Quantum droplets have recently emerged as a novel liquid state of matter in a mixture of two-component ultracold Bose gases under the equilibrium condition between the competing attractive inter- and repulsive intraspecies forces. Quantum droplets represent a self-bound liquid state in purely nonlinear systems and as such there is not any management applied to their study up to now. We here introduce the nonlinear management via space-periodic Feshbach resonance technique to a binary Bose–Einstein condensate and investigate theoretically the structure, property and dynamics of the one-dimensional quantum droplets therein, three findings are made: small droplets with single hump (solitonlike), moderate droplets composed of two solitons, large droplets feature a modulated flat-top shape. Particularly, by means of linear-stability and direct perturbed simulations, we prove that the droplets have a much wider stable region than their counterparts without taking the nonlinear management. The variational approximation is adopted and validated with numerical results in terms of small droplets. The results predicted here may be realized in the frontier ultracold atoms experiments aided by Feshbach-resonance, opening up a new channel to the quantum droplets studies.
Quantum droplets have recently emerged as a novel liquid state of matter in a mixture of two-component ultracold Bose gases under the equilibrium condition between the competing attractive inter- and repulsive intraspecies forces. Quantum droplets represent a self-bound liquid state in purely nonlinear systems and as such there is not any management applied to their study up to now. We here introduce the nonlinear management via space-periodic Feshbach resonance technique to a binary Bose–Einstein condensate and investigate theoretically the structure, property and dynamics of the one-dimensional quantum droplets therein, three findings are made: small droplets with single hump (solitonlike), moderate droplets composed of two solitons, large droplets feature a modulated flat-top shape. Particularly, by means of linear-stability and direct perturbed simulations, we prove that the droplets have a much wider stable region than their counterparts without taking the nonlinear management. The variational approximation is adopted and validated with numerical results in terms of small droplets. The results predicted here may be realized in the frontier ultracold atoms experiments aided by Feshbach-resonance, opening up a new channel to the quantum droplets studies.
The structure and dynamics of one-dimensional binary Bose gases forming quantum droplets is studied by solving the corresponding amended Gross-Pitaevskii equation. Two physically different regimes are identified, corresponding to small droplets of an approximately Gaussian shape and large ``puddles'' with a broad flat-top plateau. Small droplets collide quasielastically, featuring the solitonlike behavior. On the other hand, large colliding droplets may merge or suffer fragmentation, depending on their relative velocity. The frequency of a breathing excited state of droplets, as predicted by the dynamical variational approximation based on the Gaussian ansatz, is found to be in good agreement with numerical results. Finally, the stability diagram for a single droplet with respect to shape excitations with a given wave number is drawn, being consistent with preservation of the Weber number for large droplets.
Quantum droplets represent a striking manifestation of beyond-mean-field physics, with properties that depend sensitively on dimensionality. Although quantum droplets have been experimentally realized in one and three dimensions, their realization in two dimensions has remained elusive. Here, we observe the formation of a two-dimensional (2D) quantum droplet in a quasi-2D geometry by transferring the single-component Bose-Einstein condensates (BECs) into a spin mixture in the Lee-Huang-Yang (LHY) regime, where the LHY effect evidently deviates from its three-dimensional form. We find that, in our scheme, 2D quantum droplets are more stable and exhibit longer lifetimes than previously reported quantum droplets. By instead transferring the initial BECs into another single-spin state with a negative scattering length, we generate 2D Townes solitons. A comparison between the two types of self-bound states shows that, whereas 2D Townes solitons are stable only near a critical atom number determined by the scattering length, 2D quantum droplets remain well-defined and self-bound over a much broader parameter range. These realizations of quantum droplets and Townes solitons in two dimensions provide new insights into self-bound states and open new avenues for exploring nonlinear dynamics in quantum liquids.
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 brief review summarizes recent theoretical and experimental results which predict and establish the existence of quantum droplets (QDs), i.e., robust two- and three-dimensional (2D and 3D) self-trapped states in Bose-Einstein condensates (BECs), which are stabilized by effective self-repulsion induced by quantum fluctuations around the mean-field (MF) states [alias the Lee-Huang-Yang (LHY) effect]. The basic models are presented, taking special care of the dimension crossover, 2D → 3D. Recently reported experimental results, which exhibit stable 3D and quasi-2D QDs in binary BECs, with the inter-component attraction slightly exceeding the MF self-repulsion in each component, and in single-component condensates of atoms carrying permanent magnetic moments, are presented in some detail. The summary of theoretical results is focused, chiefly, on 3D and quasi-2D QDs with embedded vorticity, as the possibility to stabilize such states is a remarkable prediction. Stable vortex states are presented both for QDs in free space, and for singular but physically relevant 2D modes pulled to the center by the inverse-square potential, with the quantum collapse suppressed by the LHY effect.
Abstract We present simulation results of the ground state structure and dynamics of quantum droplets (QDs) in one-dimensional spin–orbit coupled binary Bose–Einstein condensates. We have considered two cases for this analysis, such as (i) the mean-field term has a vanishingly small contribution utilizing the equal and opposite inter- and intraspecies interactions and (ii) unequal inter- and intraspecies interactions. The QD exhibits remarkably different natures in each case. In the former case, it exhibits a bright sech-like droplet nature, while in the latter case, we find the flattened sech-like shape of the droplet. Further, we analyze the effect of velocity perturbation on the dynamics in both cases. For the first case, we find a systematic change from the solitonic droplet nature to the breathing droplet, which finally has a moving droplet feature upon increasing the velocity. However, the second case shows similar dynamics except having more dynamically stable features than the first. Finally, we present various dynamics that ensued in the QD due to the quenching of the interaction parameters, coupling parameters or allowing the droplet to undergo collisions.