Optical flux lattices for ultracold atomic gases

We show that simple laser configurations can give rise to "optical flux lattices," in which optically dressed atoms experience a periodic effective magnetic flux with high mean density. These potentials lead to narrow energy bands with nonzero Chern numbers. Optical flux lattices will greatly facilitate the achievement of the quantum Hall regime for ultracold atomic gases.     

Superfluidity of Bose Einstein condensates in ultracold atomic gases

Liquid helium 4 had been the only bosonic superfluid available in experiments for a long time. This situation was changed in 1995, when a new superfluid was born with the realization of the Bose–Einstein condensation in ultracold atomic gases. The liquid helium 4 is strongly interacting and has no spin; there is almost no way to change its parameters,such as interaction strength and density. The new superfluid, Bose–Einstein condensate(BEC), offers various advantages over liquid helium. On the one hand, BEC is weakly interacting and has spin degrees of freedom. On the other hand, it is convenient to tune almost all the parameters of a BEC, for example, the kinetic energy by spin–orbit coupling, the density by the external potential, and the interaction by Feshbach resonance. Great efforts have been devoted to studying these new aspects, and the results have greatly enriched our understanding of superfluidity. Here we review these developments by focusing on the stability and critical velocity of various superfluids. The BEC systems considered include a uniform superfluid in free space, a superfluid with its density periodically modulated, a superfluid with artificially engineered spin–orbit coupling, and a superfluid of pure spin current. Due to the weak interaction, these BEC systems can be well described by the mean-field Gross–Pitaevskii theory and their superfluidity, in particular critical velocities, can be examined with the aid of Bogoliubov excitations. Experimental proposals to observe these new aspects of superfluidity are discussed.     

Off-resonant light scattering from ultracold gases in optical lattices

We examine the possibility to study the statistical properties of trapped ultracold bosons with light scattering. We derive general effective hamiltonian and show that the spectrum of scattered photons contains information about density-density correlations. As a specific example we discuss light scattering as a potential tool to probe the Mott transition in optical lattice and Anderson localization in incommensurate superlattice.     

Vortex lattices in rotating atomic Bose gases with non-local interactions

We study the groundstates of rotating atomic Bose gases with non-local interactions. We focus on the weak-interaction limit of a model involving s- and d-wave interactions. With increasing d-wave interaction, the mean-field groundstate undergoes a series of transitions between vortex lattices of different symmetries (triangular, square, “stripe” and “bubble” crystal phases). We discuss the stability of these phases to quantum fluctuations. Using exact diagonalization studies, we show that with increasing d-wave interaction, the incompressible Laughlin state at filling factor ν=1/2 is replaced by compressible stripe and bubble states.     

Quench dynamics of ultracold atoms in one-dimensional optical lattices with artificial gauge fields

We study the quench dynamics of noninteracting ultracold atoms loaded in one-dimensional(1D) optical lattices with artificial gauge fields, which are modeled by lattices with complex hopping coefficients. After suddenly changing the hopping coefficient, time evolutions of the density distribution, momentum distribution, and mass current at the center are studied for both finite uniform systems and trapped systems. Effects of filling factor, system size, statistics, harmonic trap, and phase difference in hopping are identified, and some interesting phenomena show up. For example, for a finite uniform fermionic system shock and rarefaction wave plateaus are formed at two ends, whose wave fronts move linearly with speed equaling to the maximal absolute group velocity. While for a finite uniform bosonic system the whole density distribution moves linearly at the group velocity. Only in a finite uniform fermionic system there can be a constant quasisteady-state current, whose amplitude is decided by the phase difference and filling factor. The quench dynamics can be tested in ultracold atoms with minimal modifications of available experimental techniques, and it is a very interesting and fundamental example of the transport phenomena and the nonequilibrium dynamics.     

Bose gases in one-dimensional harmonic trap

Thermodynamic quantities, occupation numbers and their fluctuations of a one-dimensional Bose gas confined by a harmonic potential are studied using different ensemble approaches. Combining number theory methods, a new approach is presented to calculate the occupation numbers of different energy levels in microcanonical ensemble. The visible difference of the ground state occupation number in grand-canonical ensemble and microcanonical ensemble is found to decrease by power law as the number of particles increases.     

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.     

Einstein-Podolsky-Rosen correlations of ultracold atomic gases

We demonstrate that collective continuous variables of two species of trapped ultracold bosonic gases can be Einstein-Podolsky-Rosen-correlated (entangled) via inherent interactions between the species. We propose two different schemes for creating these correlations--a dynamical scheme and a static scheme analogous to two-mode squeezing in quantum optics. We quantify the correlations by using known measures of entanglement and study the effect of finite temperature on these quantum correlations.     

