Phase-fluctuating 3D Bose-Einstein condensates in elongated traps

We find that in very elongated 3D trapped Bose gases, even at temperatures far below the BEC transition temperature T(c), the equilibrium state will be a 3D condensate with fluctuating phase (quasicondensate). At sufficiently low temperatures the phase fluctuations are suppressed and the quasicondensate turns into a true condensate. The presence of the phase fluctuations allows for extending thermometry of Bose-condensed gases well below those established in current experiments.     

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.     

Spontaneous Formation of Antiferromagnetic Vortex Lattice in a Fast Rotating BEC with Dipole Interactions

When a Bose-Einstein condensate is set to rotate,superfluid vortices will be formed,which finally condense into a vortex lattice as the rotation frequency further increases.We show that the dipole-dipole interactions renormalize the short-range interaction strength and result in a distinction between interactions of parallel-polarized atoms and interactions of antiparallel-polarized atoms.This effect may lead to a spontaneous breakdown of the rapidly rotating Bose condensate into a novel anti-ferromagnetic-like vortex lattice.The upward-polarized Bose condensate forms a vortex lattice,which is staggered against a downward-polarized vortex lattice.A phase diagram related to the coupling strength is obtained.     

Analytical approach to quantum phase transitions of ultracold Bose gases in bipartite optical lattices using the generalized Green’s function method

In order to investigate the quantum phase transitions and the time-of-flight absorption pictures analytically in a systematic way for ultracold Bose gases in bipartite optical lattices, we present a generalized Green’s function method. Utilizing this method, we study the quantum phase transitions of ultracold Bose gases in two types of bipartite optical lattices, i.e., a hexagonal lattice with normal Bose–Hubbard interaction and a d-dimensional hypercubic optical lattice with extended Bose–Hubbard interaction. Furthermore, the time-of-flight absorption pictures of ultracold Bose gases in these two types of lattices are also calculated analytically. In hexagonal lattice, the time-of-flight interference patterns of ultracold Bose gases obtained by our analytical method are in good qualitative agreement with the experimental results of Soltan-Panahi, et al. [Nat. Phys. 7, 434 (2011)]. In square optical lattice, the emergence of peaks at \(\left( { \pm \frac{\pi }{a}, \pm \frac{\pi }{a}} \right)\) in the time-of-flight absorption pictures, which is believed to be a sort of evidence of the existence of a supersolid phase, is clearly seen when the system enters the compressible phase from charge-density-wave phase.     

Interacting bosons in an optical lattice

A strongly interacting Bose gas in an optical lattice is studied using a hard‐core interaction. Two different approaches are introduced, one is based on a spin‐1/2 Fermi gas with attractive interaction, the other one on a functional integral with an additional constraint (slave‐boson approach). The relation between fermions and hard‐core bosons is briefly discussed for the case of a one‐dimensional Bose gas. For a three‐dimensional gas we identify the order parameter of the Bose‐Einstein condensate through a Hubbard‐Stratonovich transformation and treat the corresponding theories within a mean‐field approximation and with Gaussian fluctuations. This allows us to evaluate the phase diagram, including the Bose‐Einstein condensate and the Mott insulator, the density‐density correlation function, the static structure factor, and the quasiparticle excitation spectrum. The role of quantum and thermal fluctuations are studied in detail for both approaches, where we find good agreement with the Gross‐Pitaevskii equation and with the Bogoliubov approach in the dilute regime. In the dense regime, which is characterized by the phase transition between the Bose‐Einstein condensate and the Mott insulator, we discuss a renormalized Gross‐Pitaevskii equation. This equation can describe the macroscopic wave function of the Bose‐Einstein condensate in the dilute regime as well as close to the transition to the Mott insulator. Finally, we compare the results of the attractive spin‐1/2 Fermi gas and those of the slave‐boson approach and find good agreement for all physical quantities.     

Finite-temperature phase-locking transition in three-dimensional arrays of Josephson coupled Bose–Einstein condensates

We consider theoretically a phase-locking transition in Bose–Einstein condensate in an optical lattice in the regime where system can realized as a three-dimensional Josephson junction array. The coherence between adjacent Bose condensates (trapped in the valleys of the periodic potential) caused by the Josephson tunneling can lead to a phase transition with a global phase coherence at certain critical temperature. Using a model Hamiltonian of Josephson weakly coupled Bose condensates we calculate the critical temperature for the three-dimensional system placed in a simple cubic lattice and discuss the result in the context of system parameters and possible experiments.     

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.     

Superfluidity of mesoscopic Bose gases under varying confinements

The superfluid fraction Ns/N of 27 bosons under varying confinement is investigated at finite temperature using well-known properties of the harmonic oscillator and the microscopic path integral Monte Carlo method. We find that Ns/N (i) is essentially independent of the interaction strength for all temperatures considered, (ii) changes profoundly as the effective dimensionality is varied from three to one dimensional, (iii) is approximately equal to the condensate fraction N0/N for spherical Bose gases, and (iv) deviates dramatically from N0/N for highly elongated Bose gases.     

Reentrant phenomenon in the quantum phase transitions of a gas of bosons trapped in an optical lattice

We calculate the location of the quantum phase transitions of a Bose gas trapped in an optical lattice as a function of effective scattering length a(eff) and temperature T. Knowledge of recent high-loop results on the shift of the critical temperature at weak couplings is used to locate a nose in the phase diagram above the free Bose-Einstein critical temperature T((0))(c), thus predicting the existence of a reentrant transition above T((0))(c), where a condensate should form when increasing a(eff). At zero temperature, the transition to the normal phase produces the experimentally observed Mott insulator.     

