Abstract We consider quantum droplets in dipolar Bose–Einstein condensates embedded in optical lattices (OLs) within the framework of Gross–Pitaevskii equations. In dipolar BECs, the long-range and isotropic dipole–dipole interaction (DDI) provides an additional mechanism for self-binding. We analyze the linear stability as well dynamics of quantum droplets. We find an effective potential for the width and show that the optimum width for formation of quantum droplet increases as the DDI increases. We study dynamics of the stable droplets and see that its width oscillates with time, and the amplitude of oscillation increases with the increase of DDI. In presence of OLs, width of a stable droplet changes quasi-periodically while the location of density profile changes periodically in space. The frequency of oscillation depends sensitively on the lattice parameters. We check dynamical stability of a quantum droplet through numerical simulation.
Abstract We consider quantum droplets in dipolar Bose–Einstein condensates embedded in optical lattices (OLs) within the framework of Gross–Pitaevskii equations. In dipolar BECs, the long-range and isotropic dipole–dipole interaction (DDI) provides an additional mechanism for self-binding. We analyze the linear stability as well dynamics of quantum droplets. We find an effective potential for the width and show that the optimum width for formation of quantum droplet increases as the DDI increases. We study dynamics of the stable droplets and see that its width oscillates with time, and the amplitude of oscillation increases with the increase of DDI. In presence of OLs, width of a stable droplet changes quasi-periodically while the location of density profile changes periodically in space. The frequency of oscillation depends sensitively on the lattice parameters. We check dynamical stability of a quantum droplet through numerical simulation.
We consider quantum droplets in dipolar Bose-Einstein condensates embedded in optical lattices within the framework of Gross-Pitaevskii equations. In dipolar BECs, the long-range and isotropic dipole-dipole interaction provides an additional mechanism for self-binding. We analyze the linear stability as well dynamics of quantum droplets. We find an effective potential for the width and show that the optimum width for formation of quantum droplet increases as the dipole-dipole interaction increases. We study dynamics of the stable droplets and see that its width oscillates with time, and the amplitude of oscillation increases with the increase of dipole-dipole interaction. In presence of optical lattices, width of a stable droplet changes quasi-periodically while the location of density profile changes periodically in space. The frequency of oscillation depends sensitively on the lattice parameters. We check dynamical stability of a quantum droplet through numerical simulation.
Recent observations of droplets in dipolar and binary Bose-Einstein condensate (BEC) motivates us to study the theory of droplet formation in details. Precisely, we are interested in investigating the possibility of droplet formation in a quasi one dimensional geometry. The recent observation have concluded that the droplets are stabilized by the competition between effective mean-filed and beyond mean-field interaction. Hence, it is possible to map the effective equation of motion to a cubic-quartic nonlinear Schr\odinger equation (CQNLSE). We obtain two analytical solutions of the modified Gross-Pitaevskii equation or CQNLSE and based on their stability we investigate the parameter regime for which droplets can form. The effective potential allows us to conclude about the regions of soliton domination and self bound droplet formations.
We study the stabilization properties of dipolar Bose–Einstein condensate in a deep one-dimensional optical lattice with an additional external parametrically modulated harmonic trap potential. Through both analytical and numerical methods, we solve a dimensionless nonlocal nonlinear discrete Gross–Pitaevskii equation with both the short-range contact interaction and the long-range dipole–dipole interaction. It is shown that, the stability of dipolar condensate in modulated deep optical lattice can be controled by coupled effects of the contact interaction, the dipolar interaction and the external modulation. The system can be stabilized when the dipolar interaction, the contact interaction, the average strength of potential and the ratio of amplitude to frequency of the modulation satisfy a critical condition. In addition, the breather state, the diffused state and the attractive-interaction-induced-trapped state are predicted. The dipolar interaction and the external modulation of the lattice play important roles in stabilizing the condensate.
Toroidal Confinement and Beyond: Vorticity-Defined Morphologies of Dipolar 164Dy Quantum Droplets
We investigate the formation, stability, and dynamics of 3D ring-shaped and multipole vortical quantum droplets (QDs) in non-rotating dipolar Bose-Einstein condensates held in a toroidal trapping potential. The QD dynamics are investigated in the framework of the extended Gross-Pitaevskii equation, which includes long-range dipole-dipole interactions (DDI) and the beyond-mean-field Lee-Huang-Yang (LHY) term, revealing the emergence of self-bound states. Stable stationary solutions for multipole QDs with different values of the topological charge (vorticity S) are shaped as necklace-like modes, with the number of \textquotedblleft beads" (multipole's order) n=2S, up to S=6. The stability area of the multipoles shrinks with the increase of S. For higher values of S the centrifugal effect associated with the phase winding destabilizes the annular density and drives the formation of fragmented multipole droplet states. The dependence of the chemical potential, total energy and peak density on the norm (number of particles) and S is produced. These findings uncover the stabilizing effect of the LHY correction and DDI anisotropy in maintaining complex QD states in the non-rotating configurations.
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.
We investigate the formation, stability, and dynamics of three-dimensional ring-shaped and multipole vortical quantum droplets (QDs) in nonrotating dipolar Bose-Einstein condensates held in a toroidal trapping potential. The QD dynamics are investigated in the framework of the extended Gross-Pitaevskii equation, which includes long-range dipole-dipole interactions (DDIs) and the beyond-mean-field Lee-Huang-Yang (LHY) term, revealing the emergence of self-bound states. Stable stationary solutions for multipole QDs with different values of the topological charge (vorticity S) are shaped as necklacelike modes, with the number of "beads" (multipole order) n=2S, up to S=6. The stability area of the multipoles shrinks with the increase of S. For higher values of S the centrifugal effect associated with the phase winding destabilizes the ring-shaped QDs and drives the formation of fragmented multipole droplet states. The dependence of the chemical potential, total energy, and peak density on the norm (number of particles) and S is produced. These findings uncover the stabilizing effect of the LHY correction and DDI anisotropy in maintaining complex QD states in the nonrotating configurations.