Spinor bosonic atoms in optical lattices: symmetry breaking and fractionalization

We study superfluid and Mott insulator phases of cold spin-1 Bose atoms with antiferromagnetic interactions in an optical lattice, including a usual polar condensate phase, a condensate of singlet pairs, a crystal spin nematic phase, and a spin singlet crystal phase. We suggest a possibility of exotic fractionalized phases of spinor Bose-Einstein condensates and discuss them in the language of Z2 lattice gauge theory.     

Condensation state of ultra-cold Bose atomic gases with pure gradient interactions with negative coefficient

Within the framework of quantum field theory, we find that uniform Bose atomic gases with pure gradient interactions with negative coefficient can undergo a Bardeen-Cooper-Schrieffer (BCS) condensation below a critical temperature. In the BCS condensation state, bare atoms with opposite wave vectors are bound into pairs, and unpaired bare atoms are transformed into a new kind of quasi-particle, i.e. the dressed atom. The atom-pair system is a condensate or a superfluid and the dressed-atom system is a normal fluid. At absolute zero temperature the condensate possesses a lowest negative energy. When the total interaction strength of atoms is large enough, the energy of the condensate is a monotonically increasing function of temperature and interaction strength. The critical temperature and the effective mass of dressed atoms are derived analytically. The transition from the BCS condensation state to the normal state is a first-order phase transition.     

Ground-states and rotational properties of a spin–orbit-coupled spin-1 Bose–Einstein condensate in a concentrically coupled toroidal trap

We investigate the ground states of an antiferromagnetic spin-1 Bose–Einstein condensate with spin–orbit coupling in a concentrically coupled toroidal trap. A new necklace-type state with double-ring structure is created in the system due to the spin–orbit coupling. The petal number of the necklace state is increased with enhancing the strength of the spin–orbit coupling. When the rotation is introduced, the condensate can be dragged into the outer trough of the trap by increasing the rotation frequency, which makes it possible to realize the exotic ground state combined by the necklace state at the inner trough and the persistent flow at the outer one. Once the two troughs of the toroidal trap are populated by the persistent flow at the specific effective interactions between atoms, the hidden vortices may occur in the central region of the trap and at the barrier between the two troughs. In addition, the visible vortex with the laminar structure can be generated under the more effective atomic interaction.     

Dynamics of Bec Mixtures Loaded into the Optical Lattice in the Presence of Linear Inter-Component Coupling

We consider dynamics of a two-component Bose–Einstein condensate, where the components correspond to different hyperfine states of the same sort of atoms. External microwave radiation leads to resonant transitions between the states. The condensate is loaded into the optical lattice. We invoke the tight-binding approximation and examine the interplay of spatial and internal dynamics of the mixture. We show that internal dynamics qualitatively depends on the intra-component interaction strength and the phase configuration of the initial state. We focus attention on two intriguing phenomena occurring at certain values of the parameters. The first phenomenon is the spontaneous synchronization of Rabi oscillations running inside neighboring lattice sites. The other one is demixing of the condensate with formation of immiscible solitons at sufficiently strong nonlinearity. Demixing is preceded by the transient regime with highly irregular behavior of the mixture.     

Two-component Bose-Einstein condensates with a large number of vortices

We consider the condensate wave function of a rapidly rotating two-component Bose gas with an equal number of particles in each component. If the interactions between like and unlike species are very similar (as occurs for two hyperfine states of (87)Rb or (23)Na) we find that the two components contain identical rectangular vortex lattices, where the unit cell has an aspect ratio of sqrt[3], and one lattice is displaced to the center of the unit cell of the other. Our results are based on an exact evaluation of the vortex lattice energy in the large angular momentum (or quantum Hall) regime.     

Exotic vortex structures of the dipolar Bose–Einstein condensates trapped in harmonic-like and toroidal potential

Based on the tunable intensity and waist of Gaussian laser, harmonic-like and toroidal potentials can be achieved and the ground-state properties of the dipolar Bose–Einstein condensate (BEC) trapped in such potentials are investigated. It is found that, in the harmonic-like potential, the singly and doubly quantized vortices can exist in the scale condensate and translate respectively into vortex pairs and triangular vortex lattice with increasing dipole–dipole interaction (DDI). Especially, the sandwich-like structure can be observed in the ground-state density profiles by tuning the direction and strength of DDI for some rotating frequency. In the toroidal potential, the competition between the inter-component interaction and DDI can induce the transition between immiscible and miscible states, and results in the structures of a doubly quantized vortex surrounded by a vortex ring. It is worth emphasizing that, with the increasing of DDI, the doubly quantized vortex in the harmonic-like potential becomes two singly quantized vortices, while in the toroidal potential it is no happen due to the presence of Gaussian barrier.     

