Roton excitations constitute a key feature of dipolar gases, connecting these gases with superfluid helium. We show that the density dependence of the roton minimum results in a spatial roton confinement, particularly relevant in pancake dipolar condensates with large aspect ratios. We show that roton confinement plays a crucial role in the dynamics after roton instability, and that arresting the instability may create a trapped roton gas revealed by confined density modulations. We discuss the local susceptibility against density perturbations, which we illustrate for the case of vortices. Roton confinement is expected to play a key role in experiments.

Dipolar interactions support the formation of inter-site soliton molecules in a stack of 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 1D soliton characterized by purely repulsive DDI and a 3D soliton for which a sufficiently large dipole moment renders the DDI attractive. Furthermore, we find that contrary to the case of dimers of polar molecules, the soliton dimers exhibit a nontrivial behavior of the elementary excitations that stems from the competition between on-site and inter-site 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.

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 help 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 2D 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 tilting angle.

We study the scattering of a weak and far-detuned light from a system of ultracold bosons in 1D and 3D optical lattices. We show the connection between angular distributions of the scattered light and statistical properties of a Bose gas in a periodic potential. The angular patterns are determined by the Fourier transform of the second-order correlation function, and thus they can be used to retrieve information on particle number fluctuations and correlations. We consider superfluid and Mott insulator phases of the Bose gas in a lattice, and we analyze in detail how the scattering depends on the system dimensionality, temperature and atom-atom interactions.

In our recent paper we studied the effective roton confinement induced by an inhomogeneous density profile in a dipolar condensate. We were interested in the characterization of the localized roton wave functions and in the effects of roton confinement in dipolar BECs. In that paper, we wrote an incorrect expression for the roton eigenenergies, which we now correct in this Erratum. We note, however, that the expression of the roton wave functions, which constituted the other main result of our paper, is not affected by this correction.In the following we employ, unless otherwise stated, the same notation as in our paper. Around the rotonlike minimum, the local roton spectrum fulfillsEquation (1) corrects Eq. (A9) of our paper. Associated with the effective harmonic term, we define, as in our paper, the roton localization length l * = √h /m * ω * . Using the approximate expression (q,ρ) 22 , from which l * = 2 1/4 (R/q r ) 1/2 , as in our paper. Note the absolute value appearing in the new definition of m * , unlike in our paper.We then proceed as discussed in Appendix A of our paper, the only difference appearing in Eq. (A9), whose correct form isThe wave functionsF (q) are those of the effective harmonic oscillator Hamiltonian, as discussed in Sec. V of our paper. These functions only depend on the effective oscillator length l * and therefore our conclusions about the roton wave functions are unaffected by this correction. We now evaluate the roton spectrum as discussed in Sec. V of our paper. The correct roton spectrum fulfills n,s = 2 r + 2| r |E n,swhere E n,s are the eigenenergies of the effective harmonic oscillator Hamiltonian E n,s =hω * s 2 − 1 4 2(q r l * ) 2 + n + 1 2 , which are the same as in our paper [see Eq.(3) of our paper]. Note that the expression n,s r + E n,s of our paper is only valid if 2 r is much larger than the second term on the right-hand side of Eq. (3). This is not generally the case, in particular, close to instability. Note as well that the validity of the local spectrum, and hence of the harmonic approximation of Eq. (1) and of the general form of Eq. (3), is more general than the validity of the particular expressions for r ,hω * , and l * obtained from the approximation (q,ρ) 2 h [q,μ l (ρ)] 2 . In a very recent paper, Bisset et al. [1] have studied the roton spectrum by solving numerically the corresponding Bogoliubov-de Gennes equations. The dependence of the eigenenergies n,s as a function of the quantum numbers n and s is in very good agreement with that predicted by Eq. (3) by means of the local spectrum picture.As a final remark concerning Eq.(3) we recall that 2 r < 0 marks the onset of instability for the classical problem. However, the quantization induced by the effective roton confinement results in a stabilization of the system, since the gas only becomes unstable if 2 0,0 < 0, i.e., if 2 r < −2| r |hω * 1 2 − 1 8(q r l * ) 2 < 0.(4)We thank B. Blakie for enlightening discussions.[1] R.