Novel quantum phases of dipolar bose gases in optical lattices

We investigate the quantum phases of polarized dipolar bosons loaded into a two-dimensional square and three-dimensional cubic optical lattices. We show that the long-range and anisotropic nature of the dipole-dipole interaction induces a rich variety of quantum phases, including the supersolid and striped supersolid phases in two-dimensional lattices, and the layered supersolid phase in three-dimensional lattices.     

Self-trapping of bosons and fermions in optical lattices

We theoretically investigate the enhanced localization of bosonic atoms by fermionic atoms in three-dimensional optical lattices and find a self-trapping of the bosons for attractive boson-fermion interaction. Because of this mutual interaction, the fermion orbitals are substantially squeezed, which results in a strong deformation of the effective potential for bosons. This effect is enhanced by an increasing bosonic filling factor leading to a large shift of the transition between the superfluid and the Mott-insulator phase. We find a nonlinear dependency of the critical potential depth on the boson-fermion interaction strength. The results, in general, demonstrate the important role of higher Bloch bands for the physics of attractively interacting quantum gas mixtures in optical lattices and are of direct relevance to recent experiments with 87Rb-40K mixtures, where a large shift of the critical point has been found.     

Polychromatic interface solitons in nonlinear photonic lattices

We demonstrate that interfaces between two nonlinear periodic photonic lattices offer unique possibilities for controlling the nonlinear interaction between different spectral components of polychromatic light, and a change in the light spectrum can have a dramatic effect on the propagation along the interface. We predict the existence of polychromatic surface solitons that differ fundamentally from their counterparts in infinite lattices.     

The Dzyaloshinskii-Moriya interaction in metals

The Dzyaloshinskii-Moriya (DM) interaction in metals is an important mechanism for many magnetic properties. We start with the s-d exchange model and spin-orbit interaction for weak itinerant ferromagnetic systems to establish the form of DM interaction for metallic magnetic systems. The s-d exchange interaction is treated accurately and the conduction electron-mediated magnetism gives a form of DM interaction which is different from that in insulators. The implications of our result to spiral spin states and skyrmion lattices are also discussed.     

Topological defect formation in rotating binary dipolar Bose–Einstein condensate

We investigate the topological defects and spin structures of a rotating binary Bose–Einstein condensate, which consists of both dipolar and scalar bosonic atoms confined in spin-dependent optical lattices, for an arbitrary orientation of the dipoles with respect to their plane of motion. Our results show that the tunable dipolar interaction, especially the orientation of the dipoles, can be used to control the direction of stripe phase and its related half-vortex sheets. In addition, it can also be used to obtain a regular arrangement of various topological spin textures, such as meron, circular and cross disgyration spin structures. We point out that such topological defects and regular arrangement of spin structures arise primarily from the long-range and anisotropic nature of dipolar interaction and its competition with the spin-dependent optical lattices and rotation.     

A general Mobius inversion transform formula for hcp lattices and its application

In this paper,we present a general Mobius inversion transform formula for hcp lattices.This formula can be applied to hcp lattices with a non-ideal c/a value and to obtain the pair potential between atoms in these lattices from the cohesive energy.Also,the three-body interaction among atoms in the lattices can be taken into account in the method.This method gives a useful means to obtain interatomic interactions in the interatomic force model.The method has been applied to zinc,and the pair potential obtained is used to calculate the phonon dispersion relations for some high-symmetry directions.It is found that,by properly considering a three-body interaction,one can acquire satisfactory results.     

Magnetic properties of <Superscript>3</Superscript>He on the recursive lattices

We considered the Heisenberg model on the recursive lattices with multi-spin interaction in a strong magnetic field as an approximation of the two-dimensional kagome lattice, as well as hexagonal recursive lattices as an approximation of triangular lattice, for solid ³He. In a strong magnetic field it is possible to approximate the Heisenberg model with the Izing one. Using dynamic approach, we obtain exact recursion relations for partition functions. Diagrams of the magnetization versus external magnetic field with different spin-exchange parameters and temperatures are presented. Magnetization plateaux, bifurcation points, and doublings are obtained.     

