Liu

Published Mar 20, 2009• 0 citations
Publisher

Abstract

The authors theoretically investigate the formation of ultraslow dark and bright solitons via four-wave mixing (FWM) in a crystal of molecular magnets in the presence of a uniform d.c. magnetic field, where two strong continuous wave pump electromagnetic fields and a weak-pulsed probe electromagnetic field produce a pulsed FWM electromagnetic field. By solving the Maxwell–Schrödinger equations under the slowly varying envelope approximation and rotating-wave approximations, we demonstrate that both the weak-pulsed probe and FWM electromagnetic fields can evolve into dark and bright solitons with the same shape and the same ultraslow group velocity.

DOI
10.1142/s0217984909019181

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The authors theoretically investigate the formation of ultraslow dark and bright solitons via four-wave mixing (FWM) in a crystal of molecular magnets in the presence of a uniform d.c. magnetic field, where two strong continuous wave pump electromagnetic fields and a weak-pulsed probe electromagnetic field produce a pulsed FWM electromagnetic field. By solving the Maxwell–Schrödinger equations under the slowly varying envelope approximation and rotating-wave approximations, we demonstrate that both the weak-pulsed probe and FWM electromagnetic fields can evolve into dark and bright solitons with the same shape and the same ultraslow group velocity.
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 proposed a simple model for generation of controllable ultraslow optical solitons of a weak probe laser light in a degenerated two-level atomic medium under electromagnetically induced transparency assisted by a magnetic field. It is shown that bright and dark optical solitons can be formed from a probe light with controllable ultraslow group velocities at a few m/s by tuning the strength of a coupling light and/or the magnetic field. In addition to the ultraslow velocity, the advantage of this model is to use a sole laser for delivering both pump and probe lights. Furthermore, one can switch between bright and dark solitons by reversing the direction of the magnetic field. Such controllable ultraslow solitons are interested in finding applications in optical communications and optical data processing.
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Using the Schrödinger Maxwell equations, we theoretically investigate the propagation properties of probe and mixing fields in a lifetime-broadened inverted-Y type cold atomic medium. This system is driven by two strong control (pumping and coupling) fields. The results reveal that the probe (or mixing) field consists of two modes with different group velocity and absorption. Under slowly varying envelope approximation, we discuss the propagation equation of the probe (or mixing) field, which includes the high-order nonlinear term. The solutions show that optical solitons pairs can be generated in the cold atom medium with ultra-slow group velocities.
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.