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Physical Review A

Stable weak-light ultraslow spatiotemporal solitons via atomic coherence

Hui‐jun Li, Yuan-po Wu, Guoxiang Huang

Published Sep 13, 2011• 28 citations
Publisher

Abstract

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 $N$-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.

DOI
10.1103/physreva.84.033816

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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.
A scheme is proposed to produce (3+1)-dimensional superluminal spatiotemporal optical solitons and vortices in a coherent atomic system working in an active Raman gain regime. It is shown that the evolution of the envelope of a signal field obeys a modified (3+1)-dimensional nonlinear Schr\"odinger equation, which includes dispersion, diffraction, and Kerr nonlinearity. Various solutions of light bullets, light vortices, light-bullet trains, and light-vortex trains are presented, which display many interesting characters, including superluminal propagating velocity and extremely low generating power. In addition, they can be easily manipulated in a controllable way. Stabilization of such high-dimensional superluminal light bullets and vortices can be realized using the trapping potential formed by an additional far-detuned laser field.
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 possibility of guiding stable ultraslow weak-light bullets by using Airy beams in a cold, lifetime-broadened four-level atomic system via electromagnetically induced transparency (EIT). We show that under EIT condition the light bullet with ultraslow propagating velocity and extremely low generation power formed by the balance between diffraction and nonlinearity in the probe field can be not only stabilized but also steered by the assisted field. In particular, when the assisted field is taken to be an Airy beam, the light bullet can be trapped into the main lobe of the Airy beam, propagate ultraslowly in longitudinal direction, accelerate in transverse directions, and move along a parabolic trajectory. We further show that the light bullet can bypass an obstacle when guided by two sequential Airy beams. A technique for generating ultraslow helical weak-light bullets is also proposed.
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.
Abstract We propose a scheme to realize the manipulation of a weak signal pulse by ultraslow optical soliton in a coherent inverted-Y-type atomic system via double electromagnetically induced transparency (EIT). Based on Maxwell-Bloch equations, we derive nonlinear equations governing the spatial-temporal evolution of the probe and signal pulse envelopes. We show the giant enhancement of optical Kerr nonlinearity can be obtained under the condition of the double EIT, which results in the generation of a (2+1)-dimension optical soliton and can realize the manipulation of a weak signal pulse. Applying a far-detuned laser field to the system, we find that a weak signal pulse can be trapped by a (3+1)-dimension light bullet. In particular, the trajectories of the light bullet and trapped signal pulse can be manipulated and controlled by introducing a Stern–Gerlach gradient magnetic field. The results predicted here may not only open a route for the study of weak-light nonlinear optics but also have potential applications in the precision measurements and optical information processing and transmission.
We propose a scheme to produce ultraslow (3+13+13+1)-dimensional helical optical solitons, also called helical optical bullets, in a resonant three-level $\ensuremath{\Lambda}$-type atomic system via quantum coherence. We show that, due to the effect of electromagnetically induced transparency, the helical optical bullets can propagate with an ultraslow velocity up to ${10}^{\ensuremath{-}5}$ ccc (ccc is the light speed in vacuum) in the longitudinal direction and a slow rotational motion (with velocity ${10}^{\ensuremath{-}7}$ ccc) in transverse directions. The generation power of such optical bullets can be lowered to microwatts, and their stability can be achieved by using a Bessel optical lattice potential formed by a far-detuned laser field. We also show that the transverse rotational motion of the optical bullets can be accelerated by applying a time-dependent Stern-Gerlach magnetic field. Because of the ultraslow velocity in the longitudinal direction, a significant acceleration of the rotational motion of optical bullets may be observed for a very short medium length.