We predict a scheme for the creation of isotropic three-dimensional quantum droplets in Rydbeg-dressed Bose gases, which contain both repulsive contact interactions and attractive soft-core interactions. Via manipulating laser detuning, the droplet size and particle number density could be engineered. Quantum fluctuation induced Lee-Huang-Yang (LHY) correction should be considered to stabilize droplets when LHY energy is comparable to the mean-field energy. Self-trapped droplets possess flat-top density distribution for a large particle number, and the collective excitations are calculated to determine the self-evaporation threshold. We further distinguish quantum droplets from solitons according to condensate compressibility. Finally, the dynamic stability of droplets is examined by pairwise-droplet collision. Our system could realize the most dilute quantum droplets, and establish a promising platform for further simulating topological nontrivial droplets. Published by the American Physical Society 2024
We predict a scheme for the creation of isotropic three-dimensional quantum droplets in Rydbeg-dressed Bose gases, which contain both repulsive contact interactions and attractive soft-core interactions. Via manipulating laser detuning, the droplet size and particle number density could be engineered. Quantum fluctuation induced Lee-Huang-Yang (LHY) correction should be considered to stabilize droplets when LHY energy is comparable to the mean-field energy. Self-trapped droplets possess flat-top density distribution for a large particle number, and the collective excitations are calculated to determine the self-evaporation threshold. We further distinguish quantum droplets from solitons according to condensate compressibility. Finally, the dynamic stability of droplets is examined by pairwise-droplet collision. Our system could realize the most dilute quantum droplets, and establish a promising platform for further simulating topological nontrivial droplets. Published by the American Physical Society 2024
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.
We study two-dimensional (2D) isotropic quantum droplets (QDs) in dipolar binary Bose–Einstein condensates (BECs). The QDs are supported by the competition between the 2D form of the Lee-Huang-Yang (LHY) term and the isotropic dipole-dipole interactions (DDIs). Moreover, the DDIs in the 2D plane can be tuned to be either repulsive or attractive. Before that, QDs in dipolar BECs were often explored in three-dimensional (3D) systems, with competition between the attractive DDIs and the repulsive LHY term. Unlike the 3D system, the LHY term of the 2D binary system behaves in a logarithmic form, which can feature both attraction and repulsion. In this case, the QDs can be produced regardless of the interactions (attraction, repulsion, or zero) that the mean-field effect represents. In this paper, we model the aforementioned QDs via the 2D binary dipolar BECs with the competition between isotropic DDIs and the logarithmic LHY term. Their characteristic parameters (the peak density, IP, chemical potential, μ, and effective area, Aeff) using both numerical and theoretical methods are discussed. The centripetal collision and oblique collision between moving QDs are also studied.
Abstract The static and dynamic properties of self-bound quantum droplets in a one-dimensional Bose-Bose mixture are discussed in the spirit of the Hartree–Fock-Bogoliubov theory. This latter enables us to provide beyond the Lee-Huang-Yang (LHY) quantum corrections to the equation of state at both zero and finite temperatures. In the uniform case our results for the ground-state energy and the critical temperature are confirmed through comparison with Quantum Monte-Carlo simulation and with available theoretical results. The density profiles are supported by numerical simulations of the generalized Gross-Pitaevskii equation which selfconsistently includes higher-order terms originating from the normal and anomalous fluctuations under the local density approximation. We show that the density exhibits a dip near its center in the flat-top plateau region for large interspecies interactions. We exemplify the impact of the beyond LHY corrections on the spatiotemporal evolution of the self-bound droplet in the presence of excitation induced by periodic density modulation. It is found that higher-order corrections may lead to the formation of a train of small droplets. We then extend our study for the case of inhomogeneous droplets in quasi one-dimensional Bose mixtures.
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.
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.
Among settings which have recently been elaborated for the creation of stable multidimensional solitons, most advanced, as concerns the theory and experiment alike, is the work with quantum droplets (QDs) in atomic BEC. Important theoretical predictions for fundamental and topologically structured soliton-like (stably self-trapped) QDs have been published in many papers, starting from the pioneering work of Petrov [Phys. Rev. Lett. 115, 155302 (2015)]. Simultaneously, the experimental advancement in the making of QDs in binary BECs, as well as in single-component BECs of atoms carrying magnetic dipole moments, have been really remarkable and unique. Successful experiments followed the first theoretical prediction of the QDs very quickly, and the progress in the experimental work was much faster than in other areas of physics where stable multidimensional solitons were predicted. The basis of these works is a correction to the MF (mean-field) BEC dynamics produced by quantum fluctuations around MF states. The correction was first predicted in 1957 by Lee, Huang, and Yang (LHY). The breakthrough proposal made by Petrov [Phys. Rev. Lett. 115, 155302 (2015)] was to use the effective higher-order (quartic) self-repulsion, produced by the LHY effect in the atomic BEC, as a mechanism arresting the collapse driven by mutual attraction of two self-repulsive components in a binary quantum bosonic gas. The balance between the inter-species attraction and LHY-induced self-repulsion gives rise to stable 3D and quasi-2D (pancake-shaped) localized bound states in the form of the quantum droplets (QDs). In single-component condensates of magnetic atoms, the attraction is provided by the long-range dipole–dipole interaction (Chomaz et al., 2016; Schmitt et al., 2016). The competition between the MF attraction and LHY repulsion maintains a superfluid state whose density (taking very low values) cannot exceed a certain maximum, thus making it effectively incompressible. This is a reason why this quantum macroscopic state of matter is identified as a superfluid. Accordingly, localized states filled by this quantum fluid are called “droplets.” In addition to the 3D QDs, droplets in the effectively 2D setting, which may exist under the action of tight confinement in one direction, imposed by an external potential, were theoretically predicted [Petrov and Astrakharchik, Phys. Rev. Lett. 117, 100401 (2016)] and experimentally created [Cabrera et al., Science 359, 301-304 (2018)] too. This chapter provides a condensed review of basic theoretical results for stable QDs in binary BECs, maintained through the stable balance between the inter-species attraction and intra-species LHY repulsion. Both fundamental modes and ones with embedded vorticity are considered. The presentation is partly based on a review article by Luo et al. [Front. Phys. 16, 32501 (2021)]. In addition to 2D and 3D self-trapped QDs in free space, the present chapter addresses 2D fundamental and vortex modes trapped in a singular attractive potential, ∼−1/r2, which are stabilized by the LHY repulsion. Two subsequent chapters present a summary of experimental findings for QDs in binary BECs and for QDs in single-component BECs of magnetic atoms.