Fermionic superfluid from a bilayer band insulator in an optical lattice

We propose a model to realize a fermionic superfluid state in an optical lattice circumventing the cooling problem. Our proposal exploits the idea of tuning the interaction in a characteristically low-entropy state, a band insulator in an optical bilayer system, to obtain a superfluid. By performing a detailed analysis of the model including fluctuations and augmented by a variational quantum Monte Carlo calculation of the ground state, we show that the superfluid state obtained has a high transition temperature of the order of the hopping energy. Our system is designed to suppress other competing orders such as a charge density wave. We suggest a laboratory realization of this model via an orthogonally shaken optical lattice bilayer.

Majorana edge modes in the Kitaev model

We study the Majorana modes, both equilibrium and Floquet, which can appear at the edges of the Kitaev model on the honeycomb lattice. We first present the analytical solutions known for the equilibrium Majorana edge modes for both zigzag and armchair edges of a semi-infinite Kitaev model and chart the parameter regimes in which they appear. We then examine how edge modes can be generated if the Kitaev coupling on the bonds perpendicular to the edge is varied periodically in time as periodic delta-function kicks. We derive a general condition for the appearance and disappearance of the Floquet edge modes as a function of the drive frequency for a generic d-dimensional integrable system. We confirm this general condition for the Kitaev model with a finite width by mapping it to a one-dimensional model. Our numerical and analytical study of this problem shows that Floquet Majorana modes can appear on some edges in the kicked system even when the corresponding equilibrium Hamiltonian has no Majorana mode solutions on those edges. We support our analytical studies by numerics for a finite sized system which show that periodic kicks can generate modes at the edges and the corners of the lattice.

Finite size scaling in crossover among different random matrix ensembles in microscopic lattice models

Using numerical diagonalization we study the crossover among different random matrix ensembles (Poissonian, Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE) and Gaussian symplectic ensemble (GSE)) realized in two different microscopic models. The specific diagnostic tool used to study the crossovers is the level spacing distribution. The first model is a one-dimensional lattice model of interacting hard-core bosons (or equivalently spin 1/2 objects) and the other a higher dimensional model of non-interacting particles with disorder and spin-orbit coupling. We find that the perturbation causing the crossover among the different ensembles scales to zero with system size as a power law with an exponent that depends on the ensembles between which the crossover takes place. This exponent is independent of microscopic details of the perturbation. We also find that the crossover from the Poissonian ensemble to the other three is dominated by the Poissonian to GOE crossover which introduces level repulsion while the crossover from GOE to GUE or GOE to GSE associated with symmetry breaking introduces a subdominant contribution. We also conjecture that the exponent is dependent on whether the system contains interactions among the elementary degrees of freedom or not and is independent of the dimensionality of the system.

Laterally structured ripple and square phases with one and two dimensional thickness modulations in a model bilayer system

Molecular dynamics simulations of bilayers in a surfactant/co-surfactant/water system with explicit solvent molecules show formation of topologically distinct gel phases depending upon the bilayer composition. At low temperatures, the bilayers transform from the tilted gel phase, L beta', to the one dimensional (1D) rippled, P beta' phase as the surfactant concentration is increased. More interestingly, we observe a two dimensional (2D) square phase at higher surfactant concentration which, upon heating, transforms to the gel L beta' phase. The thickness modulations in the 1D rippled and square phases are asymmetric in two surfactant leaflets and the bilayer thickness varies by a factor of similar to 2 between maximum and minimum. The 1D ripple consists of a thinner interdigitated region of smaller extent alternating with a thicker non-interdigitated region. The 2D ripple phase is made up of two superimposed square lattices of maximum and minimum thicknesses with molecules of high tilt forming a square lattice translated from the lattice formed with the thickness minima. Using Voronoi diagrams we analyze the intricate interplay between the area-per-head-group, height modulations and chain tilt for the different ripple symmetries. Our simulations indicate that composition plays an important role in controlling the formation of low temperature gel phase symmetries and rippling accommodates the increased area-per-head-group of the surfactant molecules.

Computational design of model Re/Ru bearing Ni-base superalloys

It is well established that Re and Ru additions to Ni-base superalloys result in improved creep performance and phase stability. However, the role of Re and Ru and their synergetic effects are not well understood, and the first step in understanding these effects is to design alloys with controlled microstructural parameters. A computational approach was undertaken in the present work for designing model alloys with varying levels of Re and Ru. Thermodynamic and first principles calculations were employed complimentarily to design a set of alloys with varying Re and Ru levels, but which were constrained by constant microstructural parameters, i.e., phase fractions and lattice misfit across the alloys. Three ternary/quaternary alloys of type Ni-Al-xRe-yRu were thus designed. These compositions were subsequently cast, homogenized and aged. Experimental results suggest that while the measured volume fraction matches the predicted value in the Ru containing alloy, volume fraction is significantly higher than the designed value in the Re containing alloys. This is possibly due to errors in the thermodynamic database used to predict phase fraction and composition. These errors are also reflected in the mismatch between predicted and measured values of misfit.

