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arXiv:2102.10420 · Microwave and Optical Technology Letters

Soliton‐mode proliferation induced by cross‐phase modulation of harmonic waves by a dark‐soliton crystal in optical media

Eugene Aban Chenui, Alain M. Dikandé

Published Jun 26, 2021• 3 citations
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Abstract

Abstract The generation of high‐intensity optical fields from harmonic‐wave photons, interacting with dark solitons via a cross‐phase modulation coupling, both propagating in a Kerr nonlinear medium, is examined. The focus is on a pump consisting of time‐entangled dark‐soliton patterns, forming a periodic waveguide along the path of the harmonic‐wave probe. It is shown that an increase of the strength of cross‐phase modulation coupling respective to the self‐phase modulation coupling, favors soliton‐mode proliferation in the bound‐state spectrum of the trapped harmonic‐wave probe. The induced soliton modes, which display structures of periodic soliton lattices, are not just rich in numbers, they also form a great diversity of population of soliton crystals with a high degree of degeneracy.

DOI
10.1002/mop.32945

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Abstract The generation of high‐intensity optical fields from harmonic‐wave photons, interacting with dark solitons via a cross‐phase modulation coupling, both propagating in a Kerr nonlinear medium, is examined. The focus is on a pump consisting of time‐entangled dark‐soliton patterns, forming a periodic waveguide along the path of the harmonic‐wave probe. It is shown that an increase of the strength of cross‐phase modulation coupling respective to the self‐phase modulation coupling, favors soliton‐mode proliferation in the bound‐state spectrum of the trapped harmonic‐wave probe. The induced soliton modes, which display structures of periodic soliton lattices, are not just rich in numbers, they also form a great diversity of population of soliton crystals with a high degree of degeneracy.
It is well known that high-intensity optical fields with soliton features, both bright and dark solitons, can trap and reshape photon fields of lower intensities into optical solitons by means of cross-phase modulation in optical materials with Kerr nonlinearity. In general the induced photon fields are not arbitrarily given, they are well-defined quantum states |ℓ, m〉 of a discrete spectrum which we refer to as quantum photosoliton modes. In this study we propose a scheme for the generation of quantum photosoliton states, by considering linear photon field propagating coupled to a vector high-intensity optical field with coexisting mutually transparent bright and dark solitons. It is found that features of the probe spectrum, specifically the nature, number and degeneracy of the associate quantum modes, depend on the strengths of couplings of the linear photon field to the bright and dark soliton components of the vector-soliton pump. The competition created by these simultaneous couplings leads to a rich variety of photosoliton modes, including modes that are replica of the soliton pump or translation modes of the two components of the vector-soliton pump. For the context where the optical pump consists of a single bright and a single dark soliton structures, it is found that photosoliton modes are all multiple degenerate in addition to being replica of some other modes. However, when the optical pump is a periodic multiplex of bright-dark solitons, photosoliton quantum states retain their identities (i.e. become non degenerate) but some of them are still either replica or translation modes of components of the optical pump.
The formation environment and the evolution of dark soliton with environment parameters are investigated by using the electromagnetically induced transparency effect produced high dispersion and nonlinearity. To improve the stability and operability, a dual-well semiconductor is used. Combining the quantum theory and the classical field theory, we derive the nonlinear Schrodinger equation to describe the formations and evolutions of wave and soliton. It is demonstrated that the dark soliton can form and propagate in the medium when the medium is anomalously dispersive and cross phase modulation is negative simultaneously, and that in the evolution of the soliton, the width, gray scale and phase are related to each other, the smaller the pulse duration, the bigger the gray scale is and the faster the growth is. In addition, the modulation instability of the nonlinear system is analyzed, and the gain spectrum of the nonlinear system is also discussed.
Photonic crystals doped with resonant atoms allow for uniquely advantageous nonlinear modes of optical propagation. The first type of mode is self-induced transparency (SIT) solitons and multidimensional localized “bullets” propagating at photonic-bandgap frequencies. Such modes can exist even at ultraweak intensities (few photons) and therefore differ substantially either from solitons in Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. The second type of mode is cross coupling between pulses exhibiting electromagnetically induced transparency and SIT gap solitons. We show that extremely strong correlations (giant cross-phase modulation) can be formed between the two pulses. These features may find applications in high-fidelity classical and quantum optical communications.
Abstract It is well known that an optical trap can be imprinted by a light field in an ultracold-atom system embedded in an optical cavity, and driven by three different coherent fields. Of the three fields coexisting in the optical cavity there is an intense control field that induces a giant Kerr nonlinearity via electromagnetically-induced transparency, and another field that creates a periodic optical grating of strength proportional to the square of the associated Rabi frequency. In this work elliptic-soliton solutions to the nonlinear equation governing the propagation of the probe field are considered, with emphasis on the possible generation of optical soliton trains forming a discrete spectrum with well defined quantum numbers. The problem is treated assuming two distinct types of periodic optical gratings and taking into account the negative and positive signs of detunings (detuning above or below resonance). Results predict that the competition between the self-phase and cross-phase modulation nonlinearities gives rise to a rich family of temporal soliton train modes characterized by distinct quantum numbers.
We present a systematic study of the generation of the array of optical or matter-wave kinks (dark solitons) in the ground state (GS) of binary systems. We consider quasi-one-dimensional systems described by a pair of nonlinear Schr\"odinger (NLSE's) or Gross-Pitaevskii equations (GPE's), which are coupled by the linear mixing, with local strength $\ensuremath{\Omega}$, and by nonlinear interactions. We assume the self-repulsive nonlinearity in both components, and include the effects of a harmonic trapping potential, while the nonlinear interaction between the components may be both repulsive and attractive. The model may be realized in terms of periodically modulated slab waveguides in nonlinear optics and also in Bose-Einstein condensates. Depending on the sign and strengths of the linear and nonlinear couplings between the components, the ground states in such binary systems may be symmetric, antisymmetric, or asymmetric. In this work, we introduce a periodic spatial modulation of the linear coupling, making $\ensuremath{\Omega}$ an odd or even function of the coordinate (xxx). The sign flips of $\ensuremath{\Omega}(x)$ strongly modify the structure of the GS in the binary system, as the relative sign of its components tends to lock to the local sign of $\ensuremath{\Omega}$. Using a systematic numerical analysis and an analytic approximation, we demonstrate that the GS of the trapped system contains one or several kinks (dark solitons) in one component, while the other component does not change its sign. The final results are presented in the form of maps showing the number of kinks in the GS as a function of the system's parameters, with the odd (even) modulation function giving rise to the odd (even) number of the kinks. The modulation of $\ensuremath{\Omega}(x)$ also produces a strong effect on the transition between states with nearly equal and strongly unequal amplitudes of the two components.
We investigate the {\em nonlinearity-assisted quantum tunneling} and formation of nonlinear collective excitations in a matter-wave interferometer, which is realised by the adiabatic transformation of a double-well potential into a single-well harmonic trap. In contrast to the linear quantum tunneling induced by the crossing (or avoided crossing) of neighbouring energy levels, the quantum tunneling between different nonlinear eigenstates is assisted by the nonlinear mean-field interaction. When the barrier between the wells decreases, the mean-field interaction aids quantum tunneling between the ground and excited nonlinear eigenstates. The resulting {\em non-adiabatic evolution} depends on the input states. The tunneling process leads to the generation of dark solitons, and the number of the generated dark solitons is highly sensitive to the matter-wave nonlinearity. The results of the numerical simulations of the matter-wave dynamics are successfully interpreted with a coupled-mode theory for multiple nonlinear eigenstates.