Generalized effective-potential Landau theory for the two-dimensional extended Bose-Hubbard model

We analytically study the quantum phase diagrams of ultracold dipolar Bose gases in an optical square lattice at zero temperature by using the generalized effective-potential Landau theory (GEPLT). For a weak nearest-neighbor repulsion, our analytical results are better than the third-order strong-coupling expansion theory calculation. In contrast to a previous quantum Monte Carlo (QMC) simulation, we analytically calculate phase transition boundaries up to the third-order hopping, which are in excellent agreement with QMC simulations for second-order phase transition.     

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).     

Observation of reduced three-body recombination in a correlated 1D degenerate Bose gas

We investigate the correlation properties of a one-dimensional interacting Bose gas by loading a magnetically trapped 87Rb Bose-Einstein condensate (BEC) into a deep two-dimensional optical lattice. We measure the three-body recombination rate for both the BEC in the magnetic trap and the BEC loaded into the optical lattice. The recombination rate coefficient is a factor of 7 smaller in the lattice, which we interpret as a reduction in the local three-body correlation function in the 1D case. This is a signature of correlation intermediate between that of the uncorrelated, phase coherent, 1D, mean-field regime and the strongly correlated Tonks-Girardeau regime.     

谐振子势阱囚禁玻色气体的玻色-爱因斯坦凝聚

基于Thomas-Fermi半经典近似方法研究了谐振子势阱约束下任意维理想玻色气体的玻色-爱因斯坦凝聚(BEC)．导出了玻色气体的BEC转变温度、基态粒子占据比例、内能和热容量等物理量的解析表达式,讨论了空间维度和谐振子势阱的影响．以二维和三维玻色系统为例,数值计算了上述热力学量,并与解析结果进行了对比,二者获得了较好的吻合．     

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.     

谐振子势阱囚禁玻色气体的玻色-爱因斯坦凝聚

基于Thomas-Fermi半经典近似研究了谐振子势阱约束下任意维理想玻色气体的玻色-爱因斯坦凝聚(BEC).导出了玻色气体的BEC转变温度、基态粒子占据比例、内能和热容量等物理量的解析表达式,讨论了空间维度和谐振子势阱的影响.以二维和三维玻色系统为例,数值计算了上述热力学量,并与解析结果进行了对比,二者获得了较好的吻合.     

The role of macroinstrument and microinstrument and of observable quantities in the new conception of thermodynamics

In the first part of the paper, we introduce the concept of observable quantities associated with a macroinstrument measuring the density and temperature and with a microinstrument determining the radius of a molecule and its free path length, and also the relationship between these observable quantities. The concept of the number of degrees of freedom, which relates the observable quantities listed above, is generalized to the case of low temperatures. An analogy between the creation and annihilation operators for pairs (dimers) and the creation and annihilation operators for particles (molecules) is carried out. A generalization of the concept of a Bose condensate is introduced for classical molecules as an analog of an ideal liquid (without attraction). The negative pressure in the liquid is treated as holes (of exciton type) in the density of the Bose condensate. The phase transition gas-liquid is calculated for an ideal gas (without attraction). A comparison with experimental data is carried out. In the other part of the paper, we introduce the concept of new observable quantity, namely, of a pair (a dimer), as a result of attraction between nearest neighbors. We treat in a new way the concepts of Boyle temperature T _B (as the temperature above which the dimers disappear) and of the critical temperature T _c (below which the trimers and clusters are formed). The equation for the Zeno line is interpreted as the relation describing the dependence of the temperature on the density at which the dimers disappear. We calculate the maximal density of the liquid and also the maximal density of the holes. The law of corresponding states is derived as a result of an observation by a macrodevice which cannot distinguish between molecules of distinct gases, and a comparison of theoretical and experimental data is carried out.     

Unusual Destruction and Enhancement of Superfluidity of Atomic Fermi Gases by Population Imbalance in a One-Dimensional Optical Lattice

We study the superfluid behavior of a population imbalanced ultracold atomic Fermi gases with a short range attractive interaction in a one-dimensional(1 D) optical lattice,using a pairing fluctuation theory.We show that,besides widespread pseudogap phenomena and intermediate temperature superfluidity,the superfluid phase is readily destroyed except in a limited region of the parameter space.We find a new mechanism for pair hopping,assisted by the excessive majority fermions,in the presence of continuum-lattice mixing,which leads to an unusual constant Bose-Einstein condensate(BEC) asymptote for T_c that is independent of pairing strength.In result,on the BEC side of unitarity,superfluidity,when it exists,may be strongly enhanced by population imbalance.     

On the Bose–Einstein Condensate of Excitons in Crystals with Defects

Optics and Spectroscopy - The possibility of formation of a Bose–Einstein condensate (BEC) of excitons in a model nonideal lattice of a molecular crystal is considered. The spectrum of...     

Bose Condensates in Interaction with Excitations: A Kinetic Model

This paper deals with mathematical questions for Bose gases below the temperature T _BEC where Bose-Einstein condensation sets in. The model considered is of two-component type, consisting of a kinetic equation for the distribution function of a gas of (quasi-)particles interacting with a Bose condensate, which is described by a Gross-Pitaevskii equation. Existence results and moment estimates are proved in the space-homogeneous, isotropic case.