Kodaira-Spencer formality of products of complex manifolds

We shall say that a complex manifold $X$ is emph{Kodaira-Spencer formal} if its Kodaira-Spencer differential graded Lie algebra $A^{0,*}_X(Theta_X)$ is formal; if this happen, then the deformation theory of $X$ is completely determined by the graded Lie algebra $H^*(X,Theta_X)$ and the base space of the semiuniversal deformation is a quadratic singularity.. Determine when a complex manifold is Kodaira-Spencer formal is generally difficult and we actually know only a limited class of cases where this happen. Among such examples we have Riemann surfaces, projective spaces, holomorphic Poisson manifolds with surjective anchor map $H^*(X,Omega^1_X) o H^*(X,Theta_X)$ and every compact K"{a}hler manifold with trivial or torsion canonical bundle. In this short note we investigate the behavior of this property under finite products. Let $X,Y$ be compact complex manifolds; we prove that whenever $X$ and $Y$ are K"{a}hler, then $X imes Y$ is Kodaira-Spencer formal if and only if the same holds for $X$ and $Y$. A revisit of a classical example by Douady shows that the above result fails if the K"{a}hler assumption is droppe

Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms

Topological insulators are a broad class of unconventional materials that are insulating in the interior but conduct along the edges. This edge transport is topologically protected and dissipationless. Until recently, all existing topological insulators, known as quantum Hall states, violated time-reversal symmetry. However, the discovery of the quantum spin Hall effect demonstrated the existence of novel topological states not rooted in time-reversal violations. Here, we lay out an experiment to realize time-reversal topological insulators in ultra-cold atomic gases subjected to synthetic gauge fields in the near-field of an atom-chip. In particular, we introduce a feasible scheme to engineer sharp boundaries where the "edge states" are localized. Besides, this multi-band system has a large parameter space exhibiting a variety of quantum phase transitions between topological and normal insulating phases. Due to their unprecedented controllability, cold-atom systems are ideally suited to realize topological states of matter and drive the development of topological quantum computing.Comment: 11 pages, 6 figure

Forcing function control of Faraday wave instabilities in viscous shallow fluids

We investigate the relationship between the linear surface wave instabilities of a shallow viscous fluid layer and the shape of the periodic, parametric-forcing function (describing the vertical acceleration of the fluid container) that excites them. We find numerically that the envelope of the resonance tongues can only develop multiple minima when the forcing function has more than two local extrema per cycle. With this insight, we construct a multi-frequency forcing function that generates at onset a non-trivial harmonic instability which is distinct from a subharmonic response to any of its frequency components. We measure the corresponding surface patterns experimentally and verify that small changes in the forcing waveform cause a transition, through a bicritical point, from the predicted harmonic short-wavelength pattern to a much larger standard subharmonic pattern. Using a formulation valid in the lubrication regime (thin viscous fluid layer) and a WKB method to find its analytic solutions, we explore the origin of the observed relation between the forcing function shape and the resonance tongue structure. In particular, we show that for square and triangular forcing functions the envelope of these tongues has only one minimum, as in the usual sinusoidal case.Comment: 12 pages, 10 figure

Bottom-loading dilution refrigerator with ultra-high vacuum deposition capability

A Kelvinox 400 dilution refrigerator with the ability to load samples onto the mixing chamber from the bottom of the cryostat has been combined with an ultrahigh-vacuum (UHV) deposition chamber equipped with molecular beam sources. The liquid helium cooled sample transfer mechanism is used in a manner that allows films to be grown on substrates which are kept at temperatures of order 8K with chamber pressures in the 10^-9 to 10^-10 Torr range. This system facilitates the growth of quench-condensed ultrathin films which must always be kept below ~ 12K in a UHV environment during and after growth. Measurements can be made on the films down to millikelvin temperatures and in magnetic fields up to 15 T.Comment: 10 pages text, 1figur

Quantum Metallicity on the High-Field Side of the Superconductor-Insulator Transition

We investigate ultrathin superconducting TiN films, which are very close to the localization threshold. Perpendicular magnetic field drives the films from the superconducting to an insulating state, with very high resistance. Further increase of the magnetic field leads to an exponential decay of the resistance towards a finite value. In the limit of low temperatures, the saturation value can be very accurately extrapolated to the universal quantum resistance h/e^2. Our analysis suggests that at high magnetic fields a new ground state, distinct from the normal metallic state occurring above the superconducting transition temperature, is formed. A comparison with other studies on different materials indicates that the quantum metallic phase following the magnetic-field-induced insulating phase is a generic property of systems close to the disorder-driven superconductor-insulator transition.Comment: 4 pages, 4 figures, published versio

Measuring topology in a laser-coupled honeycomb lattice: From Chern insulators to topological semi-metals

Ultracold fermions trapped in a honeycomb optical lattice constitute a versatile setup to experimentally realize the Haldane model [Phys. Rev. Lett. 61, 2015 (1988)]. In this system, a non-uniform synthetic magnetic flux can be engineered through laser-induced methods, explicitly breaking time-reversal symmetry. This potentially opens a bulk gap in the energy spectrum, which is associated with a non-trivial topological order, i.e., a non-zero Chern number. In this work, we consider the possibility of producing and identifying such a robust Chern insulator in the laser-coupled honeycomb lattice. We explore a large parameter space spanned by experimentally controllable parameters and obtain a variety of phase diagrams, clearly identifying the accessible topologically non-trivial regimes. We discuss the signatures of Chern insulators in cold-atom systems, considering available detection methods. We also highlight the existence of topological semi-metals in this system, which are gapless phases characterized by non-zero winding numbers, not present in Haldane's original model.Comment: 30 pages, 12 figures, 4 Appendice