Intersite interactions play a crucial role in polar gases in optical lattices even in the absence of hopping. We show that due to these long-range interactions a destabilized stack of quasi-one-dimensional Bose-Einstein condensates develops a correlated modulational instability in the nonoverlapping sites. Interestingly, this density pattern may evolve spontaneously into soliton filaments or into a checkerboard soliton crystal, offering a unique possibility to observe such two-dimensional arrangements in ultracold gases. These self-assembled structures may be observed under realistic conditions within current experimental feasibilities.
Intersite interactions play a crucial role in polar gases in optical lattices even in the absence of hopping. We show that due to these long-range interactions a destabilized stack of quasi-one-dimensional Bose-Einstein condensates develops a correlated modulational instability in the nonoverlapping sites. Interestingly, this density pattern may evolve spontaneously into soliton filaments or into a checkerboard soliton crystal, offering a unique possibility to observe such two-dimensional arrangements in ultracold gases. These self-assembled structures may be observed under realistic conditions within current experimental feasibilities.
Ultracold dilute atomic gases are highly controllable systems whose properties are fundamentally determined by the interatomic interactions.In typical experiments on ultra cold gases particles interact dominantly via a short-range isotropic potential.However, during the last years a new generation of experiments is starting to explore systems, where an additional interaction, the long-range and anisotropic dipole-dipole interaction plays a significant or possibly dominant role.The effects induced by the anisotropy of the dipole-dipole interaction are crucially enhanced if the dipolar gas is confined in a deep optical lattice.In this thesis we study novel phenomena in such systems of dipolar gases in deep optical lattices.The nonlocal nonlinearity introduced by the dipole-dipole interaction plays a crucial role in the physics of dipolar Bose-Einstein condensates.In particular, it may distort significantly the stability of straight vortex lines.Remarkably, in the presence of a periodic potential along the vortex line, the spectrum of transverse modes shows a roton-like minimum, which eventually destabilizes the straight vortex when the BEC as a whole is still stable, opening the possibility for new scenarios for vortex line configurations in dipolar gases.We have analyzed this instability, and showed that it leads to a second-order-like phase transition from a straight vortex line into novel helical or snake-like configurations, depending on the dipole orientation.Strong 1D lattices usually lead to unconnected two-dimensional gases.The long-range character of the dipole-dipole interactions leads to a novel scenario where non-overlapping gases at different sites may interact significantly.We show that the excitations of non-overlapping condensates in 1D optical lattices acquire a band-like character, being collectively shared by different sites.In particular, the hybridization of the modes significantly enhances the rotonization of the excitations, and may induce roton-instability.We discuss the observability of this effect in on-going experiments.Fermionic polar molecules in deep 1D optical lattices may form selfassembled filaments when the electric dipoles are oriented along the lattice axis.These composites are bosons or fermions depending on the number of molecules per chain, leading to a peculiar and complex Bose-Fermi mixture, vi which we discuss in detail for the simplest case of a three-well potential.We show that the interplay between filament binding energy, transverse filament modes, and trimer Fermi energy leads to a rich variety of possible scenarios ranging from a degenerate Fermi gas of trimers to a binary mixture of two different types of bosonic dimers.We study the intriguing zero temperature and finite temperature physics of these composites for the particular case of an ideal filament gas loaded in 1D sites, and discuss possible methods to probe these chain mixtures.
We analyze the physics of bright solitons in 2D dipolar Bose-Einstein condensates. These solitons, which are not possible in short-range interacting gases, constitute the first realistic proposal of fully mobile stable 2D solitons in ultracold gases. In particular, we discuss the necessary conditions for the existence of stable 2D bright solitary waves by means of a 3D analysis of the lowest-lying excitations. We show that the anisotropy of the dipolar potential is crucial, since sufficiently large dipolar interactions can destabilize the 2D soliton. Additionally, we study the scattering of solitary waves, which, contrary to the contact-interacting case, is inelastic and could lead to fusion of the waves. Finally, the experimental possibilities for observability are discussed.
Dipolar interactions support the formation of intersite soliton molecules in a stack of quasi-one-dimensional (quasi-1D) traps. We show that the stability and properties of individual solitons and soliton molecules in such a geometry crucially depend on the interplay between contact and dipolar interactions. In particular, two different quasi-1D soliton regimes are possible: a one-dimensional (1D) soliton characterized by purely repulsive dipole-dipole interactions (DDI) and a three-dimensional (3D) soliton for which a sufficiently large dipole moment renders the DDI attractive. Furthermore, we find that in contrast to the dimers of polar molecules the soliton dimers exhibit a nontrivial behavior of the elementary excitations that stems from the competition between onsite and intersite DDI. Finally, we prove the existence of soliton trimers in a regime where molecular trimers do not occur. We demonstrate that the soliton molecules that we report are well feasible under realistic experimental conditions.
Straight dark solitons in two-dimensional (2D) quantum fluids usually decay by transverse modulational instability, with no intrinsic suppression in contact-interacting Bose--Einstein condensates (BECs). We theoretically show that anisotropic long-range interactions in a quasi-2D dipolar BEC stabilize an embedded straight soliton, with spontaneous stripe order providing stronger pinning. The excitation spectra show that the lowest transverse solitonic branch remains gapped, while stripe-supersolid density modulation further hardens this branch and increases the soliton bending stiffness, penalizing transverse deformation. Accessible in current 166Er and 164Dy platforms, these results establish interaction-driven protection for straight dark solitons in structured quantum fluids.
We study Faraday patterns in quasi-one-dimensional dipolar Bose-Einstein condensates with parametrically driven dipolar interactions. We show that in the presence of a roton minimum in the excitation spectrum, the emergent Faraday waves differ substantially in two- and one-dimensional geometries, providing a clear example of the key role of confinement dimensionality in dipolar gases. Moreover, Faraday patterns constitute an excellent tool to study nonlocal effects in polar gases, as we illustrate with two parallel quasi-one-dimensional dipolar condensates. Nonlocal interactions between the condensates give rise to an excitation spectrum characterized by symmetric and antisymmetric modes, even in the absence of hopping. We show that this feature, absent in nondipolar gases, results in a critical driving frequency at which a marked transition occurs between correlated and anticorrelated Faraday patterns in the two condensates. Interestingly, at this critical frequency, the emergent Faraday pattern stems from a spontaneous symmetry-breaking mechanism.
We show that in contrast with contact interacting gases, an optical lattice changes drastically the stability properties of a dipolar condensate, inducing a crossover from dipolar destabilization to dipolar stabilization for increasing lattice depths. Performing stability measurements on a 52Cr Bose-Einstein condensate in an interaction-dominated regime, repulsive dipolar interaction balances negative scattering lengths down to $\ensuremath{-}17$ Bohr radii. Our findings are in excellent agreement with mean-field calculations, revealing the important destabilizing role played by intersite dipolar interactions in deep lattices.