We investigate the vortex structures and dynamics in two-dimensional uniform Bose quantum liquids, accounting for quantum fluctuation effects via solving the extended Gross-Pitaevskii equation with Lee-Huang-Yang corrections. Using effective potential field analysis and the finite difference method, we establish the conditions for the existence of vortex excitations in such systems. Our results show that vortex excitations require a minimum background density, which is lower than the equilibrium density. As the vortex topological charge increases, this minimum density approaches the equilibrium density. At the critical density, the condensate's healing length remains finite, but the vortex core size diverges---a phenomenon highlighting the distinct properties of quantum liquids compared to gaseous Bose-Einstein condensates. Furthermore, stability analysis reveals that vortex stability depends on the liquid density, confirmed by dynamical evolution under perturbations.
We investigate the vortex structures and dynamics in two-dimensional uniform Bose quantum liquids, accounting for quantum fluctuation effects via solving the extended Gross-Pitaevskii equation with Lee-Huang-Yang corrections. Using effective potential field analysis and the finite difference method, we establish the conditions for the existence of vortex excitations in such systems. Our results show that vortex excitations require a minimum background density, which is lower than the equilibrium density. As the vortex topological charge increases, this minimum density approaches the equilibrium density. At the critical density, the condensate's healing length remains finite, but the vortex core size diverges---a phenomenon highlighting the distinct properties of quantum liquids compared to gaseous Bose-Einstein condensates. Furthermore, stability analysis reveals that vortex stability depends on the liquid density, confirmed by dynamical evolution under perturbations.
We investigate the interaction and dynamics of vortices belonging to different components of a binary uniform quantum liquid. Using the coupled extended Gross-Pitaevskii equations with logarithmic beyond-mean-field corrections, we derive the asymptotic interaction potential between well-separated vortices. The interaction potential retains the asymptotic form s−2 as a function of the intervortex distance s, but its coefficient depends on the background density through the quantum fluctuation. As a result, the interaction between vortices changes from attractive to repulsive at a critical density. Real-time simulations demonstrate a corresponding reversal of orbital motion of a vortex pair from clockwise to counterclockwise, consistent with their Magnus response.
Abstract We systematically explore isotropic self-bound liquid states and topological vortex excitations in two-dimensional binary Bose-Einstein condensates with tunable Rydberg soft-core interactions, modeled by the Gross-Pitaevskii equation incorporating the two-dimensional Lee-Huang-Yang quantum correction. Combining analytical Thomas-Fermi treatment with high-precision numerical simulations, we obtain stable fundamental and vortex-carrying quantum droplet solutions and investigate their collisional dynamics. The particle number N and Rydberg coupling strength κ are shown to systematically modulate the spatial and thermodynamic properties of both vortex-free and ring-shaped vortex liquids. In the repulsive regime κ > 0, our results agree quantitatively with those of magnetic quadrupolar condensates, confirming a common stabilization scenario for two-dimensional quantum fluids. More importantly, the Rydberg system distinguishes itself by offering fully isotropic, sign-switchable interactions and sustaining stable vortex droplets with winding numbers up to m = 4 over broad parameter ranges—features that are severely constrained in anisotropic quadrupolar counterparts.Collisions between moving zero-vorticity and vortex self-bound droplets are briefly discussed, demonstrate that their collisional dynamics are universal under the competing nonlocal repulsion and the logarithmic Lee-Huang-Yang effect.
The dynamics of a two-dimensional Bose-Einstein condensate mixture, loaded into a dual-core trap, when the beyond-mean-field effects are taken into account, are considered. The effects of quantum fluctuations are described by the Lee-Huang-Yang correction terms in the extended coupled Gross-Pitaevskii equations (GPE). The spatially uniform and inhomogeneous condensate cases are studied. In the first case, the parameter regimes associated with macroscopic quantum tunneling, macroscopic self-trapping, and revival-like localization dynamics are found. The Josephson oscillation frequencies for both the zero-phase and the π -phase modes are derived. As the total atom number is varied, the dynamics exhibit a nontrivial bifurcation structure: along the zero-phase branch, two successive pitchfork bifurcations generate bistability and hysteresis, while the π -phase branch shows a single pitchfork bifurcation. In the second case, the Josephson dynamics for quantum droplets and vortices are investigated. The analytical predictions for the oscillation frequencies of the atomic population between quantum droplets are found, and results are validated by direct numerical simulations of the system of coupled extended GPE. The existence of the Andreev-Bashkin nondissipative drag through simulations of droplet-droplet interactions is shown. The Josephson dynamics of vortex states are studied. It was found that vortices with topological charge S and sufficiently small particle number are typically unstable, breaking up into S + 1 (and occasionally S + 2 ) fundamental, nonvortical fragments, with the time to breakup increasing as the particle number grows. It is also found that unstable asymmetric vortices exhibit the splitting and/or crescentlike instability. For vortices with sufficiently large norms, long-time simulations confirm robust stability against small perturbations. In this stable regime, the properties of Josephson oscillations and Andreev-Bashkin-type entrainment for vortex states with charges S = 1 , 2 , and 3 are investigated.
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.
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.
This thesis investigates the behaviour of a quantum impurity coupled to a Bose–Einstein condensate. The condensate dynamics are described by the Gross–Pitaevskii equation, while the impurity is modelled by a coupled Schrödinger equation, forming a Gross–Clark-system. The work focuses on impurity localisation, vortex structure, and the dynamical consequences of impurity-condensate coupling in effectively two-dimensional geometries. The thesis begins by establishing the Gross–Pitaevskii model and its dimensionless formulation, together with the structure and stability of quantised vortices. Both numerical and approximate analytical descriptions of vortex profiles are developed and used throughout the thesis. The localisation of impurities is then examined in a range of static settings, including idealised trapping potentials and vortex cores, revealing how condensate density depletion can generate effective confinement for the impurity. Self-consistent impurity-vortex bound states are obtained by solving coupled stationary equations. The spectrum of localised impurity states is analysed, and the dependence of localisation on interaction parameters and angular momentum is characterised. These static results provide the foundation for subsequent dynamical studies. Real-time simulations are used to investigate the stability of impurity-bound configurations. For singly quantised vortices, impurity ground states are shown to be dynamically robust, while excited impurity states relax under time evolution despite remaining localised. A quantitative overlap measure is introduced to characterise the dynamical stability of impurity states. The thesis then examines multiply quantised vortices, demonstrating that impurity coupling can modify vortex dynamics and, in certain cases, suppress intrinsic instabilities. Overall, this work provides a systematic analysis of impurity localisation and impurity–vortex interactions in Bose-Einstein condensates, combining theoretical modelling, numerical methods, and dynamical simulations to clarify the role of impurities in coupled quantum fluids.