Two-dimensional vortex quantum droplets

Abstract

It was recently found that the Lee-Huang-Yang (LHY) correction to the mean-field Hamiltonian of binary atomic boson condensates suppresses the collapse and creates stable localized modes (twocomponent "quantum droplets", QDs) in two and three dimensions (2D and 3D). In particular, the LHY effect modifies the effective Gross-Pitaevskii equation (GPE) in 2D by adding a logarithmic factor to the usual cubic term. In the framework of the accordingly modified two-component GPE system, we construct 2D self-trapped modes in the form of QDs with vorticity S embedded into each component. Due to the effect of the logarithmic factor, the QDs feature a flat-top shape, which expands with the increase of S and norm N . An essential finding, produced by a systematic numerical investigation and analytical estimates, is that the vortical QDs are stable (which is a critical issue for vortex solitons in nonlinear models) up to S = 5, for N exceeding a certain threshold value, which is predicted to scale as N th ∼ S 4 for large S (for three-dimensional QDs, the scaling is N th ∼ S 6 ). The prediction is corroborated by numerical findings. Pivots of QDs with S ≥ 2 are subject to structural instability, as specially selected perturbations can split the single pivot in a set of S or S + 2 pivots corresponding to unitary vortices; however, the structural instability remains virtually invisible, as it occurs in a broad central "hole" of the vortex soliton, where values of fields are very small, and it does not cause any dynamical instability. In the condensate of 39 K atoms, in which QDs with S = 0 and a quasi-2D shape were created recently, the vortical droplets may have radial size 30 µm, with the number of atoms in the range of 10 4 − 10 5 . The role of three-body losses is considered too, demonstrating that they do not prevent the creation of the vortex droplets, but may produce a noteworthy effect, leading to sudden splitting of "light" droplets. In addition, hidden-vorticity states in QDs, with topological charges S+ = −S− = 1 in their components, which are prone to strong instability in other settings, have their stability region too. Unstable HV states tend to spontaneously merge into zero-vorticity solitons. Collisions of QDs, which may lead to their merger, and dynamics of elliptically deformed QDs (which form rotating elongated patterns or ones with oscillations of the eccentricity) are briefly considered too.

Modulational Instability, Inter-Component Asymmetry, and Formation of Quantum Droplets in One-Dimensional Binary Bose Gases

“…The norm of the exact QD solutions given by Eqs. (13) is For other values of δ g/g, the plot can be generated from the present one by rescaling. The inset shows the density profile of the FT solution for δ g/g = 0.05 and µ = µ 0 + 0.00001, very close to the delocalization limit (the tranistion to PW).…”

Multidimensional hybrid Bose-Einstein condensates stabilized by lower-dimensional spin-orbit coupling

“…In a recent landmark advance, stabilization of Bose-Einstein condensates (BECs) against collapse [6,7] by Lee-Huang-Yang (LHY) quantum corrections to the mean-field interactions [8] has been demonstrated experimentally, leading to the creation of fundamental (zero-vorticity) solitary states in the form of "quantum droplets" in BECs with dipole-dipole [9][10][11] and with contact [12][13][14][15] interactions. Regarding "droplets" with embedded vorticity, they are unstable in the former case [16], while LHY-stabilized 3D [17] and 2D [18,19] vortical droplets have been predicted in BECs with contact nonlinearity.…”

Immiscible and miscible states in binary condensates in the ring geometry

“…In addition to Bose-Bose mixtures of different isotopes and atomic species [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], experimentalists have in the past few years created condensates with a spin degree of freedom [19], also implementing spin-orbit coupling which gives rise to exciting new states [20][21][22][23][24]; moreover, recent achievements have led to the generation of doubly-superfluid Bose-Fermi mixtures [25], in which both components are condensed, a state so far inaccessible in other settings (such as superfluid helium). Although the stability and phase diagrams of such systems have been extensively studied in the course of more than 20 years , even simple hetero-species binary mixtures still reveal unexpected features, such as the role of the trap sag, atom number and kinetic energy contribution to the extent of miscibility in trapped configurations [42,50,52], and nontrivial effects of the expansion on the mixtures' dynamics [51,53].…”