Phase structures of holographic screen themodynamics

Holographic screens are the generalization of the event horizon of a black hole in entropic force scheme, which are defined by setting Newton potential $\phi$ constant, \textit{i. e.} $e^{2\phi}=c=$const. By demonstrating that the integrated first law of thermodynamics is equivalent to the ($r-r$) component of Einstein equations, We strengthen the correspondence between thermodynamics and gravity. We show that there are not only the first law of thermodynamics, but also kinds of phase transitions of holographic screens. These phase transitions are characterized by the discontinuity of their heat capacities. In (n+1) dimensional Reissner-Nordstr\"{o}m-anti-de Sitter (RN-AdS) spacetime, we analyze three kinds of phase transitions, which are of the holographic screens with Q=0 (charge), constant $\Phi$ (electrostatic potential) and non-zero constant $Q$. In the Q=0 case, only the holographic screens with $0\le c<1$ can undergo phase transition. In the constant $\Phi$ case, the constraints become as $0\le c+16\tilde{\Gamma}^{2}\Phi^{2}<1$, where $\tilde{\Gamma}$ is a dimensional dependent parameter. By verifying the Ehrenfest equations, we show that the phase transitions in this case are all second order phase transitions. In the constant $Q$ case, there might be two, or one, or no phase transitions of holographic screens, depending on the values of $Q$ and $c$.Comment: 16 pages,11 figures, references adde

Bose-Einstein condensate in an optical lattice with Raman-assisted two-dimensional spin-orbit coupling

In a recent experiment by Wu {\textit et al.} (arXiv:1511.08170), a Raman-assisted two-dimensional spin-orbit coupling has been realized for a Bose-Einstein condensate in an optical lattice potential. In light of this exciting progress, we study in detail key properties of the system. As the Raman lasers inevitably couple atoms to high-lying bands, the behaviors of the system in both the single- and many-particle sectors are significantly affected. In particular, the high-band effects enhance the plane-wave phase and lead to the emergence of "roton" gaps at low Zeeman fields. Furthermore, we identify high-band-induced topological phase boundaries in both the single-particle and the quasi-particle spectra. We then derive an effective two-band model, which captures the high-band physics in the experimentally relevant regime. Our results not only offer valuable insights into the novel two-dimensional lattice spin-orbit coupling, but also provide a systematic formalism to model high-band effects in lattice systems with Raman-assisted spin-orbit couplings.Comment: 10 pages, 5 figure

Chiral Majorana edge states in the vortex core of a p+ipp+ip Fermi superfluid

We study a single vortex in a two-dimensional $p+ip$ Fermi superfluid interacting with a Bose-Einstein condensate. The Fermi superfluid is topologically non-trivial and hosts a zero-energy Majorana bound state at the vortex core. Assuming a repulsive $s$-wave contact interaction between fermions and bosons, we find that fermions are depleted from the vortex core when the bosonic density becomes sufficiently large. In this case, a dynamically-driven local interface emerges between fermions and bosons, along which chiral Majorana edge states should appear.We examine in detail the variation of vortex-core structures as well as the formation of chiral Majorana edge states with increasing bosonic density. In particular, when the angular momentum of the vortex matches the chirality of the Fermi superfluid, the Majorana zero mode and normal bound states within the core continuously evolve into chiral Majorana edge states. Otherwise, a first-order transition occurs in the lowest excited state within the core, due to the competition between counter-rotating normal bound states in forming chiral Majorana edge states. Such a transition is manifested as a sharp peak in the excitation gap above the Majorana zero mode, at which point the Majorana zero mode is protected by a large excitation gap.Our study presents an illuminating example on how topological defects can be dynamically controlled in the context of cold atomic gases.Comment: 6 pages 6 figure

Topological Fulde-Ferrell states in alkaline-earth-metal-like atoms near an orbital Feshbach resonance

We study the effects of synthetic spin-orbit coupling on the pairing physics in quasi-one-dimensional ultracold Fermi gases of alkaline-earth-metal-like atoms near an orbital Feshbach resonance (OFR). The interplay between spin-orbit coupling and pairing interactions near the OFR leads to an interesting topological Fulde-Ferrell state, where the nontrivial topology of the state is solely encoded in the closed channel with a topologically trivial Fulde-Ferrell pairing in the open channel. We confirm the topological property of the system by characterizing the Zak phase and the edge states. The topological Fulde-Ferrell state can be identified by the momentum-space density distribution obtained from time-of-flight images.Comment: 6 pages, 5 figure

Topological superradiant state in Fermi gases with cavity induced spin-orbit coupling

Coherently driven atomic gases inside optical cavities hold great promise for generating rich dynamics and exotic states of matter. It was shown recently that an exotic topological superradiant state exists in a two-component degenerate Fermi gas coupled to a cavity, where local order parameters coexist with global topological invariants. In this work, we characterize in detail various properties of this exotic state, focusing on the feedback interactions between the atoms and the cavity field. In particular, we demonstrate that cavity-induced interband coupling plays a crucial role in inducing the topological phase transition between the conventional and topological superradiant states. We analyze the interesting signatures in the cavity field left by the closing and reopening of the atomic bulk gap across the topological phase boundary and discuss the robustness of the topological superradiant state by investigating the steady-state phase diagram under various conditions. Furthermore, we consider the interaction effect and discuss the interplay between the pairing order in atomic ensembles and the superradiance of the cavity mode. Our work provides many valuable insights into the unique cavity--atom hybrid system under study and is helpful for future experimental exploration of the topological superradiant state.Comment: 12 pages+10 figure

