We have solved numerically the ground states of a Bose-Einstein condensate in the presence of dipolar interparticle forces using a semiclassical approach. Our motivation is to model, in particular, the spontaneous spin textures emerging in quantum gases with large dipole moments, such as 52Cr or Dy condensates, or ultracold gases consisting of polar molecules. For a pancake-shaped harmonic (optical) potential, we present the ground state phase diagram spanned by the strength of the nonlinear coupling and dipolar interactions. In an elongated harmonic potential, we observe a novel helical spin texture. The textures calculated according to the semiclassical model in the absence of external polarizing fields are predominantly analogous to previously reported results for a ferromagnetic F = 1 spinor Bose-Einstein condensate, suggesting that the spin textures arising from the dipolar forces are largely independent of the value of the quantum number F or the origin of the dipolar interactions.
We study the spontaneous spin textures induced by magnetic dipole-dipole interaction in ferromagnetic spinor condensates under various trap geometries. At the mean-field level, we show the system is dual to a Dirac string gas with a negative string tension in which the ground state spin texture can be easily determined. We find that three-dimensional condensates prefer a meron-like vortex texture, quasi one-dimensional condensates prefer the axially polarized flare texture, while condensates in quasi two dimensions exhibit either a meron texture or an in-plane polarized texture.
We describe a wavefunction engineering approach to the formation of textures in a two-component nonrotated Bose-Einstein condensate. By controlling the phases of wavepackets that combine in a three-wave interference process, a ballistically-expanding regular lattice-texture is generated, in which the phases determine the component textures. A particular example is presented of a lattice-texture composed of half-quantum vortices and spin-2 textures. We demonstrate the lattice formation with numerical simulations of a viable experiment, identifying the textures and relating their locations to a …
We study periodic crystalline spin textures in spinor condensates with dipolar interactions via a systematic symmetry analysis of the low-energy effective theory. By considering symmetry operations which combine real and spin space operations, we classify symmetry groups consistent with non-trivial experimental and theoretical constraints. Minimizing the energy within each symmetry class allows us to explore possible ground states.
We numerically study elongated helical spin textures in ferromagnetic spin-1 Bose-Einstein condensates subject to dipolar interparticle forces. Stationary states of the Gross-Pitaevskii equation are solved and analyzed for various values of the helical wave vector and dipolar coupling strength. We find two helical spin textures which differ by the nature of their topological defects. The spin structure hosting a pair of Mermin-Ho vortices with opposite mass flows and aligned spin currents is stabilized for a nonzero value of the helical wave vector.
We study the textures of F=2 spinor Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) induced by a synthetic non-Abelian gauge field. On the basis of the analysis of the SOC energy and the numerical calculation of the Gross-Pitaevskii equation, we demonstrate that the textures originate from the helical modulation of the order parameter (OP) due to the SOC. In particular, the cyclic OP consists of two-dimensional lattice textures, such as the hexagonal lattice and the 1/3-vortex lattice, commonly understandable as the two-dimensional network of the helical modulations.
For a spin-carrying particle moving in a spatially varying magnetic field, effective electromagnetic forces can arise due to the geometric phase associated with adiabatic spin rotation of the particle. We report the observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a skyrmion spin texture. Under translational oscillations of the spin texture, the condensate resonantly develops a circular motion in a harmonic trap, demonstrating the existence of an effective Lorentz force. When the condensate circulates, quantized vortices are nucleated in the boundary region of t…
We investigate the metastability of a ferromagnetic spin-1 Bose-Einstein condensate confined in a quasi-one-dimensional rotating ring trap by solving the spin-1 Gross-Pitaevskii equation. We find analytical solutions that exhibit spin textures. By performing linear stability analysis, it is shown that the solutions can become metastable states. We also find that the number of Nambu-Goldstone modes changes at a certain rotation velocity without changing the continuous symmetry of the order parameter.
