Tunable superfluidity and quantum magnetism with ultracold polar molecules

By selecting two dressed rotational states of ultracold polar molecules in an optical lattice, we obtain a highly tunable generalization of the t-J model, which we refer to as the t-J-V-W model. In addition to XXZ spin exchange, the model features density-density interactions and density-spin interactions; all interactions are dipolar. We show that full control of all interaction parameters in both magnitude and sign can be achieved independently of each other and of the tunneling. As a first step towards demonstrating the potential of the system, we apply the density matrix renormalization group method to obtain the 1D phase diagram of the simplest experimentally realizable case. Specifically, we show that the tunability and the long-range nature of the interactions in the t-J-V-W model enable enhanced superfluidity. Finally, we show that Bloch oscillations in a tilted lattice can be used to probe the phase diagram experimentally.     

Microphase separation in polydisperse miktoarm star copolymers

A two or more chemically different homopolymers attached to a single junction point form a macromolecule of miktoarm star copolymer. The model of such copolymer composed of an arbitrary number of types of homopolymer arms is considered. The lengths distributions of arms are assumed to be arbitrary, provided that average length of an each arm is long enough. The algorithm is suggested to find the contributions into the Landau free energy of this copolymer melt which are necessary to obtain a phase diagram in weak segregation regime. Using this algorithm the contributions are found up to the fourth order. The phase diagrams have been constructed for the simple model of AB₂ copolymer melt whose macromolecules consist of polydisperse A-block and two monodisperse B-blocks.     

Line tension at fluid membrane domain boundaries measured by micropipette aspiration

Line tension is a determinant of fluid phase domain formation kinetics and morphology in lipid bilayer membranes, which are models for biological membrane heterogeneity. We describe the first direct measurement of this line tension by micropipette aspiration. Our data are analyzed with a model that does not rely on independently measured (and composition dependent) secondary parameters, such as bending stiffness or membrane viscosities. Line tension is strongly composition dependent and decreases towards a critical consolute point in a quasiternary room temperature phase diagram.     

一维扩展t-J模型中密度-自旋相互作用诱导的相分离

t-J模型是研究高温超导电性的重要理论模型之一. 最近的冷分子实验表明可用极性分子模拟t-J模型. 实验模拟的t-J模型除了引进长程的偶极相互作用外, 还引进了密度-自旋相互作用. 本文使用密度矩阵重整化群方法研究了密度-自旋相互作用对一维t-J 模型基态性质的影响. 选取了t-J模型基态相图中不同相区的三个点, 计算了不同密度-自旋相互作用强度下的粒子数和自旋的实空间分布,以及密度-密度关联函数和自旋-自旋关联函数与相应的结构因子. 计算结果表明, 密度-自旋相互作用强度较弱时, 对系统的性质不会产生定性影响;当其强度足够大时, 系统会进入相分离, 该相分离与传统t-J模型的相分离有很大区别.     

Self-assembling and phase coexistence of SW trimers as complex amphiphile analogues. I. Simulations

We analyse by discrete molecular dynamics the self-assembly of SW trimer particles that contain a different number of attractive and repulsive spheres. They also have different geometries: linear, obtuse, rectangular and equilateral. We identify that some of these molecules exhibit liquid–vapour equilibria while others do not. For all of them, we show the morphological phase diagram built up from the different supra-molecular structures formed by each type of trimer. We simulated 14 different systems with a total of 321 states. The main features of the supra-molecular structures depend only on the composition and geometry of the trimer: triple SW trimers do not form supra-structures, double SW trimers and single SW trimers form monolayers, bilayers and worm-like micelles. The liquid–vapour coexistence properties are also exhibited. These trimers can be used to model complex amphiphiles beyond the standard ones, such as the Gemini and the Bola surfactants as well as colloidal particles.     

A microscopic model of annealed vacancies in long-period structures

The axial next-nearest-neighbour Ising (ANNNI) model is a spin model which locks into an infinite number of modulated phases as a function of the interaction parameters and the temperature. In this paper we discuss the effect of allowing this system to contain annealed vacancies. We find that a small concentration of vacancies does not qualitatively affect the structure of the phase diagram and that the vacancies form defect-density waves which mirror the periodicity of the underlying modulated structure.     

A simple atomistic model for the simulation of the gel phase of lipid bilayers

In this paper we present the results of a large-scale numerical investigation of structural properties of a model of cell membrane, simulated as a bilayer of flexible molecules in vacuum. The study was performed by carrying out extensive Molecular Dynamics simulations, in the (NVE) micro-canonical ensemble, of two systems of different sizes ( 2×32 and 2×256 molecules), over a fairly large set of temperatures and densities, using parallel platforms and more standard serial computers. Depending on the dimension of the system, the dynamics was followed for physical times that go from few hundred picoseconds for the largest system to 5-10 nanoseconds for the smallest one. We find that the bilayer remains stable even in the absence of water and neglecting Coulomb interactions in the whole range of temperatures and densities we have investigated. The extension of the region of physical parameters that we have explored has allowed us to study significant points in the phase diagram of the bilayer and to expose marked structural changes as density and temperature are varied, which are interpreted as the system passing from a crystal to a gel phase. Received 6 July 2000 and Received in final form 28 December 2000     

