We show that particular configurations of intense off-resonant laser beams can give rise to an attractive $1/r$ interatomic potential between atoms located well within the laser wavelength. Such a “gravitational-like” interaction is shown to give stable Bose-Einstein condensates that are self-bound (without an additional trap) with unique scaling properties and measurably distinct signatures.

We show that the dipole-dipole interatomic forces induced by an off-resonant running laser beam can lead to a self-bound pencil-shaped Bose condensate, even if the laser beam is a plane wave. For an appropriate laser intensity the ground state has a quasi-one-dimensional density modulation—a Bose-Einstein “supersolid.”

We study the family of static and moving dark solitons in quasi-one-dimensional dipolar Bose-Einstein condensates, exploring their modified form and interactions. The density dip of the soliton acts as a giant antidipole which adds a nonlocal contribution to the conventional local soliton-soliton interaction. We map out the stability diagram as a function of the strength and polarization direction of the atomic dipoles, identifying both roton and phonon instabilities. Away from these instabilities, the solitons collide elastically. Varying the polarization direction relative to the condensate axis enables tuning of this nonlocal interaction between repulsive and attractive; the latter case supports unusual dark-soliton bound states. Remarkably, these bound states are themselves shown to behave like solitons, emerging unscathed from collisions with each other.

We study the stability, form, and interaction of single and multiple dark solitons in quasi-one-dimensional dipolar Bose-Einstein condensates. The solitons are found numerically as stationary solutions in the moving frame of a nonlocal Gross Pitaevskii equation and characterized as a function of the key experimental parameters, namely the ratio of the dipolar atomic interactions to the van der Waals interactions, the polarization angle, and the condensate width. The solutions and their integrals of motion are strongly affected by the phonon and roton instabilities of the system. Dipolar matter-wave dark solitons propagate without dispersion and collide elastically away from these instabilities, with the dipolar interactions contributing an additional repulsion or attraction to the soliton-soliton interaction. However, close to the instabilities, the collisions are weakly dissipative.

We show that the light conelike structures that form in spin chains after a quench are quantum caustics. Their natural description is in terms of catastrophe theory and this implies (1) a hierarchy of light cone structures corresponding to the different catastrophes, (2) dressing by characteristic wave functions that obey scaling laws determined by the Arnol'd and Berry indices, and (3) a network of vortex-antivortex pairs in space-time inside the cone. We illustrate the theory by giving explicit calculations for the transverse field Ising model and the XY model, finding fold catastrophes dressed by the Airy functions and cusp catastrophes dressed by the Pearcey functions; multisite correlation functions are described by higher catastrophes such as the hyperbolic umbilic. Furthermore, we find that the vortex pairs created inside the cone are sensitive to phase transitions in these spin models with their rate of production being determined by the dynamical critical exponent. More broadly, this work illustrates how catastrophe theory can be applied to singularities in quantum fields.