We report the spin texture formation resulting from the magnetic dipole-dipole interaction in a spin-2 $^{87}$Rb Bose-Einstein condensate. The spinor condensate is prepared in the transversely polarized spin state and the time evolution is observed under a magnetic field of 90 mG with a gradient of 3 mG/cm using Stern-Gerlach imaging. The experimental results are compared with numerical simulations of the Gross-Pitaevskii equation, which reveals that the observed spatial modulation of the longitudinal magnetization is due to the spin precession in an effective magnetic field produced by the di…
In the present work the case of a chromium Bose-Einstein condensate is considered. The model includes not only the presence of the so-called contact interaction but also a long range and anisotropic dipole-dipole interaction has been included. Some thermodynamical properties are analyzed. For instance, the size of the condensate, chemical potential, speed of sound, number of particles, etc., are deduced. It will be shown that this dipole-dipole interaction implies the emergence of anisotropy, for example, in the speed of sound. The possible use of this anisotropy as a tool for the analyze of d…
The dynamics of a vortex dipole in a quasi-two dimensional two-component Bose-Einstein condensate are investigated. A vortex dipole is shown to penetrate the interface between the two components when the incident velocity is sufficiently large. A vortex dipole can also disappear or disintegrate at the interface depending on its velocity and the interaction parameters.
Dynamics of a vortex dipole in a spin-1 Bose-Einstein condensate in which magnetic phases are spatially distributed is investigated. When a vortex dipole travels from the ferromagnetic phase to the polar phase, or vice versa, it penetrates the phase boundary and transforms into one of the various spin vortex dipoles, such as a leapfrogging ferromagnetic-core vortex dipole and a half-quantum vortex dipole. Topological connections of spin wave functions across the phase boundary are discussed.
We propose methods to generate and manipulate vortex dipoles in a Bose-Einstein condensate using Gaussian beams of red or blue-detuned laser. Velocity-controlled vortex dipoles are shown to be created and launched by a red-detuned beam and by two blue-detuned beams. Critical velocities for the vortex nucleation are investigated. The launched vortex dipoles can be trapped, curved, accelerated, and decelerated using Gaussian beams. Collisions between vortex dipoles are demonstrated.
Based on the numerical solutions of the coupled Gross-Pitaevskii equations, the spin-textures of a Bose-Einstein condensate with two kinds of spin-1 atoms have been studied. Besides, the probability densities of an atom in spin component $μ$ and of two correlated atoms one in $μ$ and one in $ν$ have been calculated. By an analysis of the densities, four types of texture have been found. (i) Both species are in polar phase. (ii) Both species are in ferromagnetic (f) phase with all the spins lying along a direction. (iii) Both species are in f phase but the spins of different species are lying a…
We study the propagation of electromagnetic waves in the Bose-Einstein condensate of atoms with both intrinsic dipole moments and those induced by the electric field. The modified Gross--Pitaevskii equation is used, which takes into account relaxation and interaction with the electromagnetic field. Two cases are considered: 1) when the dispersion curves of the electromagnetic wave and of the condensate excitations do not intercross and 2) when the condensate excitations' spectrum has a gap and the two dispersion curves do intercross. In the second case the two branches hybridize. It is shown t…
Motivated by the recent experiment [H. Kadau \textit{et al.}, arXiv:1508.05007 (2015)], we study roton instability and droplet formation in a Bose-Einstein condensate of $^{164}$Dy atoms with strong magnetic dipole-dipole interaction. We numerically solve the cubic-quintic Gross-Pitaevskii equation with dipole-dipole interaction, and show that the three-body interaction plays a significant role in the formation of droplet patterns. We numerically demonstrate the formation of droplet patterns and crystalline structures, decay of droplets, and hysteresis behavior, which are in good agreement wit…
We investigate vortex shedding from a moving penetrable obstacle in a highly oblate Bose-Einstein condensate. The penetrable obstacle is formed by a repulsive Gaussian laser beam that has the potential barrier height lower than the chemical potential of the condensate. The moving obstacle periodically generates vortex dipoles and the vortex shedding frequency $f_v$ linearly increases with the obstacle velocity $v$ as $f_v=a(v-v_c)$, where $v_c$ is a critical velocity. Based on periodic shedding behavior, we demonstrate deterministic generation of a single vortex dipole by applying a short line…
