Dynamical symmetry breaking with optimal control: Reducing the number of pieces

We analyze the production of defects during the dynamical crossing of a mean-field phase transition with a real order parameter. When the parameter that brings the system across the critical point changes in time according to a power-law schedule, we recover the predictions dictated by the well-known Kibble-Zurek theory. For a fixed duration of the evolution, we show that the average number of defects can be drastically reduced for a very large but finite system, by optimizing the time dependence of the driving using optimal control techniques. Furthermore, the optimized protocol is robust against small fluctuations.

Ca(2+) signals coordinate zygotic polarization and cell cycle progression in the brown alga Fucus serratus

Zygotes of the fucoid brown algae provide excellent models for addressing fundamental questions about zygotic symmetry breaking. Although the acquisition of polarity is tightly coordinated with the timing and orientation of the first asymmetric division-with zygotes having to pass through a G1/S-phase checkpoint before the polarization axis can be fixed -the mechanisms behind the interdependence of polarization and cell cycle progression remain unclear. In this study, we combine in vivo Ca(2+) imaging, single cell monitoring of S-phase progression and multivariate analysis of high-throughput intracellular Ca(2+) buffer loading to demonstrate that Ca(2+) signals coordinate polarization and cell cycle progression in the Fucus serratus zygote. Consistent with earlier studies on this organism, and in contrast to animal models, we observe no fast Ca(2+) wave following fertilization. Rather, we show distinct slow localized Ca(2+) elevations associated with both fertilization and S-phase progression, and we show that both S-phase and zygotic polarization are dependent on pre-S-phase Ca(2+) increases. Surprisingly, this Ca(2+) requirement cannot be explained by co-dependence on a single G1/ S-phase checkpoint, as S phase and zygotic polarization are differentially sensitive to pre-S-phase Ca(2+) elevations and can be uncoupled. Furthermore, subsequent cell cycle progression through M phase is independent of localized actin polymerization and zygotic polarization. This absence of a morphogenesis checkpoint, together with the observed Ca(2+)dependences of S phase and polarization, show that the regulation of zygotic division in the brown algae differs from that in other eukaryotic model systems, such as yeast and Drosophila.

Bilinear-biquadratic spin-1 chain undergoing quadratic Zeeman effect

The Heisenberg model for spin-1 bosons in one dimension presents many different quantum phases, including the famous topological Haldane phase. Here we study the robustness of such phases in front of a SU(2) symmetry-breaking field as well as the emergence of unique phases. Previous studies have analyzed the effect of such uniaxial anisotropy in some restricted relevant points of the phase diagram. Here we extend those studies and present the complete phase diagram of the spin-1 chain with uniaxial anisotropy. To this aim, we employ the density-matrix renormalization group together with analytical approaches. The complete phase diagram can be realized using ultracold spinor gases in the Mott insulator regime under a quadratic Zeeman effect.

Detection of Entanglement in Ultracold Lattice Gases

Probing non trivial magnetic ordering in quantum magnets realized with ultracold lattice gases demands detection methods with some spatial resolution built on it. Here we demonstrate that the Faraday matter-light interface provides an experimentally feasible tool to distinguish indubitably different quantum phases of a given many-body system in a non-demolishing way. We illustrate our approach by focussing on the Heisenberg chain for spin-1 bosons in the presence of a SU(2) symmetry breaking field. We explain how using the light signal obtained via homodyne detection one can reconstruct the phase diagram of the model. Further we show that the very same technique that provides a direct experimentally measurable signal of different order parameters can be extended to detect also the presence of multipartite entanglement in such systems.

Dynamical symmetries and crossovers in a three-spin system with collective dissipation

We consider the non-equilibrium dynamics of a simple system consisting of interacting spin-1/2 particles subjected to a collective damping. The model is close to situations that can be engineered in hybrid electro/opto-mechanical settings. Making use of large-deviation theory, we find a Gallavotti-Cohen symmetry in the dynamics of the system as well as evidence for the coexistence of two dynamical phases with different activity levels. We show that additional damping processes smooth out this behavior. Our analytical results are backed up by Monte Carlo simulations that reveal the nature of the trajectories contributing to the different dynamical phases.