光折变光子晶格中空间二次谐波的产生

用干涉法在自散焦光折变晶体 LiNbO₃：Fe中写入光子晶格的动态过程中，发现了双光束干涉条纹一分为二，四光束干涉点阵一分为四的分裂现象. 研究证明：这是干涉条纹空间频率的倍频现象，是入射的干涉光场与写入的光子晶格之间相互作用的结果. 本实验说明利用光折变效应可以容易地实现干涉光场空间频率的倍频和空间高次谐波的产生，并可利用产生的空间谐波感应出二倍频和高倍频的光折变光子晶格. 关键词： 光折变晶体 光子晶格 空间谐波     

三体相互作用下Bessel型光晶格中物质波孤立子的稳定性研究

研究了两体和三体相互作用空间调制情形下Bessel型光晶格中准二维玻色-爱因斯坦凝聚体系中物质波孤立子的稳定性. 利用标准的变分法程序, 得出体系有效势能的表达式, 进而根据有效势能结构给出了体系的稳定性条件. 结果表明, 在有Bessel型光晶格和没有Bessel型光晶格的情况下, 体系均能形成稳定的孤立子解, 但是有晶格参与时, 体系有很大范围的稳定区间. 另外, 稳定性受两体相互作用和三体相互作用共同支配, 其中两体相互作用对体系的稳定性起主导作用, 三体相互作用和相互作用的空间调制只对稳定性起调节作用, 但是在特定情况下, 必须要有三体相互作用或者相互作用空间调制的参与才能形成稳定的孤立子解.     

三体相互作用下Bessel型光晶格中物质波孤立子的稳定性研究

研究了两体和三体相互作用空间调制情形下Bessel型光晶格中准二维玻色-爱因斯坦凝聚体系中物质波孤立子的稳定性.利用标准的变分法程序,得出体系有效势能的表达式,进而根据有效势能结构给出了体系的稳定性条件.结果表明,在有Bessel型光晶格和没有Bessel型光晶格的情况下,体系均能形成稳定的孤立子解,但是有晶格参与时,体系有很大范围的稳定区间.另外,稳定性受两体相互作用和三体相互作用共同支配,其中两体相互作用对体系的稳定性起主导作用,三体相互作用和相互作用的空间调制只对稳定性起调节作用,但是在特定情况下,必须要有三体相互作用或者相互作用空间调制的参与才能形成稳定的孤立子解.     

Re-entrant phase transitions of the Blume-Emery-Griffiths model

We have investigated the spin-1 Ising model on the simple cubic lattice with bilinear, biquadratic interaction and anisotropic energy (BEG model). We have been specially interested in the case of antiferro biquadratic interaction, because the interaction will cause the competition with bilinear interaction and anisotropy. A two-sublattice ordering, so called the staggered quadrupole (SQ) phase, occurs as long as biquadratic interaction is negative large enough. We have obtained a full phase diagram in the whole interaction parameter space (for the positive bilinear interaction) by the Bethe approximation, and found several kinds of phase transitions, such as successive, re-entrant and double re-entrant transitions. These transitions are also confirmed by Monte Carlo simulations on simple cubic lattices.     

Interaction-dependent temperature effects in Bose-Fermi mixtures in optical lattices

We present a quantitative finite temperature analysis of a recent experiment with Bose-Fermi mixtures in optical lattices, in which the dependence of the coherence of bosons on the interspecies interaction was analyzed. Our theory reproduces the characteristics of this dependence and suggests that intrinsic temperature effects play an important role in these systems. Namely, under the assumption that the ramping up of the optical lattice is an isentropic process, adiabatic temperature changes of the mixture occur that depend on the interaction between bosons and fermions. Matching the entropy of two regimes-no lattice on the one hand and deep lattices on the other-allows us to compute the temperature in the lattice and the visibility of the quasimomentum distribution of the bosonic atoms, which we compare to the experiment.     

Nonlinear wave interaction in photonic band gap materials

We present detailed analytical and numerical studies of nonlinear wave interaction processes in one-dimensional (1D) photonic band gap (PBG) materials with a Kerr nonlinearity. We demonstrate that some of these processes provide efficient mechanisms for dynamically controlling so-called gap-solitons. We derive analytical expressions that accurately determine the phase shifts experienced by nonlinear waves for a large class of non-resonant interaction processes. We also present comprehensive numerical studies of inelastic interactions, and show that rather distinct regimes of interaction exist. The predicted effects should be experimentally observable, and can be utilized for probing the existence and parameters of gap solitons. Our results are directly applicable to other nonlinear periodic structures such as Bose–Einstein condensates in optical lattices.     