Phase diagram of the half-filled ionic Hubbard model

We study the phase diagram of the ionic Hubbard model (IHM) at half filling on a Bethe lattice of infinite connectivity using dynamical mean-field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered ionic potential Delta and the on-site Hubbard U. We find that for a finite Delta and at zero temperature, long-range antiferromagnetic (AFM) order sets in beyond a threshold U = U-AF via a first-order phase transition. For U smaller than U-AF the system is a correlated band insulator. Both methods show a clear evidence for a quantum transition to a half-metal (HM) phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U. We show that the results obtained within both methods have good qualitative and quantitative consistency in the intermediate-to-strong-coupling regime at zero temperature as well as at finite temperature. On increasing the temperature, the AFM order is lost via a first-order phase transition at a transition temperature T-AF(U,Delta) or, equivalently, on decreasing U below U-AF(T,Delta)], within both methods, for weak to intermediate values of U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. At a finite temperature T, DMFT + CTQMC shows a second phase transition (not seen within DMFT + IPT) on increasing U beyond U-AF. At U-N > U-AF, when the Neel temperature T-N for the effective Heisenberg model becomes lower than T, the AFM order is lost via a second-order transition. For U >> Delta, T-N similar to t(2)/U(1 - x(2)), where x = 2 Delta/U and thus T-N increases with increase in Delta/U. In the three-dimensional parameter space of (U/t, T/t, and Delta/t), as T increases, the surface of first-order transition at U-AF(T,Delta) and that of the second-order transition at U-N(T,Delta) approach each other, shrinking the range over which the AFM order is stable. There is a line of tricritical points that separates the surfaces of first- and second-order phase transitions.

Detection of a quantum particle on a lattice under repeated projective measurements

We consider a quantum particle, moving on a lattice with a tight-binding Hamiltonian, which is subjected to measurements to detect its arrival at a particular chosen set of sites. The projective measurements are made at regular time intervals tau, and we consider the evolution of the wave function until the time a detection occurs. We study the probabilities of its first detection at some time and, conversely, the probability of it not being detected (i.e., surviving) up to that time. We propose a general perturbative approach for understanding the dynamics which maps the evolution operator, which consists of unitary transformations followed by projections, to one described by a non-Hermitian Hamiltonian. For some examples of a particle moving on one-and two-dimensional lattices with one or more detection sites, we use this approach to find exact expressions for the survival probability and find excellent agreement with direct numerical results. A mean-field model with hopping between all pairs of sites and detection at one site is solved exactly. For the one-and two-dimensional systems, the survival probability is shown to have a power-law decay with time, where the power depends on the initial position of the particle. Finally, we show an interesting and nontrivial connection between the dynamics of the particle in our model and the evolution of a particle under a non-Hermitian Hamiltonian with a large absorbing potential at some sites.

Feshbach modulation spectroscopy of the Fermi-Hubbard model

In the vicinity of a Feshbach resonance, a system of ultracold atoms in an optical lattice undergoes rich physical transformations which involve molecule formation and hopping of molecules on the lattice and thus goes beyond a single-band Hubbard model description. We explore theoretically the response of this system to a harmonic modulation of the magnetic field, and thus of the scattering length, across the Feshbach resonance. In the regime in which the single-band Hubbard model is still valid, we provide results for the doublon production as a function of the various parameters, such as frequency, amplitude, etc., that characterize the field modulation, as well as the lattice depth. The method may uncover a route towards the efficient creation of ultracold molecules and also provide an alternative to conventional lattice-depth-modulation spectroscopy.

ASYMPTOTIC PRESERVING SCHEME FOR A KINETIC MODEL DESCRIBING IN COMPRESSIBLE FLUIDS

The kinetic theory of fluid turbulence modeling developed by Degond and Lemou in 7] is considered for further study, analysis and simulation. Starting with the Boltzmann like equation representation for turbulence modeling, a relaxation type collision term is introduced for isotropic turbulence. In order to describe some important turbulence phenomenology, the relaxation time incorporates a dependency on the turbulent microscopic energy and this makes difficult the construction of efficient numerical methods. To investigate this problem, we focus here on a multi-dimensional prototype model and first propose an appropriate change of frame that makes the numerical study simpler. Then, a numerical strategy to tackle the stiff relaxation source term is introduced in the spirit of Asymptotic Preserving Schemes. Numerical tests are performed in a one-dimensional framework on the basis of the developed strategy to confirm its efficiency.