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arXiv:0907.3040 · Physical Review A

Storage by trapping and spatial staggering of multiple interacting solitons in Λ -type media

Willem P. Beeker, Chris Lee, Edip Can, Klaus J. Boller

Published Nov 30, 2010• 5 citations
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Abstract

In this paper we investigate the properties of self-induced transparency (SIT) solitons, propagating in a $\ensuremath{\Lambda}$-type medium. We find that the interaction between SIT solitons can lead to trapping with their phases preserved in the ground-state coherence of the medium. These phases can be altered in a systematic way by the application of appropriate light fields, such as additional SIT solitons. Furthermore, multiple independent SIT solitons can be made to propagate as bisolitons through their mutual interaction with a separate light field. Finally, we demonstrate that control of the SIT soliton phase can be used to implement an optical exclusive-or (xor) gate.

DOI
10.1103/physreva.82.053839

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The Review of Laser Engineering•Jan 1, 1992•0 citations
In this paper we investigate the properties of self-induced transparency (SIT) solitons, propagating in a \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type medium. We find that the interaction between SIT solitons can lead to trapping with their phases preserved in the ground-state coherence of the medium. These phases can be altered in a systematic way by the application of appropriate light fields, such as additional SIT solitons. Furthermore, multiple independent SIT solitons can be made to propagate as bisolitons through their mutual interaction with a separate light field. Finally, we demonstrate that control of the SIT soliton phase can be used to implement an optical exclusive-or (xor) gate.
The optical solitons that play the role of information carriers, are moving, requiring careful experimental timing to achieve the desired logic operation. In contrast, self-induced transparency (SIT) is a strong resonant nonlinear effect, supporting the propagation of optical solitons and are usually associated with a two-level system. By the appropriate application of light fields, the optical soliton, resonant with the SIT transition, can generate an excited region with ground state coherence in the medium, allowing logic operations to be performed on this coherence.
We propose a scheme to realize the coherent control of optical soliton propagation and interaction in a three level Λ type electromagnetically induced transparency system with the control field being spatially modulated. We show that the spatial perturbation of the control field has no influence on the linear propagation properties and self-phase modulation of the probe field but can produce an equivalent external potential to affect the nonlinear propagation of the probe field. For single soliton propagation, we realize the transmission and trapping of optical solitons via external potential. For double soliton interaction, we realize the coherent control of attractive and repulsion interactions of two optical solitons and design an XNOR logical operation. Finally, for the triple soliton incident case, based on the coherent control of interaction between three solitons via external potential, we design a beam selector. The results obtained here are useful not only for the deep understanding of optical soliton interaction but also for applications in all optical quantum information processing.
Using a numerical approach we report on the cloning dynamics of simultaneous self-induced transparency (SIT) and nonlinear Schrödinger (NLS) solitons in a doped nonlinear dispersive medium. This technique involves a three-level atomic system interacting resonantly with two optical fields within a Lambda scheme. As a result, a pulse in the signal frequency is transformed into a replica of the pulse in the pump frequency. The atomic population evolution shows that the basic mechanism behind the cloning process is the coherent population trapping effect. Furthermore, it is shown that the signal clone presents characteristics of both the SIT soliton and NLS soliton.
Electromagnetically induced transparency (EIT) is well known as a quantum optical phenomenon that permits a normally opaque medium to become transparent due to the quantum interference between transition pathways. This work addresses multi-soliton dynamics in an EIT system modeled by the integrable Maxwell–Bloch (MB) equations for a three-level Λ-type atomic configuration. By employing a generalized gauge transformation, we systematically construct explicit N-soliton solutions from the corresponding Lax pair. Explicit forms of one-, two-, three-, and four-soliton solutions are derived and analyzed. The resulting pulse structures reveal various nonlinear phenomena, such as temporal asymmetry, energy trapping, and soliton interactions. They also highlight coherent propagation, elastic collisions, and partial storage of pulses, which have potential implications for the design of quantum memory, slow light, and photonic data transport in EIT media. In addition, the conservation of fundamental physical quantities, such as the excitation norm and Hamiltonian, is used to provide direct evidence of the integrability and stability of the constructed soliton solutions.
The possibility of observing a self-induced transparency (SIT) in an erbium-doped optical fiber is investigated. A general equation that includes the SIT, the group-velocity dispersion (GVD) of the fiber, and the nonlinear refractive index is discussed. It is shown that for one particular value of waveguide parameters the nonlinear index can balance the GVD, that is, the nonlinear Schr\"odinger equation (NLS), while maintaining a SIT soliton. This is called a SIT-NLS soliton. The phase change of the SIT-NLS soliton is governed solely by the NLS component, and the pulse delay due to resonance is determined solely by the SIT component when the detuning is zero. Practical parameters for silica-based fibers do not allow the coexistence of a mixed soliton state. A simple derivation of a condition for a SIT-NLS soliton is also presented. The SIT-NLS soliton is computer-run, and it is shown that a stable 2\ensuremath{\pi}/N=1 SIT-NLS soliton exists. However, high-order SIT-NLS solitons always split into multiple 2\ensuremath{\pi}/N=1 solitons. The NLS property can be preserved when Zsp{\mathit{Z}}_{\mathrm{sp}}Zsp​\ensuremath{\ll}Labs.{\mathit{L}}_{\mathrm{abs}.}Labs.​ Finally, the NLS soliton that interacts coherently with erbium ions is studied, and the coherent pulsation that produces multiple narrow pulses is described.
Self-induced transparency (SIT) is a kind of coherent transient phenomena in two-level atomic system. The optical pulse with an area that is an integer multiple of 2π, which causes SIT in an absorber, is stable and a kind of soliton. Thus SIT is expected to be useful in pulse compression and pulse shaping. In this paper, we discuss some problems in experiments of SIT and surveys the experimental results of SIT. It is also described the recent experimental results of coherent nonlinear pulse propagation in BiI3 crystal using tunable sub-picosecond pulses.