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While usually the optical diffraction limit is setting a limit for the lengthscales on which a typical alkali Bose-Einstein condensate can be controlled, we show that in certain situations control via matter waves can achieve smaller resolutions. For this we consider a small number of impurity atoms which are trapped inside the density dip of a dark soliton state and show that any grey soliton can be obtained by just driving the impurity atoms. By controlling the driving force on the impurity, one can therefore fully control the position and velocity of the dark soliton, and also study controlled collisions between these non-linear objects., Comment: 7 pages, 6 figures

Dark soliton is one of most interesting nonlinear excitations in physical systems, manifesting a spatially localized density "dip" on a uniform background accompanied with a phase jump across the dip. However, the topological properties of the dark solitons are far from fully understood. Our investigation for the first time uncover a vector potential underlying the nonlinear excitation whose line integral gives the striking phase jump. More importantly, we find that the vector potential field has a topological configuration in analogous to the Wess-Zumino term in a Lagrangian representation. It can induce some point-like magnetic fields scattered periodically on a complex plane, each of them has a quantized magnetic flux of elementary $\pi$. We then calculate the Euler characteristic of the topological manifold of the vector potential field and classify all known dark solitions according to the index., Comment: 6 pages, 3 figures

In this work, we explore systematically various SO(2)-rotation-induced multiple dark-dark soliton breathing patterns obtained from stationary and spectrally stable multiple dark-bright and dark-dark waveforms in trapped one-dimensional, two-component atomic Bose-Einstein condensates (BECs). The stationary states stem from the associated linear limits (as the eigenfunctions of the quantum harmonic oscillator problem) and are parametrically continued to the nonlinear regimes by varying the respective chemical potentials, i.e., from the low-density linear limits to the high-density Thomas-Fermi regimes. We perform a Bogolyubov-de Gennes (BdG) spectral stability analysis to identify stable parametric regimes of these states. Upon SO(2)-rotation, the stable steady-states, one-, two-, three-, four-, and many dark-dark soliton breathing patterns are observed in the numerical simulations. Furthermore, analytic solutions up to three dark-bright solitons in the homogeneous setting, and three-component systems are also investigated., Comment: 14 pages, 12 figures

Dark solitons are common topological excitations in a wide array of nonlinear waves. The dark soliton excitation energy, crucial for exploring dark soliton dynamics, is necessarily calculated in a renormalized form due to its existence on a finite background. Despite its tremendous importance and success, the renormalized energy form was firstly only suggested with no detailed derivation, and was then "derived" in the grand canonical ensemble. In this work, we revisit this fundamental problem and provide an alternative and intuitive derivation of the energy form from the fundamental field energy by utilizing a limiting procedure that conserves number of particles. Our derivation yields the same result, putting therefore the dark soliton energy form on a solid basis., Comment: 4 pages

Solitons in multi-component Bose-Einstein condensates have been paid much attention, due to the stability and wide applications of them. The exact soliton solutions are usually obtained for integrable models. In this paper, we present four families of exact spin soliton solutions for non-integrable cases in spin-1 Bose-Einstein Condensates. The whole particle density is uniform for the spin solitons, which is in sharp contrast to the previously reported solitons of integrable models. The spectrum stability analysis and numerical simulation indicate the spin solitons can exist stably. The spin density redistribution happens during the collision process, which depends on the relative phase and relative velocity between spin solitons. The non-integrable properties of the systems can bring spin solitons experience weak amplitude and location oscillations after collision. These stable spin soliton excitations could be used to study the negative inertial mass of solitons, the dynamics of soliton-impurity systems, and the spin dynamics in Bose-Einstein condensates., Comment: 8 pages, 6 figures

The recent experimental realization of spin-orbit coupling for ultracold atomic gases opens a new avenue for engineering solitons with internal spatial structures through tuning atomic band dispersions. However, the types of the resulting stripe solitons in a spin-1/2 Bose-Einstein condensate (BEC) have been limited to dark-dark or bright-bright with the same density profiles for different spins. Here we propose that general types of stripe solitons, including magnetic stripe (e.g., dark-bright) and localized stripe waves (neither bright nor dark), could be realized in a spin-1 BEC with widely tunable band dispersions through modulating the coupling between three spin states and the linear momentum of atoms. \ Surprisingly, a moving magnetic stripe soliton can possess both negative and positive effective masses at different velocities, leading to a zero mass soliton at certain velocity. Our work showcases the great potential of realizing novel types of solitons through band dispersion engineering, which may provide a new approach for exploring soliton physics in many physical branches., Comment: 6 pages, 7 figures