Existence of several surface-reconstructed phases in a two-dimensional lattice model

The zero-temperature phase diagram is rigorously obtained for a two-dimensional lattice model with four energy parameters. It is shown that the parameter space can be divided into regions, together with their boundaries, such that in each region the ground-state configurations are of one of seven different types. These types include one which is nondegenerate, four which are doubly degenerate, one which is infinitely degenerate but with no residual entropy, and one which is infinitely degenerate and has a nonzero residual entropy. The Pirogov-Sinai extension of the Peierls argument is used to establish the existence at low temperatures of four different types of ordered surface-reconstructed phases.     

Ground state of the half-filled extended Hubbard model beyond the Hartree-Fock approximation

The local approach for the intraatomic correlation is applied to study the ground state phase diagram of the extended Hubbard model with a half-filled band. The long-range orders are not destroyed by the correlation effect in the limit of weak interaction, though the values of the order parameters are reduced from those of the Hartree-Fock approximation, especially for the antiferromagnetic-state. We find that the antiferromagnetic-charge order phase boundary is only slightly shifted towards the charge ordered state, while the phase boundary between the singlet superconducting and the charge ordered phases remains the same as that derived from the Hartree-Fock approximation.     

Ground state phase diagram of the infinite dimensional Hubbard model: A variational study

We use the Gutzwiller variational method to study the ground state phase diagram of the infinite dimensional Hubbard model, paying special attention to features associated with the Gaussian form of the tight binding band density of states. We only consider trial states for which the validity of the Gutzwiller approximation has been proven, i.e., the paramagnetic, ferromagnetic, and two-sublattice antiferromagnetic states. We map out the phase diagram numerically, and give approximate analytic arguments to explain the behaviour in the small-U, and large-U limits. We give two versions of the phase diagram: one restricted to homogeneous phases, and another when phase separation is allowed. In the latter case, a homogeneous antiferromagnetic state is found only at exact half-filling, where the state is also insulating. Off half-filling, four different regions are found: pure paramagnetic, and ferromagnetic states, as well as antiferromagnetic-paramagnetic, and antiferromagnetic-ferromagnetic mixed phases.Dedicated to Professor W. Brenig on the occasion of his 60th birthdayResearch performed within the program of the Sonderforschungsbereich 341 supported by the Deutsche Forschungsgemeinschaft     

Intramolecular bonding in a statistical associating fluid theory of ring aggregates

The first-order thermodynamic perturbation theory of Wertheim (TPT1) is extended to treat ring aggregates, formed by inter- and intramolecular association. The expression for the residual association contribution to the Helmholtz free energy for ring aggregates, incorporating the appropriate terms in Wertheim's fundamental graph sum of the TPT1 density expansion, is derived to calculate the distribution of the molecular bonding states. This requires the introduction of two new parameters to characterise each possible ring type: the ring size τ, which is equal to one in the case of intramolecular association, and a parameter W that captures the likelihood of two ring-forming sites bonding. The resulting framework can be incorporated in equations of state that account for the residual association contribution to the free energy, such as the statistical associating fluid theory (SAFT) family, or the cubic plus association (CPA) equation of state. This extends the applicability of these equations of state to mixtures with an arbitrary number of association sites capable of hydrogen bonding to form intramolecular and intermolecular rings. The formalism is implemented within SAFT-VR Mie to calculate the fluid-phase equilibria of model chain-like molecules containing two associating sites A and B, allowing for the formation of open-chain aggregates and intramolecular bonds. The effect of adding a second component that competes for the association sites that mediate intramolecular association in the chain is also examined. Accounting for intramolecular bonding is shown to have a significant impact on the phase equilibria of such systems.     

Quantum phases in a resonantly interacting boson-fermion mixture

We consider a resonantly interacting boson-fermion mixture of 40K and 87Rb atoms in an optical lattice. We show that by using a red-detuned optical lattice the mixture can be accurately described by a generalized Hubbard model for 40K and 87Rb atoms, and 40K-87Rb molecules. The microscopic parameters of this model are fully determined by the details of the optical lattice and the interspecies Feshbach resonance in the absence of the lattice. We predict a quantum phase transition to occur in this system already at low atomic filling fraction, and present the phase diagram as a function of the temperature and the applied magnetic field.     

Stochastic ballistic annihilation and coalescence

We study a class of stochastic ballistic annihilation and coalescence models with a binary velocity distribution in one dimension. We obtain an exact solution for the density which reveals a universal phase diagram for the asymptotic density decay. By universal we mean that all models in the class are described by a single phase diagram spanned by two reduced parameters. The phase diagram reveals four regimes, two of which contain the previously studied cases of ballistic annihilation. The two new phases are a direct consequence of the stochasticity. The solution is obtained through a matrix product approach and builds on properties of a q-deformed harmonic oscillator algebra.     

