We present a novel class of stable nonlinear traveling waves that can exist within symmetric two-dimensional quantum droplets. We have made a comprehensive analysis of these topological bubbles characterizing distinct regions, classified by their velocity. We also generalize the study to unstable cases, incorporating higher-order vortex-antivortex pairs and arrays of vortices that can move with a common velocity through the fluid. Analytic approximations that aid the understanding of the results in different regimes are provided for all the cases.
We present a novel class of stable nonlinear traveling waves that can exist within symmetric two-dimensional quantum droplets. We have made a comprehensive analysis of these topological bubbles characterizing distinct regions, classified by their velocity. We also generalize the study to unstable cases, incorporating higher-order vortex-antivortex pairs and arrays of vortices that can move with a common velocity through the fluid. Analytic approximations that aid the understanding of the results in different regimes are provided for all the cases.
We present a novel class of stable nonlinear traveling waves that can exist within symmetric two-dimensional quantum droplets. We have made a comprehensive analysis of these topological bubbles characterizing distinct regions, classified by their velocity. We also generalize the study to unstable cases, incorporating higher-order vortex-antivortex pairs and arrays of vortices that can move with a common velocity through the fluid. Analytic approximations that aid the understanding of the results in different regimes are provided for all the cases.
We disclose a class of stable nonlinear traveling waves moving at specific constant velocities within symmetric two-dimensional quantum droplets. We present a comprehensive analysis of these traveling bubbles and identify three qualitatively distinct regions within the one-parameter family of solutions, classified by velocity: (i) well-separated phase singularities at low velocity, (ii) singularities within the same density dip at intermediate velocity, and (iii) rarefaction pulses without singularities at higher (subsonic) velocities. Then, we generalize the discussion to unstable cases, incorporating higher-order vortex-antivortex pairs and arrays of vortices that move cohesively with a common velocity within the fluid. In all cases, we provide analytic approximations that aid the understanding of the results in different regimes.
We analyze quantum droplets formed in a two-dimensional symmetric mixture of Bose-Einstein condensed atoms. For sufficiently large atom numbers, these droplets exhibit a flattop density profile with sharp boundaries governed by surface tension. Within the bulk of the droplet, traveling matter waves-localized density dips-can propagate at constant velocity while maintaining their shape. Using numerical simulations and qualitative analysis, we investigate the rich phenomenology that arises when such excitations reach the boundary of a finite droplet. We show that they can emit a small outgoing droplet, excite internal modes of the host soliton, or, in the case of vortex-antivortex pairs, split into individual vortices propagating backward near the edge. Furthermore, we demonstrate that traveling waves can be dynamically generated near the boundary through the collision of distinct droplets, and we discuss their trajectories and interactions.
A method for the creation of three-dimensional (3D) solitary topological modes, corresponding to vortical droplets of a two-component dilute superfluid, is presented. We use the recently introduced system of nonlinearly coupled Gross-Pitaevskii equations, which include contact attraction between the components, and quartic repulsion stemming from the Lee-Huang-Yang correction to the mean-field energy. Self-trapped vortex tori, carrying the topological charges m1=m2=1 or m1=m2=2 in their components, are constructed by means of numerical and approximate analytical methods. The analysis reveals stability regions for the vortex droplets (in broad and relatively narrow parameter regions for m1,2=1 and m1,2=2, respectively). The results provide a scenario for the creation of stable 3D self-trapped states with the double vorticity (m1,2=2). The stable modes are shaped as flat-top ones, with the space between the inner hole, induced by the vorticity, and the outer boundary filled by a nearly constant density. On the other hand, all modes with hidden vorticity, i.e., topological charges of the two components ${m}_{1}=\ensuremath{-}{m}_{2}=1$, are unstable. The stability of the droplets with m1,2=1 against splitting (which is the main scenario of possible instability) is explained by estimating analytically the energy of the split and unsplit states. The predicted results may be implemented, exploiting dilute quantum droplets in mixtures of Bose-Einstein condensates.
We discuss the stability of topological quantum droplets with the shape of two-dimensional soliton rings endowed with angular momentum that stem from a symmetric binary mixture in a Bose–Einstein condensate, with a strong trapping in one of the three spatial dimensions. We show that, in the lossless symmetric case, modeled by a Schrödinger equation with a Shannon-type nonlinear potential function, stable eigenstates can exist for arbitrarily large values of their topological charge l, provided the number of atoms is above a certain threshold. By comprehensive numerical computations, we analyze in detail cases up to l=50. We have found the perturbation modes and their eigenvalues, determining in each case which one dominates and destabilizes the solutions that lie below the stability threshold. We compare these results to the fate of the eigenstates that evolve in time. We also study the stability of the droplets under dynamical conditions by simulating collisions with potential barriers.
Bose-Einstein condensation(BEC) has been a research hotspot in cold atom physics for the past few decades. Recently, experiments on BECs have reported the observation of liquid-like quantum droplets, attracting significant interest. The physics for forming quantum droplets can be explained by zero-point quantum fluctuation which effectively prohibit the collapse caused by the mean-field interactions between the atoms. The stabilization mechanism beyond the mean-field theory, induced by quantum fluctuations, can be described by the Lee–Huang–Yang(LHY) correction. Normally, forming stable 2D or 3D solitons in free space is a challenging problem. Additionally, an intriguing question is how to generate 2D or 3D solitons with embedded vorticity. The LHY stability mechanism offers a new approach to producing stable solitons and vortex solitons in BECs. In this thesis, two-dimensional vortex quantum droplets in Bose-Einstein condensates, including those with and without external potential, are examined. The study of solitons and vortex solitons in BECs under mean-field interactions and external potential has yielded significant results. This thesis expands this field by introducing the LHY correction to study stable quantum droplets and vortex droplets in BECs. The work chapters begin with studying binary quantum droplets in free space, considering the case where interspecies interactions are weakly attractive and intraspecies interactions are weakly repulsive. The zero-vorticity, semi-vortex, and binary vortex quantum droplets are studied in Chapter 3. Stable semi-vortex quantum droplets with embedded vorticity up to 8 are found in this system. This result gives a way to form stable vortex droplets with high topological charges in free space by controlling one component with zero vorticity and the other component with embedded vorticity. The stability and properties of these droplets are systematically studied. Chapter 4 explores the vortex quantum droplets and hidden vortex droplets confined within a radial lattice trap. It is found that the existence curves of the droplets confined within this optical trap could violate the Vakhitov-Kolokolov(VK) criterion, which is a necessary condition to form a stable soliton. A remarkable finding is that the vortex and hidden vortex quantum droplets in this radial lattice remain stable when they carry the embedded vorticity up to 11. The double-ring vortex and hidden vortex quantum droplets confined within this radial lattice are also discussed. The work expands from non-magnetic atoms to magnetic atoms in Chapter 5, which needs to consider the dipole-dipole interactions(DDIs). The anisotropic dipolar vortex quantum droplets trapped in an annular potential are studied. Under the effect of the ring shape potential, the double peak ring-shaped vortex droplets remain stable when they carry the embedded vorticity up to 11. It is the first time stable droplets with high topological charges have been formed in a dipolar system. Additionally, the shape transformation of dipolar vortex droplets induced by the strength of the mean-field interaction is examined. Finally, the behavior of dipolar vortex droplets confined within a weak-depth annular potential is also discussed. The results of this thesis may prove highly useful in creating stable vortex quantum droplets in Bose-Einstein condensates and advancing the broader field of ultracold atoms.