Correlation between the variation of the ionizing continuum and broad absorption lines

In this Letter, we present an analysis of the relation between the variability of broad absorption lines (BALs) and that of the continuum. Our sample is multi-epoch observations of 483 quasars by the Sloan Digital Sky Survey-I/II/III (SDSS-I/II/III). We derive the fractional flux variations of the continuum and fractional equivalent width (EW) variations for C IV and Si IV BALs, and explore the correlations between the three. Our results reveal moderate anticorrelations with high significance level between the fractional flux variations of the continuum and fractional EW variations for both C IV and Si IV BALs. We also prove a significant positive correlation between the fractional EW variations for C IV and Si IV BALs, which is in agreement with several previous studies. Our discoveries can serve as evidence for the idea: Change of an ionizing continuum is the primary driver of BAL variability

Interaction-induced exotic vortex states in an optical lattice clock with spin-orbit coupling

Motivated by a recent experiment [L. F. Livi, et al., Phys. Rev. Lett. 117, 220401(2016)], we study the ground-state properties of interacting fermions in a one-dimensional optical lattice clock with spin-orbit coupling. As the electronic and the hyperfine-spin states in the clock-state manifolds can be treated as effective sites along distinct synthetic dimensions, the system can be considered as multiple two-leg ladders with uniform magnetic flux penetrating the plaquettes of each ladder. As the inter-orbital spin-exchange interactions in the clock-state manifolds couple individual ladders together, we show that exotic interaction-induced vortex states emerge in the coupled-ladder system, which compete with existing phases of decoupled ladders and lead to a rich phase diagram. Adopting the density matrix renormalization group approach, we map out the phase diagram, and investigate in detail the currents and the density-density correlations of the various phases. Our results reveal the impact of interactions on spin-orbit coupled systems, and are particularly relevant to the on-going exploration of spin-orbit coupled optical lattice clocks

Observation of the Hopf Links and Hopf Fibration in a 2D topological Raman Lattice

A dynamical Hopf insulator is experimentally synthesized with a quenched two-dimensional quantum anomalous Hall system on a square Raman lattice. The quench dynamics for the quasimomentum-time-dependent Bloch vectors defines a Hopf map from $(q_x,q_y,t)\in T^3$ to the Bloch sphere $S^2$. In this Hopf map, a dynamical Hopf number can be defined, and it exactly equals the Chern number of the post-quench Hamiltonian. We experimentally measure the Hopf link between the fibers for the North and South Poles on $S^2$, which are the trajectories in $(q_x,q_y,t)$ space with maximal spin polarization, to extract the topological Chern number of the post-quench Hamiltonian. We also observe the structure of Hopf fibration for the mutually nested Hopf tori. Our study sheds some new light on the interplay between topology (Hopf number) and geometry (fiber bundle) in quantum dynamics.Comment: 5 pages, 4 figures for main text and 7 pages, 5 figures for supplementary materia

A topological phase transition on the edge of the 2d Z2\mathbb{Z}_2 topological order

The unified mathematical theory of gapped and gapless edges of 2d topological orders was developed by two of the authors. It provides a powerful tool to study pure edge topological phase transitions on the edges of 2d topological orders (without altering the bulks). In particular, it implies that the critical points are described by enriched fusion categories. In this work, we illustrate this idea in a concrete example: the 2d $\mathbb{Z}_2$ topological order. In particular, we construct an enriched fusion category, which describes a gappable non-chiral gapless edge of the 2d $\mathbb{Z}_2$ topological order; then use an explicit lattice model construction to realize the critical point and, at the same time, all the ingredients of this enriched fusion category.Comment: 31 pages, 58 figures, Comments are welcom

Spatial Filter with Volume Gratings for High-peak-power Multistage Laser Amplifiers

The regular spatial filters comprised of lens and pinhole are essential component in high power laser systems, such as lasers for inertial confinement fusion, nonlinear optical technology and directed-energy weapon. On the other hand the pinhole is treated as a bottleneck of high power laser due to harmful plasma created by the focusing beam. In this paper we present a spatial filter based on angular selectivity of Bragg diffraction grating to avoid the harmful focusing effect in the traditional pinhole filter. A spatial filter consisted of volume phase gratings in two-pass amplifier cavity were reported. Two-dimensional filter was proposed by using single Pi-phase-shifted Bragg grating, numerical simulation results shown that its angular spectrum bandwidth can be less than 160urad. The angular selectivity of photo-thermo-refractive glass and RUGATE film filters, construction stability, thermal stability and the effects of misalignments of gratings on the diffraction efficiencies under high-pulse-energy laser operating condition are discussed. Keywords: spatial filter, pinhole spatial filter, RUGATE filter, angular selectivity of volume phase grating, Pi-phase-shifted Bragg grating, high-energy pulsed laser, multi-pass laser amplifierComment: 6 pages, 7 figures, 2 table