A study of the headgroup motion of sphingomyelin using 31P NMR and an analytically soluble model

A 31P NMR investigation has been carried out of the headgroup dynamics of sphingomyelin molecules in bilayers for the L alpha and L beta' phases. The resulting line shapes have been analysed in terms of a reduced-parameter model, using van Faassen's method for obtaining an analytic solution to first-order stochastic differential equations to simulate the line shapes of oriented and non-oriented samples. Our treatment results in good fits to measured data but using fewer parameters than traditional methods. Angles and correlation times (tau parallel and tau perpendicular) describing the geometry and dynamics of the headgroup are obtained by optimising the agreement between simulated and experimental data. The results are contrasted with those obtained for the lecithins DMPC and DPPC using a similar analysis. Not only are tau parallel and tau perpendicular now equal in value for the L alpha phase, but this value is also found to be nearly four times larger than the longest correlation time for the lecithins. We interpret this as evidence of inter- and intramolecular hydrogen bonding in the L(alpha) phase of sphingomyelin. In the L beta' phase of sphingomyelin, however, although tau(parallel) and tau(perpendicular) remain equal their value is now 32% smaller than that of the lecithins in the same phase. This indicates less difference between the fluidities in the headgroup region of the two phases of sphingomyelin as compared to that of the lecithins. Another significant difference between the L beta' phases is that the tilt angle for sphingomyelin is found to be nearly twice as large as for the lecithins. We argue that these combined observations point to the existence of hydrogen bonding in this phase also. Again in contrast to our previous work on lecithins, our results provide evidence of a negative diamagnetic anisotropy in sphingomyelin molecules, even in the L beta' phase. This is provided for in our model by the assumption that our unoriented samples consist of prolate ellipsoidal liposomes whose major axes are oriented parallel to the static magnetic field. The apparently different diamagnetic behaviour of sphingomyelin in the present work is due to the higher static field used rather than any intrinsic difference in this respect between sphingomyelin and the lecithins DMPC and DPPC.     

Phase transition properties of ferroelectric thin films with two surface layers

The phase diagrams of ferroelectric thin films with two surface layers described by the transverse Ising model have been studied under the mean-field approximation. We discuss the effects of the exchange interaction and transverse field parameters on the phase diagrams. The results indicate that the phase transition properties of the phase diagrams can be greatly modified by changing the transverse Ising model parameters. In addition, the crossover features of the parameters from the ferroelectric dominant phase diagram to the paraelectric dominant phase diagram are determined for ferroelectric thin films with two surface layers.     

Solids and supersolids of three-body interacting polar molecules on an optical lattice

We study the physics of cold polar molecules loaded into an optical lattice in the regime of strong three-body interactions, as put forward recently by Büchler et al. [Nature Phys. 3, 726 (2007)]. To this end, quantum Monte Carlo simulations, exact diagonalization, and a semiclassical approach are used to explore hard-core bosons on the 2D square lattice which interact solely by long-ranged three-body terms. The resulting phase diagram shows a sequence of solid and supersolid phases. Our findings are directly relevant for future experimental implementations and open a new route towards the discovery of a lattice supersolid phase in experiment.     

Extended JC-Dicke model for two-component atomic BEC inside a cavity

We consider a trapped two-component atomic Bose-Einstein condensate (BEC), where each atom with three energy-levels is coupled to an optical cavity field and an external classical optical field as well as a microwave field to form the so-called Δ-type configuration. After adiabatically eliminating the atomic excited state, an extended JC-Dicke model is derived under the rotating-wave approximation. The scaled ground-state energy and the phase diagram of this model Hamiltonian are investigated in the framework of mean-field approach. A new phase transition is revealed when the amplitude of microwave field changes its sign.     

Stability of MgAl 2 O 4 Under High-Pressure Conditions

A theoretical investigation of the MgAl 2 O 4 crystal response to high-pressure conditions has been carried out to determine its stability against decomposition towards MgO and f -Al 2 O 3 , and towards recently observed orthorhombic phases. We have evaluated total energy versus volume curves using the density functional formalism under the non-local B3LYP approximation, as implemented in the CRYSTAL package. Numerical and analytical fittings have been carried out to determine the equilibrium unit cell geometry and equation of state parameters for all the structures and compounds involved in the phase diagram. The macroscopic compressibility of the spinel phase is interpreted considering the compressibility of its elementary MgO 4 and AlO 6 coordination polyhedra, and implications to understand the phase stability are suggested.     

Role of the attractive intersite interaction in the extended Hubbard model

We consider the extended Hubbard model in the atomic limit on a Bethe lattice with coordination number z. By using the equations of motion formalism, the model is exactly solved for both attractive and repulsive intersite potential V. By focusing on the case of negative V, i.e., attractive intersite interaction, we study the phase diagram at finite temperature and find, for various values of the filling and of the on-site coupling U, a phase transition towards a state with phase separation. We determine the critical temperature as a function of the relevant parameters, U/|V|, n and z and we find a reentrant behavior in the plane (U/|V|, T). Finally, several thermodynamic properties are investigated near criticality.