It has been shown that dipolar Bose-Einstein condensates that are tightly trapped along the polarization direction can feature a rich phase diagram. In this paper we show that finite temperature can assist in accessing parts of the phase diagram that otherwise appear hard to realize due to excessively large densities and number of atoms being required. These include honeycomb and stripe phases both unconfined and with a finite extent. To map out a phase-diagram, we employ both variational analysis and full numerical calculations solving the finite-temperature extended Gross-Pitaevskii equation (TeGPE). Furthermore, we exhibit real-time evolution simulations leading to such states. We account for the effect of thermal fluctuations by means of Bogoliubov theory, employing the local density approximation. We find that finite temperatures can lead to a significant decrease in the necessary particle number and density that might ultimately pave a route for future experimental realizations.

The compensation of chromatic dispersion opened new avenues and extended the level of control upon pattern formation in the temporal domain. In this paper, we propose the use of a nearly degenerate laser cavity as a general framework allowing for the exploration of higher contributions to diffraction in the spatial domain. Our approach leverages the interplay between optical aberrations and the proximity to the self-imaging condition, which allows us to cancel or reverse paraxial diffraction. As an example, we show how spherical aberrations materialize into a transverse bi-Laplacian operator and, thereby, explain the stabilization of temporal solitons traveling off-axis in an unstable mode-locked broad-area surface-emitting laser. We disclose an analogy between these regimes and the dynamics of a quantum particle in a double-well potential.

We analyze the finite-temperature phase diagram of a dipolar Bose-Einstein condensate confined in a tubular geometry. The effect of thermal fluctuations is accounted for by means of Bogoliubov theory employing the local density approximation. In the considered geometry, the superfluid-supersolid phase transition can be of first and second order. We discuss how the corresponding transition point is affected by the finite temperature of the system.

In this paper we study metastable states in single- and two-component dipolar Bose-Einstein condensates. We show that this system supports a rich variety of states that are remarkably stable despite not being ground states. In a parameter region where striped phases are ground states, we find such metastable states that are energetically favorable compared to triangular and honeycomb lattices. Among these metastable states we report a peculiar ring-lattice state, which is led by the competition between triangular and honeycomb symmetries and rarely seen in other systems. In the case of dipolar mixtures we show that via tuning the miscibility these states can be stabilized in a broader domain by utilizing interspecies interactions.

The beyond mean-field physics due to quantum fluctuations is often described with the Lee-Huang-Yang correction, which can be approximately written as a simple analytical expression in terms of the mean-field wave function employing local density approximation. This model has proven to be very successful in predicting the dynamics in dipolar Bose-Einstein condensates both qualitatively and quantitatively. Yet a small deviation between experimental results and the theoretical prediction has been observed when comparing experiment and theory of the phase boundary of a free-space quantum droplet. For this reason we revisit the theoretical description of quantum fluctuations in dipolar quantum gases. We study alternative cutoffs, compare them to experimental results, and discuss limitations.