Vortex dipoles are generated when an obstacle moves through a superfluid. In case of phase-separated binary condensates, with appropriate interaction parameters in pan-cake shaped traps, we show that coreless vortex dipoles are created when a Gaussian obstacle beam traverses across them above a critical speed. As the obstacle passes through the inner component, it carries along a bubble of the outer component. Using Thomas-Fermi approximation, we show that phase-separated binary condensates can either support vortices with empty or filled cores. For time dependent obstacle potentials, ramped d…
Recently, Freilich et al. [Science 329, 1182 (2010)] experimentally discovered stationary states of vortex dipoles, pairs of vortices of opposite circulation, in dilute Bose-Einstein condensates. To explain their observations, we perform simulations based on the Gross-Pitaevskii equation and obtain excellent quantitative agreement on the size of the stationary dipole. We also investigate how their imaging method, in which atoms are repeatedly extracted from a single condensate, affects the vortex dynamics. We find that it mainly induces isotropic size oscillations of the condensate without oth…
We theoretically and numerically investigate the generation of fractional-charge vortex dipoles in spinor condensates with non-zero magnetization. We find that in the antiferromagnetic phase of spin-1 and spin-2 and the cyclic phase of spin-2 condensate with non-zero magnetization coupling of the density (phonon) and a spin-excitation mode results in two critical speeds for vortex-antivortex pair creation in the condensate. As a result, a Gaussian obstacle potential moving across the antiferromagnetic spin-1 or spin-2 and cyclic spin-2 spinor condensates with non-zero magnetization can lead to…
We consider a spin-1 Bose-Einstein condensate with Rashba spin-orbit coupling and dipole-dipole interaction confined in a cigar-shaped trap. Due to the combined effects of spin-orbit coupling, dipole-dipole interaction, and trap geometry, the system exhibits a rich variety of ground-state spin structures, including twisted spin vortices. The ground-state phase diagram is determined with respect to the strengths of the spin-orbit coupling and dipole-dipole interaction.
We study the motion of the Gaussian obstacle potential created by blue detuned laser beam through a phase-separated binary condensate in pancake-shaped traps. For the velocity of the obstacle above a critical velocity, we observe the generation of vortex dipoles in the outer component which can penetrate the inner component. This is equivalent to finite, although small, transport of outer component across the inner component. In the inner component, the same method can lead to the formation of coreless vortex dipoles.
We observe cavity mediated spin-dependent interactions in an off-resonantly driven multi-level atomic Bose-Einstein condensate that is strongly coupled to an optical cavity. Applying a driving field with adjustable polarization, we identify the roles of the scalar and the vectorial components of the atomic polarizability tensor for single and multi-component condensates. Beyond a critical strength of the vectorial coupling, we observe a spin texture in a condensate of two internal states, providing perspectives for global dynamic gauge fields and self-consistently spin-orbit coupled gases.
We report experimental observations and numerical simulations of the formation, dynamics, and lifetimes of single and multiply charged quantized vortex dipoles in highly oblate dilute-gas Bose-Einstein condensates (BECs). We nucleate pairs of vortices of opposite charge (vortex dipoles) by forcing superfluid flow around a repulsive gaussian obstacle within the BEC. By controlling the flow velocity we determine the critical velocity for the nucleation of a single vortex dipole, with excellent agreement between experimental and numerical results. We present measurements of vortex dipole dynamics…
We analyze the dynamics of Josephson vortex states in two-component Bose-Einstein condensates with Rashba-Dresselhaus spin-orbit coupling by using the Gross-Pitaevskii equation. In 1D, both in homogeneous and harmonically trapped systems, we report on stationary states containing doubly charged, static Josephson vortices. In multidimensional systems, we find stable Josephson vortices in a regime of parameters typical of current experiments with $^{87}$Rb atoms. In addition, we discuss the instability regime of Josephson vortices in disk-shaped condensates, where the snake instability operates …
We consider a dipolar Bose-Einstein condensate confined in an annular potential, with all the dipoles being aligned along some arbitrary direction. In addition to the dipole-dipole interaction, we also assume a zero-range hard-core potential. We investigate the stability of the system against collapse, as well as the stability of persistent currents as a function of the orientation of the dipoles and of the strength of the hard-core interaction.
