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Physical Review A

Three coupled ultraslow temporal solitons in a five-level tripod atomic system

Wen‐Xing Yang, Ai-Xi Chen, Liu-Gang Si, Kaijun Jiang, Xiaoxue Yang, Ray‐Kuang Lee

Published Feb 16, 2010• 74 citations
Publisher

Abstract

We propose a scheme to generate three coupled ultraslow optical solitons in a five-level tripod atomic system. We show that the detrimental distortions of the three weak probe fields due to dispersion effects under weak driving conditions can be well balanced by self- and cross-phase-modulation effects, which leads to the three coupled ultraslow temporal optical solitons with the temporal, group velocity, and amplitude values nearly matched. In contrast to other schemes, our model uses optical fibers, including multichromatic optical solitons in the stimulated Raman scattering, and produces three coupled ultraslow optical solitons in a small propagation distance of less than $1$ cm with $\frac{1}{2}$ Rabi frequency of the driving field, typically less than 100 MHz.

DOI
10.1103/physreva.81.023814

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We propose a scheme to generate three coupled ultraslow optical solitons in a five-level tripod atomic system. We show that the detrimental distortions of the three weak probe fields due to dispersion effects under weak driving conditions can be well balanced by self- and cross-phase-modulation effects, which leads to the three coupled ultraslow temporal optical solitons with the temporal, group velocity, and amplitude values nearly matched. In contrast to other schemes, our model uses optical fibers, including multichromatic optical solitons in the stimulated Raman scattering, and produces three coupled ultraslow optical solitons in a small propagation distance of less than 111 cm with 12\frac{1}{2}21​ Rabi frequency of the driving field, typically less than 100 MHz.
We show the possibility of generating ultraslow temporal vector optical solitons in a cold lifetime-broadened four-level tripod atomic medium under Raman excitation. We demonstrate that the two orthogonally polarized components of the low-intensity signal field can evolve into various distortion-free temporal vector optical solitons, such as bright-bright vector solitons with ultraslow group velocity. These results are produced from the balance of self- and cross-phase modulation effects and dispersion. We also show that Manakov temporal vector solitons may be realized by adjusting the corresponding self- and cross-phase modulation and dispersion effects of our 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.
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 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.
Abstract A theoretical scheme is proposed to investigate the formation of three coupled slow temporal vector optical solitons in a lifetime-broadened seven-state atomic medium. We demonstrate that the three polarized components of a low intensity linear-polarized pulsed probe field can evolve into three coupled slow temporal vector optical solitons due to the fact that group-velocity dispersion can be well compensated by the self- and cross-phase-modulation effects. Moreover, this atomic system could support the existence of various types of three coupled slow temporal vector solitons, such as bright–bright–bright, bright–dark–bright, dark–dark–dark, and bright–dark–dark vector solitons.
We investigate generation of three-wave coupled superluminal vector optical solitons in an active-Raman-gain (ARG) seven-level atomic system. By solving the probability amplitude equations, the linear, nonlinear and dispersion of the optical properties are analyzed for the three probe fields, which show that the dispersion effects of the probe fields can be well balanced by self-phase and cross-phase modulation of the Kerr nonlinearities and the gain can be well suppressed under certain conditions. Therefore, three-wave coupled optical vector solitons with superluminal propagating group velocity can be formed in the system. Moreover, this atomic system allows the existence of various types of three-wave superluminal vector solitons by adjusting the system parameters. We also give real parameters of 87Rb atoms for generating three-wave superluminal vector solitons, which may provide reference for experiments.