Dynamics of straight vortex filaments in a Bose–Einstein condensate with the Gaussian density profile

The dynamics of interacting quantized vortex filaments in a rotating Bose–Einstein condensate existing in the Thomas–Fermi regime at zero temperature and obeying the Gross–Pitaevskii equation has been considered in the hydrodynamic “nonelastic” approximation. A noncanonical Hamilton equation of motion for the macroscopically averaged vorticity has been derived for a smoothly inhomogeneous array of filaments (vortex lattice) taking into account spatial nonuniformity of the equilibrium density of the condensate, which is determined by the trap potential. The minimum of the corresponding Hamiltonian describes the static configuration of the deformed vortex lattice against the preset density background. The condition of minimum can be reduced to a nonlinear second-order partial differential vector equation for which some exact and approximate solutions are obtained. It has been shown that if the condensate density has an anisotropic Gaussian profile, the equation of motion for the averaged vorticity has solutions in the form of a vector exhibiting a nontrivial time dependence, but homogeneous in space. An integral representation has also been obtained for the matrix Green function that determines the nonlocal Hamiltonian of a system of several quantized vortices of an arbitrary shape in a Bose–Einstein condensate with the Gaussian density. In particular, if all filaments are straight and oriented along one of the principal axes of the ellipsoid, we have a finitedimensional reduction that can describe the dynamics of the system of pointlike vortices against an inhomogeneous background. A simple approximate expression is proposed for the 2D Green function with an arbitrary density profile and is compared numerically with the exact result in the Gaussian case. The corresponding approximate equations of motion, describing the long-wavelength dynamics of interacting vortex filaments in condensates with a density depending only on transverse coordinates, have been derived.     

On the theory of slowing down gracefully

We discuss the transport of a tracer particle through the Bose?CEinstein condensate of a Bose gas. The particle interacts with the atoms in the Bose gas through two-body interactions. In the limiting regime where the particle is very heavy and the Bose gas is very dense, but very weakly interacting (??mean-field limit??), the dynamics of this system corresponds to classical Hamiltonian dynamics. We show that, in this limit, the particle is decelerated by emission of gapless modes into the condensate (Cerenkov radiation). For an ideal gas, the particle eventually comes to rest. In an interacting Bose gas, the particle is decelerated until its speed equals the propagation speed of the Goldstone modes of the condensate. This is a model of ??Hamiltonian friction??. It is also of interest in connection with the phenomenon of ??decoherence?? in quantum mechanics. This note is based on work we have carried out in collaboration with D Egli, I M Sigal and A Soffer.     

Producing Bose-Einstein condensates using optical lattices

We relate the entropies of ensembles of atoms in optical lattices to atoms in simple traps. We then determine which ensembles of lattice-bound atoms will adiabatically transform into a Bose condensate. This shows a feasible approach to Bose condensation without evaporative cooling.     

The Higgs boson in fractal quantum systems with active nanoelements

Stochastic deformation and stress fields within a fractal multilayer nanosystem are investigated theoretically and by numerical modeling. It is shown that the averaged displacement functions of lattice nodes are complex. Their behavior changes from regular to stochastic when the control parameters are altered. A set of ultracold ²³Na atoms in an optical trap is chosen as the active nanoelement. It is demonstrated that certain physical properties (rate and quantization of the flow; hysteresis) of elementary excitations such as a vortex–antivortex pair are associated with the influence of a superfluid Bose–Einstein condensate (where a Higgs boson is the elementary excitation).     

自旋轨道耦合的23Na自旋-1玻色-爱因斯坦凝聚体中的涡旋斑图的研究

利用阻尼映射Gross-Pitaevkii方程, 研究了二维体系中自旋轨道耦合的 ²³Na自旋-1 玻色-爱因斯坦凝聚体中的涡旋斑图, 探索自旋轨道耦合强度对涡旋斑图的影响. 研究发现, 较弱的自旋轨道耦合就可以完全破坏不考虑自旋轨道耦合情况下出现的周期性涡旋晶格; 在自旋轨道耦合较强的情况下, 各自旋态的涡旋易形成涡旋组, 它们绕凝聚体中心形成花瓣状涡旋斑图. 关键词： 玻色-爱因斯坦凝聚体 自旋 涡旋     

Vortex lattice formation in Bose-Einstein condensates

We show that the formation of a vortex lattice in a weakly interacting Bose condensed gas can be modeled with the nonlinear Schr?dinger equation for both T=0 and finite temperatures without the need for an explicit damping term. Applying a weak rotating anisotropic harmonic potential, we find numerically that the turbulent dynamics of the field produces an effective dissipation of the vortex motion and leads to the formation of a lattice. For T=0, this turbulent dynamics is triggered by a rotational dynamic instability of the condensate. For finite temperatures, noise is present at the start of the simulation and allows the formation of a vortex lattice at a lower rotation frequency, the Landau frequency. These two regimes have different vortex dynamics. We show that the multimode interpretation of the classical field is essential.     

Dynamical instability of a rotating dipolar Bose-Einstein condensate

We analyze the hydrodynamic solutions for a dilute Bose-Einstein condensate with long-range dipolar interactions in a rotating, elliptical harmonic trap. The static solutions and their regimes of dynamical instability vary nontrivially with the strength of the dipolar interactions. We comprehensively map out this behavior, and, in particular, examine the experimental routes toward unstable dynamics, which, in analogy to conventional condensates, may lead to vortex lattice formation.     