Collapse in dipolar Bose-Einstein condensates may be arrested by quantum fluctuations. Due to the anisotropy of the dipole-dipole interactions, the dipole-driven collapse induced by soft excitations is compensated by the repulsive Lee-Huang-Yang contribution resulting from quantum fluctuations of hard excitations, in a similar mechanism as that recently proposed for Bose-Bose mixtures. The arrested collapse results in self-bound filament-like droplets, providing an explanation to recent dysprosium experiments. Arrested instability and droplet formation are novel general features directly linke…
We present the creation and time evolution of two-dimensional Skyrmion excitations in an antiferromagnetic spinor Bose-Einstein condensate. Using a spin rotation method, the Skyrmion spin textures were imprinted on a sodium condensate in a polar phase, where the two-dimensional Skyrmion is topologically protected. The Skyrmion was observed to be stable on a short time scale of a few tens of ms but to have dynamical instability to deform its shape and eventually decay to a uniform spin texture. The deformed spin textures reveal that the decay dynamics involves breaking the polar phase inside th…
We demonstrate a production of large-area $^{87}$Rb Bose-Einstein condensates (BECs) using a non-Gaussian optical dipole trap (ODT). The ODT is formed by focusing a symmetrically truncated Gaussian laser beam and it is shown that the beam clipping causes the trap geometry elongated and flattened along the beam axis direction. In the clipped-Gaussian ODT, an elongated, highly oblate BEC of $^{87}$Rb is generated with length and width of approximately $470~μ\textrm{m}$ and $130~μ\textrm{m}$, respectively, where the condensate healing length is estimated to be $ξ\approx 0.25~μ\textrm{m}$ at the t…
We used the Gross--Pitaevskii equations to investigate ferromagnetic resonance in spin-1 Bose--Einstein condensates with a magnetic dipole-dipole interaction. By introducing the dipole interaction, we obtained equations similar to the Kittel equations used to represent ferromagnetic resonance in condensed matter physics. These equations indicated that the ferromagnetic resonance originated from dipolar interaction, and that the resonance frequency depended upon the shape of the condensate. Furthermore, spin currents driven by spin diffusions are characteristic of this system.
We study the dynamics of vortex dipoles in erbium ($^{168}$Er) and dysprosium ($^{164}$Dy) dipolar Bose-Einstein condensates (BECs) by applying an oscillating blue-detuned laser (Gaussian obstacle). For observing vortex dipoles, we solve a nonlocal Gross-Pitaevskii (GP) equation in quasi two-dimensions in real-time. We calculate the critical velocity for the nucleation of vortex dipoles in dipolar BECs with respect to dipolar interaction strengths. We also show the dynamics of the group of vortex dipoles and rarefaction pulses in dipolar BECs. In the dipolar BECs with Gaussian obstacle, we obs…
The s-wave interaction is usually the dominant form of interactions in atomic Bose-Einstein condensates (BECs). Recently, Feshbach resonances have been employed to reduce the strength of the s-wave interaction in many atomic speicies. This opens the possibilities to study magnetic dipole-dipole interactions (MDDI) in BECs, where the novel physics resulting from long-range and anisotropic dipolar interactions can be explored. Using a variational method, we study the effect of MDDI on the statics and dynamics of atomic BECs with tunable s-wave interactions. We benchmark our calculation against p…
Polarization textures of light may reflect fundamental phenomena such as topological defects, and can be utilized in engineering light beams. Three main routes are applied during their creation: spontaneous appearance in phase transitions, steering by an excitation beam, or structural engineering of the medium. We present an approach that uses all three in a platform offering advantages that are not simultaneously provided in any previous system: advanced structural engineering, strong-coupling condensate with effective photonic interactions, as well as room temperature and sub-picosecond oper…
Several new features arise in the ground-state phase diagram of a spin-1 condensate trapped in an optical trap when the magnetic dipole interaction between the atoms is taken into account along with confinement and spin precession. The boundaries between the regions of ferromagnetic and polar phases move as the dipole strength is varied and the ferromagnetic phases can be modulated. The magnetization of the ferromagnetic phase perpendicular to the field becomes modulated as a helix winding around the magnetic field direction, with a wavelength inversely proportional to the dipole strength. Thi…
We consider the ground-state properties of Rashba spin-orbit-coupled pseudo-spin-1/2 Bose-Einstein condensates (BECs) in a rotating two-dimensional (2D) toroidal trap. In the absence of spin-orbit coupling (SOC), the increasing rotation frequency enhances the creation of giant vortices for the initially miscible BECs, while it can lead to the formation of semiring density patterns with irregular hidden vortex structures for the initially immiscible BECs. Without rotation, strong 2D isotropic SOC yields a heliciform-stripe phase for the initially immiscible BECs. Combined effects of rotation, S…
We examine the dynamics of a vortex dipole in the Bose-Einstein condensates (BECs) of trapped dilute atomic gases at zero temperature in the presence of a Gaussian barrier potential. The density-anisotropy induced by the barrier enhances the acoustic radiation from the vortex dipole. This is due to the deviation of the condensate density from the equipotential curves and variation in the curvature of the vortex dipole trajectory. Due to the acoustic radiation, the vortex dipole dissipates energy and spirals towards the edge of the condensate. As a result, we observe an increase in the vortex-a…
The knot of spin texture is studied within the two-component Bose-Einstein condensates which are described by the nonlinear Gross-Pitaevskii equations. We start from the non-interacting equations including an axisymmetric harmonic trap to obtain an exact solution, which exhibits a non-trivial topological structure. The spin-texture is a knot with an integral Hopf invariant. The stability of the knot is verified by numerically evolving the nonlinear Gross-Pitaevskii equations along imaginary time.
