We study the ground-state density patterns of a population-imbalanced two-component dipolar Bose-Einstein condensate confined in a circular quasi-two-dimensional box. Using a mean-field model, we map out phase diagrams as functions of the axial confinement, interaction imbalance, and population ratio. The system supports a rich sequence of stationary morphologies, including a nearly uniform pancake state, pancake-droplet and ring-droplet coexistence states, droplet arrays, and concentric rings. These patterns show a close structural correspondence to microphase-separated morphologies in diblock-copolymer systems, with the population imbalance acting as an effective volume fraction that selects the pattern topology. Analysis of the density profiles and structure factors reveals that the modulated states possess an intrinsic nonzero characteristic wave vector, which remains essentially unchanged when the box size is varied. We also find that the characteristic pattern spacing scales linearly with the axial confinement length, indicating that the transverse thickness of the condensate controls the effective in-plane length scale. In a finite circular box, this smooth scaling is interrupted by discrete steps, reflecting geometric frustration and the integer locking of the number of rings or droplets. Our results show that box-trapped dipolar mixtures provide a controllable platform for studying finite-size pattern selection and nonlocal microphase formation in quantum fluids.
We study the ground-state density patterns of a population-imbalanced two-component dipolar Bose-Einstein condensate confined in a circular quasi-two-dimensional box. Using a mean-field model, we map out phase diagrams as functions of the axial confinement, interaction imbalance, and population ratio. The system supports a rich sequence of stationary morphologies, including a nearly uniform pancake state, pancake-droplet and ring-droplet coexistence states, droplet arrays, and concentric rings. These patterns show a close structural correspondence to microphase-separated morphologies in diblock-copolymer systems, with the population imbalance acting as an effective volume fraction that selects the pattern topology. Analysis of the density profiles and structure factors reveals that the modulated states possess an intrinsic nonzero characteristic wave vector, which remains essentially unchanged when the box size is varied. We also find that the characteristic pattern spacing scales linearly with the axial confinement length, indicating that the transverse thickness of the condensate controls the effective in-plane length scale. In a finite circular box, this smooth scaling is interrupted by discrete steps, reflecting geometric frustration and the integer locking of the number of rings or droplets. Our results show that box-trapped dipolar mixtures provide a controllable platform for studying finite-size pattern selection and nonlocal microphase formation in quantum fluids.
We investigate non-equilibrium pattern formation in an antiparallel two-component dipolar Bose-Einstein condensate by varying the polarization angle and the trap aspect ratio. At finite tilt, the condensate supports stripe order. Quenching the angle to zero triggers a roton-assisted, mushroom-like corrugation that destroys translational order and drives the system into labyrinthine textures, whereas a slow linear ramp produces long-lived curved stripes that ultimately converge to labyrinths. Population imbalance strongly biases the evolution: the minority component preferentially fragments into a stable droplet array while the majority remains comparatively diffuse; once formed, the droplet crystal is robust under polarization hysteresis with largely reversible shape changes and unchanged lattice topology. The trap aspect ratio controls both the initial stripe number and the instability timescale, with tighter axial confinement accelerating corrugation and yielding denser labyrinths at late times. All behaviors arise within a quasi-two-dimensional mean-field regime where beyond-mean-field corrections are negligible; accordingly, the droplets reported here are not self-bound in free space. The observed textures (such as stripes, curved stripes, and labyrinths) mirror the taxonomy and instability pathways of nuclear "pasta" morphologies (rods and slabs) known from neutron-star and supernova matter, highlighting polarization angle, trap geometry, and population imbalance as practical, experimentally accessible controls for selecting and steering patterns in dipolar mixtures.
Using Crank–Nicolson method, we calculate ground state wave functions of two-component dipolar Bose–Einstein condensates (BECs) and show that, due to dipole–dipole interaction (DDI), the condensate mixture displays anisotropic phase separation. The effects of DDI, inter-component s-wave scattering, strength of trap potential and particle numbers on the density profiles are investigated. Three types of two-component profiles are present, first cigar, along z-axis and concentric torus, second pancake (or blood cell), in xy-plane, and two non-uniform ellipsoid, separated by the pancake and third two dumbbell shapes.
