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Journal of the Optical Society of America B

Depletion of control field during the propagation of ultraslow optical solitons

Hui‐jun Li, Chao Hang, Guoxiang Huang

Published Oct 9, 2009• 3 citations
Publisher

Abstract

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.

DOI
10.1364/josab.26.002028

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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.
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 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.
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 propose a scheme to generate stable ultraslow three-dimensional spatiotemporal optical solitons, or ultraslow optical bullets, at very low light levels via atomic coherence. The system we consider is an ensemble of resonant, lifetime-broadened NNN-type four-level atoms, working in a regime of electromagnetically induced transparency. Due to the quantum interference effect induced by a control field, the absorption of a probe field is largely suppressed. Moreover, the Kerr nonlinearity is greatly enhanced, and the dispersion property of the probe field is drastically changed. Using a method of multiple scales, we derive two coupled nonlinear envelope equations controlling the evolution of the envelopes of the probe field and an assisted field. We show that under certain conditions the envelope of the probe field satisfies a three-dimensional nonlinear Schr\"odinger equation and the envelope of the assisted field obeys a linear Helmholtz equation. We obtain various optical bullet solutions for the probe-field envelope and demonstrate that such optical bullets have many novel features, including very slow propagating velocity and very low generation power. In addition, they can be actively controlled and manipulated by adjusting system parameters. The stabilization of the optical bullets obtained can be easily realized by the trapping potential contributed by the assisted field, which is also investigated in detail.
We propose a scheme to obtain stable nonlinear optical pulses and realize their storage and retrieval in an ultracold ladder-type three-level atomic gas via electromagnetically induced transparency. Based on Maxwell-Bloch equations we derive a nonlinear equation governing the evolution of probe field envelope, and show that optical solitons with ultraslow propagating velocity and extremely low generation power can be created in the system. Furthermore, we demonstrate that such ultraslow optical solitons can be stored and retrieved by switching off and on a control field. Due to the balance between dispersion and nonlinearity, the ultraslow optical solitons are robust during propagation, and hence their storage and retrieval are more desirable than that of linear optical pulses. This raises the possibility of realizing the storage and retrieval of light and quantum information by using solitonic pulses.