The effect of dipolar orientation with respect to the soliton plane on the physics of two-dimensional bright solitons in dipolar Bose-Einstein condensates is discussed. Previous studies on such a soliton involved dipoles either perpendicular or parallel to the condensate plane. The tilting angle constitutes an additional tuning parameter, which helps us to control the in-plane anisotropy of the soliton as well as provides access to previously disregarded regimes of interaction parameters for soliton stability. In addition, it can be used to drive the condensate into phonon instability without changing its interaction parameters or trap geometry. The phonon instability in a homogeneous two-dimensional condensate of tilted dipoles always features a transient stripe pattern, which eventually breaks into a metastable soliton gas. Finally, we demonstrate how a dipolar BEC in a shallow trap can eventually be turned into a self-trapped matter wave by an adiabatic approach involving the tuning of the tilting angle.
The effect of dipolar orientation with respect to the soliton plane on the physics of two-dimensional bright solitons in dipolar Bose-Einstein condensates is discussed. Previous studies on such a soliton involved dipoles either perpendicular or parallel to the condensate plane. The tilting angle constitutes an additional tuning parameter, which helps us to control the in-plane anisotropy of the soliton as well as provides access to previously disregarded regimes of interaction parameters for soliton stability. In addition, it can be used to drive the condensate into phonon instability without changing its interaction parameters or trap geometry. The phonon instability in a homogeneous two-dimensional condensate of tilted dipoles always features a transient stripe pattern, which eventually breaks into a metastable soliton gas. Finally, we demonstrate how a dipolar BEC in a shallow trap can eventually be turned into a self-trapped matter wave by an adiabatic approach involving the tuning of the tilting angle.
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 propose a realistic experimental setup for creating quasi-two-dimensional (2D) bright solitons in dipolar Bose-Einstein condensates (BECs), the existence of which was proposed by Tikhonenkov et al. [Phys. Rev. Lett. 100, 090406 (2008)]. A challenging feature of the expected solitons is their strong inherent anisotropy due to the necessary in-plane orientation of the local moments in the dipolar gas. This may be the first chance of making multidimensional matter-wave solitons, as well as solitons featuring the anistropy due to their intrinsic dynamics. Our analysis is based on the extended Gross-Pitaevskii equation, which includes three-body losses and noise in the scattering length, induced by fluctuations of currents inducing the necessary magnetic fields, which are factors crucial to the adequate description of experimental conditions. By means of systematic three-dimensional (3D) simulations, we find a ramping scenario for the change of the scattering length and trap frequencies which results in the creation of robust solitons, that readily withstand the concomitant excitation of the condensate.
We predict the existence of stable fundamental and vortical bright solitons in dipolar Bose-Einstein condensates (BECs) with repulsive dipole-dipole interactions (DDI). The condensate is trapped in the 2D plane with the help of the repulsive contact interactions whose local strength grows ∼r4 from the center to periphery, while dipoles are oriented perpendicular to the self-trapping plane. The confinement in the perpendicular direction is provided by the usual harmonic-oscillator potential. The objective is to extend the recently induced concept of the self-trapping of bright solitons and solitary vortices in the pseudopotential, which is induced by the repulsive local nonlinearity with the strength growing from the center to periphery, to the case when the trapping mechanism competes with the long-range repulsive DDI. Another objective is to extend the analysis for elliptic vortices and solitons in an anisotropic nonlinear pseudopotential. Using the variational approximation (VA) and numerical simulations, we construct families of self-trapped modes with vorticities ℓ=0 (fundamental solitons), ℓ=1, and ℓ=2. The fundamental solitons and vortices with ℓ=1 exist up to respective critical values of the eccentricity of the anisotropic pseudopotential, being stable in the entire existence regions. The vortices with ℓ=2 are stable solely in the isotropic model.
We study a two-dimensional spin-orbit-coupled dipolar Bose-Einstein condensate with repulsive contact interactions by both the variational method and the imaginary-time evolution of the Gross-Pitaevskii equation. The dipoles are completely polarized along one direction in the two-dimensional plane to provide an effective attractive dipole-dipole interaction. We find two types of solitons as the ground states arising from such attractive dipole-dipole interactions: a plane-wave soliton with a spatially varying phase and a stripe soliton with a spatially oscillating density for each component. Both types of solitons possess smaller size and higher anisotropy than the soliton without spin-orbit coupling. Finally, we discuss the properties of moving solitons, which are nontrivial because of the violation of Galilean invariance.
In the framework of the Gross-Pitaevskii equation, we study the formation and stability of effectively two-dimensional solitons in dipolar Bose-Einstein condensates (BECs), with dipole moments polarized at an arbitrary angle $\ensuremath{\theta}$ relative to the direction normal to the system's plane. Using numerical methods and the variational approximation, we demonstrate that unstable Townes solitons, created by the contact attractive interaction, may be completely stabilized (with an anisotropic shape) by the dipole-dipole interaction (DDI), in the interval ${\ensuremath{\theta}}^{\text{cr}}<\ensuremath{\theta}\ensuremath{\le}\ensuremath{\pi}/2$. The stability boundary ${\ensuremath{\theta}}^{\text{cr}}$ weakly depends on the relative strength of the DDI, remaining close to the magic angle ${\ensuremath{\theta}}_{m}=arccos(1/\sqrt{3})$. The results suggest that DDIs provide a generic mechanism for the creation of stable BEC solitons in higher dimensions.
The partially attractive character of the dipole-dipole interaction leads to phonon instability in dipolar Bose-Einstein condensates, which is followed by collapse in 3D geometries. We show that in 2D, the nature of the post-instability dynamics is fundamentally different, due to the stabilization of 2D solitons. As a result, a transient gas of attractive solitons is formed, and collapse may be avoided. In the presence of an harmonic trap, the post-instability dynamics is characterized by a transient pattern formation followed by the creation of stable 2D solitons. This dynamics should be observable in ongoing experiments, allowing for the creation of stable 2D solitons for the first time ever in quantum gases.