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Optics Express

Generation and propagation of hyperbolic secant solitons, Peregrine solitons, and breathers in a coherently prepared atomic system

J. Guan, Chengjie Zhu, Chao Hang, Yaping Yang

Published Sep 27, 2020• 2 citations
Publisher

Abstract

We study the generation and propagation of hyperbolic secant solitons, Peregrine solitons, and various breathers in a coherently prepared three-level atomic system, where two lower states are coherently prepared prior to the injection of a strong pump field and a weak probe field. We show that a flat dispersion without gain and loss along with a large Kerr nonlinearity can be achieved in a broad range of probe field frequency. Moreover, optical hyperbolic secant solitons can be easily achieved in such a broad range at a very low light intensity and propagate stably. Due to the enhanced Kerr nonlinearity, we also show that it is possible to generate optical rogue waves and breathers with very weak light stimulus, which is three orders of magnitude smaller than that used in nonlinear fibers. Because the gain/absorption is negligible and the quantum noise of the probe field can be significantly suppressed, our work may pave the way for realizing solitons, rogue waves, and breathers at the quantum level.

DOI
10.1364/oe.398424

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We study the generation and propagation of hyperbolic secant solitons, Peregrine solitons, and various breathers in a coherently prepared three-level atomic system, where two lower states are coherently prepared prior to the injection of a strong pump field and a weak probe field. We show that a flat dispersion without gain and loss along with a large Kerr nonlinearity can be achieved in a broad range of probe field frequency. Moreover, optical hyperbolic secant solitons can be easily achieved in such a broad range at a very low light intensity and propagate stably. Due to the enhanced Kerr nonlinearity, we also show that it is possible to generate optical rogue waves and breathers with very weak light stimulus, which is three orders of magnitude smaller than that used in nonlinear fibers. Because the gain/absorption is negligible and the quantum noise of the probe field can be significantly suppressed, our work may pave the way for realizing solitons, rogue waves, and breathers at the quantum level.
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.
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 consider an active-Raman-gain scheme for realizing giant Kerr nonlinearity and superluminal optical solitons in a four-state atomic system with a gain doublet. We show that this scheme, which is fundamentally different from those based on electromagnetically induced transparency (EIT), is capable of working at room temperature and eliminating nearly all attenuation and distortion.We demonstrate that, due to the appearance of a gain spectrum hole induced by the quantum interference effect induced by a signal field, a significant enhancement of Kerr nonlinearity of probe field can be realized effectively, which can be more than ten times larger than that arrived by the EIT-based scheme with the same energy-level configuration. Based on these important features, we obtain a giant cross-phase modulation effect and hence a stable long-distance propagation of optical solitons, which have superluminal propagating velocity and very low generating power.
Abstract We propose a scheme that excites rogue waves via electromagnetically induced transparency (EIT), which can also excite breathers and solitons. The system is a resonant Λ-type atomic ensemble. Under EIT conditions, the envelope equation of the probe field can be reduced to several different models, such as the saturable nonlinear Schrödinger equation (SNLSE), and SNLSE with the trapping potential provided by a far-detuned laser field or a magnetic field. In this scheme, rogue waves can be generated by different initial pulses, such as the Gaussian wave with (or without) the uniform background. The scheme can be used to obtain rogue waves, breathers and solitons. We show the existence regions of rogue waves, breathers, and solitons as the function of the amplitude and width of the initial pulse. The novelty of our paper is that, we not only show rogue waves in the integrable system numerically, but also present the method to generate and control rogue waves in the non-integrable system.
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.
The linear and nonlinear pulse propagations in lifetime-broadened three-state media with spontaneously generated coherence (SGC) are investigated theoretically. Three generic systems of V-, ΛΛΛ-, and ΞΞΞ-type level configurations are considered and compared. It is shown that in linear propagation regime the SGC in the V-type system can result in a significant change of dispersion and absorption and may be used to completely eliminate the absorption and largely reduce the group velocity of a probe field. However, the SGC has no effect on the dispersion and absorption of the ΛΛΛ- and ΞΞΞ-type systems. In nonlinear propagation regime, the SGC displays different influences on Kerr nonlinearity for different systems. Specifically, it can enhance the Kerr nonlinearity of the V-type system whereas weaken the Kerr nonlinearity of the ΛΛΛ-type system. Using the SGC, stable optical solitons with ultraslow propagating velocity and very low pump power can be produced in the V-type system by exploiting only one laser field in the system.