We consider a $^{168}$Er-$^{164}$Dy dipolar mixture, trapped by a cigar shaped harmonic potential. We derive the quasi-1D inter-species effective potential exhibiting the tilting angles and show that it is a quite natural generalization of the situation of a single dipolar gas. By solving the coupled Gross-Pitaevskii equations, we observe a transition from miscible to immiscible mixture as the orientations of the magnetic moments are varied. The atom numbers are also shown to lead to noticeable effects on the mixture.
We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ordinary differential equations describing the vortices' motion, which is in turn a reduced model of the Gross-Pitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. We uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leadin…
We have performed a quantum mechanic calculation (including solving the coupled Gross-Pitaevskii equations to obtain the spatial wave functions, and diagonalizing the spin-dependent Hamiltonian in the spin-space to obtain the total spin state) together with an analytical analysis based on a classical model. Then, according to the relative orientations of the spins $S_A$, $S_B$ and $S_C$ of the three species, the spin-textures of the ground state can be classified into two types. In Type-I the three spins are either parallel or anti-parallel to each others, while in Type-II they point to differ…
We study the merging and splitting of quasi-two-dimensional Bose-Einstein condensates with strong dipolar interactions. We observe that if the dipoles have a non-zero component in the plane of the condensate, the dynamics of merging or splitting along two orthogonal directions, parallel and perpendicular to the projection of dipoles on the plane of the condensate are different. The anisotropic merging and splitting of the condensate is a manifestation of the anisotropy of the roton-like mode in the dipolar system. The difference in dynamics disappears if the dipoles are oriented at right angle…
Recent experimental studies of $^{87}$Rb spinor Bose Einstein condensates have shown the existence of a magnetic field driven quantum phase transition accompanied by structure formation on the ferromagnetic side of the transition. In this theoretical study we examine the dynamics of the unstable modes following the transition taking into account the effects of the trap, non-linearities, finite temperature and dipole-dipole interactions. Starting from an initial state which includes quantum fluctuations, we attempt to make quantitative comparisons with recent experimental data on this system an…
By numerical simulation and variational analysis of the Gross-Pitaevskii equation we study the localization, with an exponential tail, of a dipolar Bose-Einstein condensate (DBEC) of $^{52}$Cr atoms in a three-dimensional bichromatic optical-lattice (OL) generated by two monochromatic OL of incommensurate wavelengths along three orthogonal directions. For a fixed dipole-dipole interaction, a localized state of a small number of atoms ($\sim 1000$) could be obtained when the short-range interaction is not too attractive or not too repulsive. A phase diagram showing the region of stability of a …
We report on the measurement of the spin-dipole (SD) polarizability and of the frequency of the SD oscillation of a two-component Bose-Einstein condensate of sodium atoms occupying the $|3^2S_{1/2}, F=1, m_F=\pm1\rangle$ hyperfine states. This binary spin-mixture presents the important properties of being, at the same time, fully miscible and rid of the limit set by buoyancy. It is also characterized by a huge enhancement of the SD polarizability and by the consequent softening of the frequency of the SD oscillation, due to the vicinity to the transition to the immiscible phase. The experiment…
We investigate half-vortex sheets and domain-wall trains of rotating two-component Bose-Einstein condensates in spin-dependent optical lattices. The two-component condensates undergo phase separation in the form of stripes arranged alternatively. The vortices of one component are aligned in lines in the low-density regions and filled with the other component, which results in a stable vortex configuration, straight half-vortex sheets. A train of novel domain walls, with spatially periodic "eyebrow-like" spin textures embedded on them, are formed at the interfaces of the two components. We reve…
