Solitonic excitations of the one-dimensional quantum droplets are obtained, which smoothly connect vacuum with the flat-top droplet, akin to compactons in classical liquids. These solitons are of the kink type, necessarily residing on a constant pedestal, determined by the mean-field repulsion and beyond mean field quantum correction and having exactly one-third of the uniform condensate amplitude. Akin to the kinks, the propagating modes occur in pairs and are phase-locked with the background. The lowest chemical potential and condensate amplitude at the flat-top boundary matches with the self-trapped quantum droplet. More general excitations of analogous kind are obtained through the Möbius transform, which connect the required solutions to elliptic functions in general.
Attractive Bose-Einstein condensates can host two types of macroscopic self-bound states of different nature: bright solitons and quantum liquid droplets. Here, we investigate the connection between them with a Bose-Bose mixture confined in an optical waveguide. We develop a simple theoretical model to show that, depending on atom number and interaction strength, solitons and droplets can be smoothly connected or remain distinct states coexisting only in a bi-stable region. We experimentally measure their spin composition, extract their density for a broad range of parameters and map out the b…
We report a droplet to a soliton crossover by tuning the external confinement potential in a dilute Bose-Eienstein condensate by numerically solving the modified Gross-Pitaevskii equation. The testimony of such a crossover is presented via studying the fractional density of the condensate which smoothly migrates from being a flat-head curve at weak confinement to a bright soliton at strong confinement. Such a transition occurs across a region of the potential whose strength varies over an order of magnitude and thus should be fit to be termed as a crossover. We supplement our studies via explo…
We look into dark solitons in a quasi-1D dipolar Bose gas and in a quantum droplet. We derive the analytical solitonic solution of a Gross-Pitaevskii-like equation accounting for beyond mean-field effects. The results show there is a certain critical value of the dipolar interactions, for which the width of a motionless soliton diverges. Moreover, there is a peculiar solution of the motionless soliton with a non-zero density minimum. We also present the energy spectrum of these solitons with an additional excitation subbranch appearing. Finally, we perform a series of numerical experiments rev…
We study the stability of quantum droplet and its associated phase transitions in ultracold Bose-Bose mixtures uniformly confined in quasi-two-dimension. We show that the confinement-induced boundary effect can be significant when increasing the atom number or reducing the confinement length, which destabilizes the quantum droplet towards the formation of a soliton bound state. In particular, as increasing the atom number we find the reentrance of soliton ground state, while the droplet is stabilized only within a finite number window that sensitively depends on the confinement length. Near th…
We address the existence and stability of one-dimensional (1D) holes and kinks and two-dimensional (2D) vortex-holes nested in extended binary Bose mixtures, which emerge in the presence of Lee-Huang-Yang (LHY) quantum corrections to the mean-field energy, along with self-bound quantum droplets. We consider both the symmetric system with equal intra-species scattering lengths and atomic masses, modeled by a single (scalar) LHY-corrected Gross-Pitaevskii equation (GPE), and the general asymmetric case with different intra-species scattering lengths, described by two coupled (spinor) GPEs. We fo…
We study quantum dynamics of bosonic atoms that are excited to form a phase kink, or several kinks, by an imprinting potential in a one-dimensional trap. We calculate dissipation due to quantum and thermal fluctuations in soliton trajectories, collisions and the core structure. Single-shot runs show weak filling of a soliton core, typically deeper solitons in the case of stronger fluctuations and spreading/disappearing solitons due to collisions. We also analyze a soliton system in an optical lattice that shows especially strong fluctuation-induced phenomena.
When two Bose-Einstein condensates -- labelled 1 and 2 -- overlap spatially, the equilibrium state of the system depends on the miscibility criterion for the two fluids. Here, we theoretically focus on the non-miscible regime in two spatial dimensions and explore the properties of the localized wave packet formed by the minority component 2 when immersed in an infinite bath formed by component 1. We address the zero-temperature regime and describe the two-fluid system by coupled classical field equations. We show that such a wave packet exists only for an atom number $N_2$ above a threshold va…
We study the collective modes of a binary Bose mixture across the soliton to droplet crossover in a quasi one dimensional waveguide with a beyond-mean-field equation of state and a variational Gaussian ansatz for the scalar bosonic field of the corresponding effective action. We observe a sharp difference in the collective modes in the two regimes. Within the soliton regime modes vary smoothly upon the variation of particle number or interaction strength. On the droplet side collective modes are inhibited by the emission of particles. This mechanism turns out to be dominant for a wide range of…
In this article, we illustrate the scaling properties of a family of solutions for N attractive bosonic atoms in the limit of large $N$. These solutions represent the quantized dynamics of solitonic degrees of freedom in atomic droplets. In dimensions lower than two, or $d=2-ε$, we demonstrate that the number of isotropic droplet states scales as $N^{3/2}/ε^{1/2}$, and for $ε=0$, or $d=2$, scales as ${N^2}$. The ground state energies scale as $N^{2 / ε+ 1}$ in $d=2-ε$, and when $d=2$, scale as an exponential function of N. We obtain the universal energy spectra and the generalized Tjon relatio…
We study two-dimensional (2D) matter-wave solitons in spinor Bose-Einstein condensates (BECs) under the action of the spin-orbit coupling (SOC) and opposite signs of the self- and cross-interactions. Stable 2D two-component solitons of the mixed-mode (MM) type are found if the cross-interaction between the components is attractive, while the self-interaction is repulsive in each component. Stable solitons of the semi-vortex type are formed in the opposite case, under the action of competing self-attraction and cross-repulsion. The solitons exist with the total norm taking values below a collap…
We exhaust all exact self-consistent solutions of complex-valued fermionic condensates in the 1+1 dimensional Bogoliubov-de Gennes and chiral Gross-Neveu systems under uniform boundary conditions. We obtain $n$ complex (twisted) kinks, or grey solitons, with $2n$ parameters corresponding to their positions and phase shifts. Each soliton can be placed at an arbitrary position while the self-consistency requires its phase shift to be quantized by $π/N$ for $N$ flavors.
