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Physical Review A

Two-color ultraslow optical solitons via four-wave mixing in cold-atom media

Ying Wu

Published May 31, 2005• 270 citations
Publisher

Abstract

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 $({V}_{g}∕c<0)$ optical soliton propagation may occur.

DOI
10.1103/physreva.71.053820

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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 (Vg∕c\ensuremath∼10\ensuremath−3)({V}_{g}∕c\ensuremath{\sim}{10}^{\ensuremath{-}3})(Vg​∕c\ensuremath∼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 investigate the simultaneous formation and propagation of coupled ultraslow optical soliton pairs in a cold, lifetime-broadened three-state double-Lambda atomic system. Starting from the equations of motion of atomic response and two-mode probe-control electromagnetic fields, we derive coupled nonlinear Schrödinger equations that govern the nonlinear evolution of the envelopes of the probe fields in this four-wave mixing scheme by means of the standard method of multiple scales. We demonstrate that for weak probe fields and with suitable operation conditions, a pair of coupled optical solitons moving with remarkably slow propagating velocity can be established in such a highly resonant atomic medium. The key elements to such a shape preserving, well matched yet interacting soliton pair is the balance between dispersion effect and self- and cross-phase modulation effects of the system.
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.
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 theoretically investigate the formation of ultraslow temporal vector optical solitons in a lifetime-broadened five-state atomic system under Raman excitation. By analysing the interaction between the atomic system and two strong, linear-polarized continuous wave control fields and a weak, linear-polarized pulsed signal field, having two orthogonally polarized components, we find that the Maxwell equations of describing the propagation of two orthogonal polarization components can evolve into two coupled nonlinear Schrödinger equations, which admit solutions describing vector solitons, including bright–bright, bright–dark, dark–bright and dark–dark vector solitons with ultraslow group velocity. More importantly, the Manakov temporal vector solitons can be easily realized in our system by adjusting the corresponding parameters such as the Rabi frequencies of the control fields, one- and two-photon detunings. The unique features of the two coupled nonlinear Schrödinger equations are also discussed.