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Optics and Photonics News

Entangling Fiber Solitons: Quantum Noise Engineering for Interferometry and Communication

Gerd Leuchs, Natalia Korolkova

Published Feb 1, 2002• 8 citations
Publisher

Abstract

Many particle systems follow a complex time evolution. If system interactions are governed by nonlinear behavior, the theoretical description is often difficult to address. The nonlinear dynamics of some systems feature solitary waves or solitons, which are dynamically stable excitations. They come about whenever the ubiquitous dispersion of a wave is compensated for by some nonlinear, i.e., amplitude-dependent response. First observed in water, today solitons are known to appear in many systems in different fields of physics.

DOI
10.1364/opn.13.2.000064

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Many particle systems follow a complex time evolution. If system interactions are governed by nonlinear behavior, the theoretical description is often difficult to address. The nonlinear dynamics of some systems feature solitary waves or solitons, which are dynamically stable excitations. They come about whenever the ubiquitous dispersion of a wave is compensated for by some nonlinear, i.e., amplitude-dependent response. First observed in water, today solitons are known to appear in many systems in different fields of physics.
Solitons are non-dispersive wave packets that balance the wave dispersion with a focusing nonlinearity. They maintain their shape and velocity after collisions with other solitons, owing to the integrability of the underlying nonlinear partial differential equations. They appear in various physical systems, such as water waves, light waves in optical fiber, and matter waves. In our laboratory, we study solitons and their interactions in a Bose-Einstein condensate with an attractive nonlinearity, trapped in a quasi-one-dimensional waveguide. We investigate the collisions of a pair of solitons and explore the relative phase implications on the boundary of integrability. We study soliton train formation with the quench of the nonlinearity strength, and interactions between neighboring solitons in the train. We form a composite soliton, known as a breather, where multiple solitons overlap and the wavefunction ``breathes'' in time. We also explore the response of an elongated condensate to an external modulation of the nonlinearity. These experiments characterize the mean-field descriptions of solitons and Bose-Einstein condensates and explore the boundaries between the mean-field theory and quantum many-body theory.
Solitons are fascinating entities that are known to exist in many different branches of physics. They represent self-localized wave packets that do not expand while propagating in a dispersive environment. The localization (self-trapping) relies on a nonlinear effect, and it can result from a variety of nonlinear mechanisms. In general, solitons exhibit a rich, particlelike behavior that is clearly manifested during their interactions (collisions). Despite their diversity, solitons are a universal phenomenon and thus share many common features. In their most frequent realization, these particlelike wave packets are fully coherent entities. In this case, given the soliton phase at a particular location as well as the frequency of the carrier wave, one can deterministically predict the phase everywhere (at any given point in space and time) upon the soliton.
In recent years, bright soliton-like structures composed of gaseous Bose-Einstein condensates have been generated at ultracold temperature. The experimental capacity to precisely engineer the nonlinearity and potential landscape experienced by these solitary waves offers an attractive platform for fundamental study of solitonic structures. The presence of three spatial dimensions and trapping implies that these are strictly distinct objects to the true soliton solutions. Working within the zero-temperature mean-field description, we explore the solutions and stability of bright solitary waves, as well as their interactions. Emphasis is placed on elucidating their similarities and differences to the true bright soliton. The rich behaviour introduced in the bright solitary waves includes the collapse instability and symmetry-breaking collisions. We review the experimental formation and observation of bright solitary matter waves to date, and compare to theoretical predictions. Finally we discuss the current state-of-the-art of this area, including beyond-mean-field descriptions, exotic bright solitary waves, and proposals to exploit bright solitary waves in interferometry and as surface probes.
The dynamics of nonlinear solitary waves in studied by using the model of nonlinear Schrodinger equations(NSE) with an external harmonic potential. The model allows one to analyze on the general basis a variety of nonlinear phenomena appearing both in Bose-Einstein condensate in a magnetic trap, whose profile is describe by a quadratic function of coordinates, and an nonlinear optics, physics of lasers, and biophysics. It is shown that exact solutions for a quantum-mechanical particle in a harmonic potential and solutions obtained within the framework of the adiabatic perturbation theory of bright solitons in a parabolic trap are completely identical. This fact not only proves once more that solitons behave like particles but also that they can preserve such properties in different traps for the which the parabolic approximation is valid near potential energy minima. The conditions are found for formation of stable stationary states of antiphase soliton in a harmonic potential. The interaction dynamics of solitons in nonstationary potentials is studied and the possibility of the appearance of a soliton parametric resonance at with the amplitude of soliton oscillation in a trap exponentially increases with time is shown.
A soliton is a class of solitary-wave solutions having specific mathematical properties, which universally appears in integrable systems.A quantum dark soliton is an emerging concept having theoretical and experimental relevance.Although recent studies have proposed quantum states with density profiles similar to those of classical dark solitons, the concept of quantum dark solitons is not yet fully established in that their collision dynamics have not been examined.Here, we first construct dark soliton states that possess stable scattering properties that are unique to solitons using the Lieb-Liniger model, establishing a direct link between quantum and classical dark soliton theories.
The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured quantum systems, necessary to explain actual experimental results. The dynamics of such systems is intrinsically nonlinear even at the level of distribution functions, both classically as well as quantum mechanically. Aside from being physically more complete, this treatment reveals the existence of dynamical regimes, such as chaos, that have no counterpart in the linear case. Here, we present a short introductory review of some of these aspects, with a few illustrative results and examples.