The effect of dipolar orientation with respect to the condensate plane on the mean-field dynamics of dipolar Bose-Einstein condensates in a pancake-shaped confinement is discussed. The stability of a quasi-two-dimensional condensate, with respect to the tilting angle, is found to be different from a two-dimensional layer of dipoles, indicating the relevance of the transverse extension while characterizing two-dimensional dipolar systems. An anisotropic excitation spectrum exhibiting a highly tunable, rotonlike minimum can arise entirely from the dipole-dipole interactions, by tilting the dipoles. At the magic angle and in the absence of contact interactions, the long-wavelength excitations are not phononlike and always unstable. The post-roton-instability dynamics, in contrast to phonon instability, in a uniform condensate, is featured by a transient, defect-free, stripe pattern, which eventually undergoes local collapses, and driving the condensate back into the stable regime can make them sustained for longer. Hopping between stripes has been observed before it melts into a uniform state in the presence of dissipation. Finally, we discuss a class of solutions, in which a quasi-two-dimensional condensate is self-trapped in one direction, as well as a regime of interaction parameters, including attractive short-range interactions, at which a two-dimensional anisotropic soliton can be stabilized, and we show that a chromium condensate with a relatively small number of atoms is well suited for this.
We explore the phase diagram of a finite-sized dysprosium dipolar Bose-Einstein condensate in a cylindrical harmonic trap. We monitor the final state after the scattering length is lowered from the repulsive BEC regime to the quantum droplet regime. Either an adiabatic transformation between a BEC and a quantum droplet is obtained or, above a critical trap aspect ratio ${\ensuremath{\lambda}}_{\mathrm{c}}=1.87(14)$, a modulational instability results in the formation of multiple droplets. This is in full agreement with the predicted structure of the phase diagram with a crossover region below ${\ensuremath{\lambda}}_{\mathrm{c}}$ and a multistable region above. Our results provide the missing piece connecting the previously explored regimes resulting in a single or multiple dipolar quantum droplets.
Motivated by a recent experiment [L. Chomaz et al., Nat. Phys. 14, 442 (2018)], we perform numerical simulations of a dipolar Bose-Einstein condensate (BEC) in a tubular, periodic confinement at T=0 within density functional theory, where the beyond-mean-field correction to the ground-state energy is included in the local density approximation. We study the excitation spectrum of the system by solving the corresponding Bogoliubov--de Gennes equations. The calculated spectrum shows a roton minimum, and the roton gap decreases by reducing the effective scattering length. As the roton gap disappears, the system spontaneously develops a periodic linear structure formed by denser clusters of atomic dipoles immersed in a dilute superfluid background. This structure shows the hallmarks of a supersolid system, i.e., (i) a finite nonclassical translational inertia along the tube axis and (ii) the appearance of two gapless modes, i.e., a phonon mode associated with density fluctuations and resulting from the translational discrete symmetry of the system, and a Nambu-Goldstone gapless mode corresponding to phase fluctuations, resulting from the spontaneous breaking of the gauge symmetry. A further decrease in the scattering length eventually leads to the formation of a periodic linear array of self-bound droplets.
We study the effect of intercondensate dipole-dipole interactions in a setup consisting of physically disconnected, single-species dipolar Bose-Einstein condensates. In particular, making use of the long-range and anisotropic nature of dipole-dipole interactions, we show that the density of a target dipolar Bose-Einstein condensate can be axially confined and engineered using a trapped control dipolar condensate. Increasing the number of control condensates leads to exotic ground-state structures, including periodic patterns in the target condensate. These periodic patterns display a structural transition between single- and double-peaked structures with coherence between the peaks controlled via the separation between the control condensates.