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We unravel stationary states in the form of dark soliton stripes, bubbles, and kinks embedded in a two-dimensional droplet-bearing setting emulated by an extended Gross-Pitaevskii approach. The existence of these configurations is corroborated through an effectively reduced potential picture demonstrating their concrete parametric regions of existence. The excitation spectra of such configurations are analyzed within the Bogoliubov-de-Gennes framework exposing the destabilization of dark soliton stripes and bubbles, while confirming the stability of droplets, and importantly unveiling spectral stability of the kink against transverse excitations. Additionally, a variational approach is constructed providing access to the transverse stability analysis of the dark soliton stripe for arbitrary chemical potentials and widths of the structure. This is subsequently compared with the stability analysis outcome demonstrating very good agreement at small wavenumbers. Dynamical destabilization of dark soliton stripes via the snake instability is showcased, while bubbles are found to feature both a splitting into a gray soliton pair and a transverse instability thereof. These results shed light on unexplored stability and instability properties of nonlinear excitations in environments featuring a competition of mean-field repulsion and beyond-mean-field attraction that can be probed by state-of-the-art experiments., Comment: 14 pages, 6 figures

We demonstrate the existence and stability of one-dimensional (1D) topological kink configurations immersed in higher-dimensional bosonic gases and nonlinear optical setups. Our analysis pertains, in particular, to the two- and three-dimensional extended Gross-Pitaevskii models with quantum fluctuations describing droplet-bearing environments but also to the two-dimensional cubic-quintic nonlinear Schr\"odinger equation containing higher-order corrections to the nonlinear refractive index. Contrary to the generic dark soliton transverse instability, the kink structures are generically robust under the interplay of low-amplitude attractive and high-amplitude repulsive interactions. A quasi-1D effective potential picture dictates the existence of these defects, while their stability is obtained through linearization analysis and direct dynamics in the presence of external fluctuations showcasing their unprecedented resilience. These generic (across different models) findings should be detectable in current cold atom and optics experiments. They also offer insights towards controlling topological excitations and their usage in topological quantum computers., Comment: 4 pages, 3 figures

We explore the dynamics and interactions of multiple bright droplets and bubbles, as well as the interactions of kinks with droplets and with antikinks, in the extended one-dimensional Gross-Pitaevskii model including the Lee-Huang-Yang correction. Existence regions are identified for the one-dimensional droplets and bubbles in terms of their chemical potential, verifying the stability of the droplets and exposing the instability of the bubbles. The limiting case of the droplet family is a stable kink. The interactions between droplets demonstrate in-phase (out-of-phase) attraction (repulsion), with the so-called Manton's method explicating the observed dynamical response, and mixed behavior for intermediate values of the phase shift. Droplets bearing different chemical potentials experience mass-exchange phenomena. Individual bubbles exhibit core expansion and mutual attraction prior to their destabilization. Droplets interacting with kinks are absorbed by them, a process accompanied by the emission of dispersive shock waves and gray solitons. Kink-antikink interactions are repulsive, generating counter-propagating shock waves. Our findings reveal dynamical features of droplets and kinks that can be detected in current experiments., Comment: To be published in Condensed Matter (a special issue on "Quantum droplets")

We experimentally realize the Peregrine soliton in a highly particle-imbalanced two-component repulsive Bose-Einstein condensate in the immiscible regime. The effective focusing dynamics and resulting modulational instability of the minority component provide the opportunity to dynamically create a Peregrine soliton with the aid of an attractive potential well that seeds the initial dynamics. The Peregrine soliton formation is highly reproducible, and our experiments allow us to separately monitor the minority and majority components, and to compare with the single component dynamics in the absence or presence of the well with varying depths. We showcase the centrality of each of the ingredients leveraged herein. Numerical corroborations and a theoretical basis for our findings are provided through three-dimensional simulations emulating the experimental setting and via a one-dimensional analysis further exploring its evolution dynamics., Comment: 6 pages, 3 figures, Supplemental Material

We unravel the existence and stability properties of dark soliton solutions as they extend from the regime of trapped quantum droplets towards the Thomas-Fermi limit in homonuclear symmetric Bose mixtures. Leveraging a phase-plane analysis, we identify the regimes of existence of different types of quantum droplets and subsequently examine the possibility of black and gray solitons and kink-type structures in this system. Moreover, we employ the Landau dynamics approach to extract an analytical estimate of the oscillation frequency of a single dark soliton in the relevant extended Gross-Pitaevskii model. Within this framework, we also find that the single soliton immersed in a droplet is stable, while multisoliton configurations exhibit parametric windows of oscillatory instabilities. Our results pave the way for studying dynamical features of nonlinear multisoliton excitations in a droplet environment in contemporary experimental settings., Comment: 16 pages, 9 figures, fixed some typos

Solitons are nonlinear solitary waves which maintain their shape over time and through collisions, occurring in a variety of nonlinear media from plasmas to optics. We present an experimental and theoretical study of hydrodynamic phenomena in a two-component atomic Bose-Einstein condensate where a soliton array emerges from the imprinting of a periodic spin pattern by a microwave pulse-based winding technique. We observe the ensuing dynamics which include shape deformations, the emergence of dark-antidark solitons, apparent spatial frequency tripling, and decay and revival of contrast related to soliton collisions. For the densest arrays, we obtain soliton complexes where solitons undergo continued collisions for long evolution times providing an avenue towards the investigation of soliton gases in atomic condensates.

The present work is motivated by the recent experimental realization of the Townes soliton in an effective two-component Bose-Einstein condensate by B. Bakkali-Hassan et al. [Phys. Rev. Lett. 127, 023603 (2021)]. Here, we use a similar multicomponent platform to exemplify theoretically and numerically, within the mean-field Gross-Pitaevskii framework, the potential toward the experimental realization of a different fundamental wave structure, namely the Peregrine soliton. Leveraging the effective attractive interaction produced within the mixture's minority species in the immiscible regime, we illustrate how initialization of the condensate with a suitable power-law decaying spatial density pattern yields the robust emergence of the Peregrine wave in the absence and in the presence of a parabolic trap. We then showcase the spontaneous emergence of the Peregrine soliton via a suitably crafted wide Gaussian initialization, again both in the homogeneous case and in the trap scenario. It is also found that narrower wave packets may result in periodic revivals of the Peregrine soliton, while broader ones give rise to a cascade of Peregrine solitons arranged in a so-called Christmas-tree structure. Strikingly, the persistence of these rogue-wave structures is demonstrated in certain temperature regimes as well as in the presence of transversal excitations through three-dimensional computations in a quasi-one-dimensional regime. This proof-of-principle illustration is expected to represent a practically feasible way to generate and observe this rogue wave in realistic current ultracold atom experimental settings., Comment: 14 pages, 8 figures