Periodic solutions for a class of nonlinear lattices

Exact periodic solutions of the equation of motion have been found for a class of one-dimensional nonlinear lattices with nearest neighbour interaction. As particular cases, our class contains the Fermi-Pasta-Ulam and the Toda lattices.     

Superlight small bipolarons in the presence of a strong Coulomb repulsion

We study a lattice bipolaron on a staggered triangular ladder and triangular and hexagonal lattices with both long-range electron-phonon interaction and strong Coulomb repulsion using a novel continuous-time quantum Monte Carlo algorithm to solve the two-particle Coulomb-Fr?hlich model. The algorithm is preceded by an exact integration over phonon degrees of freedom, and as such is extremely efficient. The bipolaron effective mass and radius are computed. Bipolarons on lattices constructed from triangular plaquettes have a novel crablike motion, and are small but very light over a wide range of parameters. We discuss the conditions under which such particles may form a Bose-Einstein condensate with high transition temperature, proposing a route to room temperature superconductivity.     

Anti-ferroelectric polarization transitions in quantum-dot-quantum-well arrays

With the improvement in fabrication techniques it is now possible to produce atom-like semiconductor structures with unique electronic properties. This makes possible periodic arrays of nanostructures in which the Coulomb interaction, polarizability and tunneling may all be varied. This theoretical study investigates the collective properties of 2D arrays and 3D face-centered cubic lattices of singly charged nanospherical shells, sometimes called 'quantum dot-quantum wells' or 'core-shell quantum dots'. We find that, for square arrays, the classical ground state is an Ising anti-ferroelectric (AFE), while the quantum ground state undergoes a transition from a uniform state to an AFE. The triangular lattice, in contrast, displays properties characteristic of frustration. Three-dimensional face-centered cubic lattices polarize in planes, with each layer alternating in direction. We discuss the possible experimental signals of these transitions.     

Superfrustration of charge degrees of freedom

We review recent results, obtained with P. Fendley, on frustration of quantum charges in lattice models for itinerant fermions with strong repulsive interactions. A judicious tuning of kinetic and interaction terms leads to models possessing supersymmetry. In such models frustration takes the form of what we call superfrustration: an extensive degeneracy of supersymmetric ground states. We present a gallery of examples of superfrustration on a variety of 2D lattices.     

Exploiting quantum parallelism to simulate quantum random many-body systems

We present an algorithm that exploits quantum parallelism to simulate randomness in a quantum system. In our scheme, all possible realizations of the random parameters are encoded quantum mechanically in a superposition state of an auxiliary system. We show how our algorithm allows for the efficient simulation of dynamics of quantum random spin chains with known numerical methods. We propose an experimental realization based on atoms in optical lattices in which disorder could be simulated in parallel and in a controlled way through the interaction with another atomic species.     

一维光晶格中超流Fermi气体基态性质的研究

研究了一维光晶格中超流Fermi气体基态解的性质.在平均场理论框架下,利用超流Fermi体系中原子间相互作用能与晶格势能相互平衡的条件,得到了一维光晶格中超流Fermi气体在整个BEC-BCS跨越区的一组基态解,给出了基态的原子数密度空间分布、总原子数和能量.进一步对系统从BEC端转变到BCS端时的基态解性质进行了深入分析和对比.结果表明,一维光晶格中超流Fermi气体基态分布具有一些特殊的性质,由于Fermi压力,相比而言超流Fermi气体在BCS端的基态原子数密度空间分布较为扩展,平均能量明显偏高.     

Entropy of a one-dimensional mixed lattice gas

This paper deals with the grand canonical entropy of a lattice gas mixture. The entropy is a function of the multisite densities corresponding to the interaction pattern of the system in question. It is first evaluated for a nearest-neighborinteraction, one-dimensional simple lattice gas to show how the structure of bulk fluid is locally maintained. Generalization requires one set of interrelations among multisite densities presented in closed form for an arbitrary lattice, and one set between Boltzmann factors and multisite densities which is written down for simply connected lattices. Application is made to two-row lattices, which turn out to have local behavior from this viewpoint, as do all single-row or Bethe lattices with complete range-p interactions. Nonlocal examples are also given, and suggestions made for approximation sequences in general lattices.