We propose a two-dimensional model for a multilayer stack of dipolar Bose-Einstein condensates formed by a strong optical lattice. We derive effective intra- and interlayer dipole-dipole interaction potentials and provide simple analytical approximations for a given number of lattice sites at arbitrary polarization. We find that the interlayer dipole-dipole interaction changes the transverse aspect ratio of the ground state in the central layers depending on its polarization and the number of lattice sites. The changing aspect ratio should be observable in time of flight images. Furthermore, w…
We consider quasi-one-dimensional dipolar spinor Bose-Einstein condensates in the homogeneous-local-spin-orientation approximation, that is with unidirectional local magnetization. By analytically calculating the exact effective dipole-dipole interaction, we derive a Landau-Lifshitz-Gilbert equation for the dissipative condensate magnetization dynamics, and show how it leads to the Stoner-Wohlfarth model of a uni-axial ferro-magnetic particle, where the latter model determines the stable magnetization patterns and hysteresis curves for switching between them. For an external magnetic field poi…
We show how a singly quantized vortex can exhibit energetically stable defect cores with different symmetries in an atomic spin-1 polar Bose-Einstein condensate, and how a stable topologically nontrivial Skyrmion texture of lower dimensionality can be confined inside the core. The core isotropy and the stability of the confined texture are sensitive to Zeeman level shifts. The observed structures have analogies, respectively, in pressure-dependent symmetries of superfluid liquid He-3 vortices and in the models of superconducting cosmic strings.
We study the static and the dynamic response of coherently coupled two component Bose-Einstein condensates due to a spin-dipole perturbation. The static dipole susceptibility is determined and it is shown to be a key quantity to identify the second order ferromagnetic transition occurring at large inter-species interaction. The dynamics, which is obtained by quenching the spin-dipole perturbation, is very much affected by the system being paramagnetic or ferromagnetic and by the correlation between the motional and the internal degrees of freedom. In the paramagnetic phase the gas exhibits wel…
Dynamics of skyrmionic spin texture in the spin-1 Bose-Einstein condensate is examined by analytical and numerical means. We show the skyrmion (coreless vortex) to be inherently unstable in the sense that the state initially prepared purely within the antiferromagnetic (ferromagnetic) order parameter manifold inevitably evolves into a mixture of both. The vorticity-dependent drift in the presence of the trapping potential also contributes to the disintegration of the initial spin texture manifold. We argue that the notion of a skyrmion as a topologically protected entity becomes ill defined du…
We report on fundamental properties of superfluids with d-wave pairing symmetry. We consider neutral atomic Fermi gases in a harmonic trap, the pairing being produced by a Feshbach resonance via a d-wave interaction channel. A Ginzburg-Landau (GL) functional is constructed which is symmetry constrained for five component order parameters (OP). We find OP textures in the cyclic phase and stability conditions for a non-Abelian fractional 1/3-vortex under rotation. It is proposed how to create the intriguing 1/3-vortex experimentally in atomic gases via optical means.
We analytically and numerically investigate the ground state of the spin-orbit coupled spin-1 Bose-Einstein condensates in an external parabolic potential. When the spin-orbit coupling strength $κ$ is comparable with that of the trapping potential, the density distribution centers of different components of the spinor condensate deviate evidently from the trap center in the plane wave and stripe phases. When $κ\gg1$, the magnitude of this deviation decreases as $κ$ is getting larger and larger. Correspondingly, periphery half-skyrmions textures arise. This deviation can be reflected by the non…
We have numerically solved the low-energy excitation spectra of ferromagnetic Bose-Einstein condensates subject to dipolar interparticle interactions. The system is assumed to be harmonically confined by purely optical means, thereby maintaining the spin degree of freedom of the condensate order parameter. Using a zero-temperature spin-1 model, we solve the Bogoliubov excitations for different spin textures, including a spin-vortex state in the absence of external magnetic fields and a rapidly rotating polarized spin texture in a finite homogeneous field. In particular, we consider the effect …
