We study dynamical processes in coherently coupled atomic Bose-Einstein condensates. Josephson effects in ring-shaped and dumbbell geometries are theoretically investigated. Conditions for observation of the Josephson effect are revealed. We found that multicharged persistent current in toroidal condensate can be robust even for supersonic atomic flow. In numerical simulations the acoustic analogues of event horizon in quantized superflow was observed. These theoretical finding open perspectives for investigation of Bose Josephson junctions and quantum aspects of acoustic analogue of Hawking radiation in existing experimental setups.

In contrast to conservative systems, in nonlinear media with gain and loss the dynamics of localized topological structures can exhibit unique features that can be controlled externally. We propose a robust mechanism to perform topological transformations changing characteristics of dissipative vortices and their complexes in a controllable way. We show that a properly chosen control carries out the evolution of dissipative structures to regime with spontaneous transformation of the topological excitations or drives generation of vortices with control over the topological charge.

We consider a platform featuring the minimal ingredients relevant both to a driven-dissipative cavity quantum optics system and to a spintronically pumped magnon condensate. We extend the Dicke model for a bosonic mode collectively coupled to a coherent spin ensemble, by weakly coupling it to an out-of-equilibrium spin bath which is tunable by incoherent pumping. Our model exhibits competition between coherent couplings and dissipative channels, which leads to various collective quantum behaviors, static and dynamic, depending on the interplay of spin-boson interactions and spin pump/loss rates. Our analysis exposes a hybrid lasing-superradiant regime which does not take place in an ordinary pumped Dicke spin ensemble. We interpret the resultant non-equilibrium phase diagram from both a quantum optics and a spintronics standpoint, supplying a conceptual bridge between the two fields. The implications of our results concern dynamical control in spintronics and frequency-dependent gain media in quantum optics.

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Topological defects have strong impact on both elastic and inelastic properties of materials. In this article, we investigate the possibility to controllably inject topological defects in quantum simulators of solid state lattice structures. We investigate the quench dynamics of a Frenkel-Kontorova chain, which is used to model discommensurations of particles in cold atoms and trapped ionic crystals. The interplay between an external periodic potential and the inter-particle interaction makes lattice discommensurations, the topological defects of the model, energetically favorable and can tune a commensurate-incommensurate structural transition. Our key finding is that a quench from the commensurate to incommensurate phase causes a controllable injection of topological defects at periodic time intervals. We employ this mechanism to generate quantum states which are a superposition of lattice structures with and without topological defects. We conclude by presenting concrete perspectives for the observation and control of topological defects in trapped ion experiments.