The stability of a quantized vortex in a dilute Bose gas confined to a toroidal trap

We investigate the stability of a quantized vortex in a weakly interacting Bose gas, trapped in a toroidal container with hard walls. Calculating the excitation spectrum numerically and determining the stability condition by the Landau criterion, we examine the effect of reducing the confinement region of the condensate on the vortex stability. We find that tight confinement of the condensate increases the stabilization of the quantized vortex because an increase in the zero sound velocity due to tight confinement prevents the emergence of the elementary excitation which breaks superfluidity of the Bose system. We also discuss the experimental setup to observe such an effect.     

Transport of cold atoms in optical lattices

The work discusses transport of cold atoms in optical lattices. Two related but different problems are considered: interacting Bose atoms subject to a static field (i.e., the atoms in a tilted lattice); and non-interacting atoms in a tilted lattice in the presence of a buffer gas. For these two systems we found, respectively: periodic, quasiperiodic, or decaying Bloch oscillations, as it depends on the strength of atom-atom interactions and the magnitude of the static field; diffusive directed current of atoms, similar to the electron current in ordinary conductors.     

Vortex lattices in planar Bose-Einstein condensates with dipolar interactions

In this Letter, we investigate the effects of dipole-dipole interactions on the vortex lattices in fast rotating Bose-Einstein condensates. For single planar condensate, we show that the triangular lattice structure will be unfavorable when the s-wave interaction is attractive and exceeds a critical value. It will first change to a square lattice, and then become more and more flat with the increase of s-wave attraction, until the collapse of the condensate. For an array of coupled planar condensates, we discuss how the dipole-dipole interactions between neighboring condensates compete with quantum tunneling processes, which affects the relative displacement of two neighboring vortex lattices and leads to the loss of phase coherence between different condensates.     

Delocalization in two-dimensional disordered Bose systems and depinning transition in the vortex state in superconductors

We investigate a two-dimensional (2D) Bose system with the long range interactions in the presence of disorder. Formation of the bound states at strong impurity sites gives rise to a depletion of the superfluid density. We predict the intermediate superfluid state where the condensate and localized bosons are present simultaneously. We find that interactions suppress localization and that with the increase of the boson density the system experiences a sharp delocalization crossover into a state where all bosons are delocalized. We map our results onto a 3D system of vortices in type II superconductors in the presence of columnar defects; the intermediate superfluid state maps to an intermediate vortex liquid where vortex liquid neighbors pinned vortices. We predict the depinning crossover within the vortex liquid and depinning induced vortex lattice-Bose glass melting.     

Experimental realization of two-dimensional single-layer ultracold gases of 87Rb in an accordion lattice

We experimentally realize two-dimensional (2D) single-layer ultracold gases of ⁸⁷Rb by dynamically tuning the periodicity of a standing wave, known as accordion lattice. In order to load ⁸⁷Rb Bose—Einstein condensate into single dark fringe node of the blue detuning optical lattice, we reduce the lattice periodicity from 26.7 μ to 3.5 μ with the help of an acousto-optic deflector (AOD) to compress the three-dimensional BEC adiabatically into a flat and uniform quasi-2D single-layer. We describe the experimental procedure of the atoms loading into the accordion lattice in detail and present the characteristics of the quasi-2D ultracold gases. This setup provides an important platform for studying in- and out-of equilibrium physics, phase transition and 2D topological matter.     

Experimental study of coupling Bose–Einstein condensates into weakly non-trapping and trapping states

We study the production of an atom laser from a Bose–Einstein condensate using radio-frequency out-coupling. Single frequency coupling from the Bose–Einstein condensate leads to unstable production of an atom laser due to the extreme sensitivity of this process to magnetic field fluctuations. The extent of this experimental instability is quantified. Stable, repeatable production of an atom laser is achieved by the frequency modulation of the coupling, which forms a frequency comb across the condensate. Different regimes of modulated coupling are discussed. In addition the coupling of atoms into a weakly trapping state is studied. The oscillation frequency of this state in the vertical direction is measured. Preliminary results indicating qualitative difference between condensate and thermal cloud coupling are presented.     

Application of potential harmonic expansion method to BEC: Thermodynamic properties of trapped23Na atoms

We adopt the potential harmonics expansion method for anab initio solution of the many-body system in a Bose condensate containing interacting bosons. Unlike commonly adopted mean-field theories, our method is capable of handling two-body correlation properly. We disregard three- and higher-body correlations. This simplification is ideally suited to dilute Bose Einstein condensates, whose number density is required to be so small that the interparticle separation is much larger than the range of two-body interaction to avoid three- and higher-body collisions, leading to the formation of molecules and consequent instability of the condensate. In our method we can incorporate realistic finite range interactions. We calculate energies of low-lying states of a condensate containing²³Na atoms and some thermodynamical properties of the condensate.