The wave properties of solitons in a two-component Bose-Einstein condensates with attractive interactions or repulsive interactions are investigated in detail. We demonstrate that dark solitons in one of component admit interference and tunneling behaviour, in sharp contrast to the scalar dark solitons and vector dark solitons. The analytic analysis of interference properties shows that spatial interference pattern is determined by the relative velocity of solitons, while temporal interference pattern depends on the velocities and widths of two solitons, differing from the interference properties of scalar bright solitons. Especially, for attractive interactions system, we show that interference effects can induce some short-time density humps (whose densities are higher than background density) during the collision process of dark solitons. Moreover, the maximum hump value is remarkably sensitive to the variation of the solitons' parameters. For repulsive interactions system, the temporal-spatial interference periods have lower limits. Numerical simulations results suggest that interference patterns for dark-bright solitons are more robust against noises than bright-dark solitons. These explicit interference properties can be used to measure the velocities and widths of solitons. It is expected that these interference behaviour can be observed experimentally and could be used to design matter wave soliton interferometry in vector systems.

The properties of nonlinear interference pattern between atomic bright solitons are characterized analytically, with the aid of exact solutions of dynamical equation in mean-field approximation. It is shown that relative velocity, relative phase, and nonlinear interaction strength can be measured from the interference pattern. The nonlinear interference properties are proposed to design atomic soliton interferometry in Bose-Einstein condensate. As an example, we apply them to measure gravity acceleration in a ultra-cold atom systems with a high precision degree. The results are also meaningful for precise measurements in optical fiber, water wave tank, plasma, and other nonlinear systems., Comment: 7 pages, 3 figures

We study the beating effects of solitons in multi-component coupled Bose-Einstein condensate systems. Our analysis indicate that the period of beating behavior is determined by the energy eigenvalue difference in the effective quantum well induced by solitons, and the beating pattern is determined by the eigen-states of quantum well which are involved in the beating behavior. We show that the beating solitons correspond to linear superpositions of eigen-states in some quantum wells, and the correspondence relations are identical for solitons in both attractive interaction and repulsive interaction condensate. This provides a possible way to understand the beating effects of solitons for attractive and repulsive interaction cases in a unified way, based on the knowledge of quantum eigen-states. Moreover, our results demonstrate many different beating patterns for solitons in three-component coupled condensate, in sharp contrast to the beating dark soliton reported before. The beating behavior can be used to test the eigenvalue differences of some certain quantum wells, and more abundant beating patterns are expected to exist in more components coupled systems., Comment: 7 papes, 3 figures

We study rogue wave excitation dynamics on a double-plane wave background through deriving rogue wave solution on the background. The results indicate that rogue wave still can be excited successfully from resonant perturbations with the two plane wave backgrounds. The obtained vector rogue wave can be decomposed to two rogue waves located on the two backgrounds separately. This enables us to investigate the superpositions of two of the three well-known fundamental rogue wave patterns, mainly including eye-shaped, anti-eye-shaped, and four-petaled one. The explicit conditions for different possible superpositions are clarified by a phase diagram for rogue wave pattern on each plane wave background. The detail analysis indicate that the rogue wave admits many different profiles, in contrast to the ones reported before. The studies can be extended directly to investigate other localized waves on double-plane wave background and even more plane waves involved cases., Comment: 5 pages, 5 figures

We investigate the localized waves of the coupled two-mode nonlinear Schr\"{o}dinger equations with a pair-tunneling term representing strongly interacting particles can tunnel between the modes as a fragmented pair. Facilitated by Darboux transformation, we have derived exact solution of nonlinear vector waves such as bright solitons, Kuznetsov-Ma soliton, Akhmediev breathers and rogue waves and demonstrated their interesting temporal-spatial structures. The phase diagram that demarcates the parameter ranges of the nonlinear waves is obtained. Our results have implications in such diverse fields as Bose-Einstein condensate, nonlinear fibers and super fluids., Comment: 5 pages, 6 figures

We present a simple representation for arbitrary-order rogue wave solution and study on the trajectories of them explicitly. We find that the global trajectories on temporal-spatial distribution all look like "X" shape for rogue waves. Short-time prediction on rogue wave can be done through measuring the information contained in the initial perturbation twice., Comment: Research paper, 6 pages, 6 figures