Phase fluctuations in atomic Bose gases

We improve on the Popov theory for partially Bose-Einstein condensed atomic gases by treating the phase fluctuations exactly. As a result, the theory becomes valid in arbitrary dimensions and is able to describe the low-temperature crossover between three-, two-, and one-dimensional Bose gases, which is currently being explored experimentally. We consider both homogeneous and trapped Bose gases.     

Dynamical soliton structures in one-dimensional lattices

The dynamics of the one-dimensional incommensurate crystals is investigated. It is shown that the moving chain can be considered as a dynamical soliton superstructure, the sample boundary being the source of solitons. The results based on Frenkel-Kontorowa model are applied to the Josephson junctions, superconducting films with thickness modulation, etc. The “current-voltage” characteristics are calculated. The critical behaviour is investigated.     

Local pair correlations in one-dimensional Bose gases

We measure photoassociation rates in one-dimensional Bose gases, and so determine the local pair correlation function over a wide range of coupling strengths. As bosons become more strongly coupled, we observe a tenfold decrease in their wave function overlap, thus directly observing the fermionization of bosons.     

Ground-state properties of interacting two-component Bose gases in a one-dimensional harmonic trap

We study ground-state properties of interacting two-component boson gases in a one-dimensional harmonic trap by using the exact numerical diagonalization method. Based on numerical solutions of many-body Hamiltonians, we calculate the ground-state density distributions in the whole interaction regime for different atomic number ratio, intra- and inter-atomic interactions. For the case with equal intra- and inter-atomic interactions, our results clearly display the evolution of density distributions from a Bose condensate distribution to a Fermi-like distribution with the increase of the repulsive interaction. Particularly, we compare our result in the strong interaction regime to the exact result in the infinitely repulsive limit which can be obtained by a generalized Bose-Fermi mapping. We also discuss the general case with different intra- and inter-atomic interactions and show the rich configurations of the density profiles.     

Pseudogap phenomena in ultracold atomic Fermi gases

The pairing and superfluid phenomena in a two-component ultracold atomic Fermi gas is an analogue of Cooper pairing and superconductivity in an electron system, in particular, the high Tc superconductors. Owing to the various tunable parameters that have been made accessible experimentally in recent years, atomic Fermi gases can be explored as a prototype or quantum sinmlator of superconductors. It is hoped that, utilizing such an analogy, the study of atomic Fermi gases may shed light to the mysteries of high Tc superconductivity. One obstacle to the ultimate understand- ing of high Tc superconductivity, from day one of its discovery, is the anomalous yet widespread pseudogap phenomena, for which a consensus is yet to be reached within the physics comnnmity, after over 27 years of intensive research efforts. In this article, we shall review the progress in the study of pseudogap phenomena in atomic Fermi gases in terms of both theoretical understanding and experimental observations. We show that there is strong, unambiguous evidence for the existence of a pseudogap in strongly interacting Fermi gases. In this context, we shall present a pairing fuctuation theory of the pseudogap physics and show that it is indeed a strong candidate theory for high Tc superconductivity.     

Magnetic properties of commensurate Bose-Bose mixtures in one-dimensional optical lattices

We investigate magnetic properties of strongly interacting bosonic mixtures confined in one dimensional geometries, focusing on recently realized ⁸⁷Rb-⁴¹K gases with tunable interspecies interactions. By combining analytical perturbation theory results with density-matrix-renormalization group calculations, we provide quantitative estimates of the ground state phase diagram as a function of the relevant microscopic quantities, identifying the more favorable experimental regimes in order to access the various magnetic phases. Finally, we qualitatively discuss the observability of such phases in realistic setups when finite temperature effects have to be considered.     

Topological gapless matters in three-dimensional ultracold atomic gases

Three-dimensional topological gapless matters with gapless degeneracies protected by a topological invariant defined over a closed manifold in momentum space have attracted considerable interest in various fields ranging from condensed matter materials to ultracold atomic gases. As a highly controllable and disorder free system, ultracold atomic gases provide a versatile platform to simulate topological gapless matters. Here, the current progress in studies of topological gapless phenomena in three-dimensional cold atom systems is summarized in the review. It is mainly focused on Weyl points, structured (type-II) Weyl points, Dirac points, nodal rings and Weyl exceptional rings in cold atoms. Since interactions in cold atoms can be controlled via Feshbach resonances, the progress in both superfluids for attractive interactions and non-interacting cold atom gases is reviewed.     

Mott-insulator phase of coupled one-dimensional atomic gases in a two-dimensional optical lattice

We consider the 2D Mott-insulator state of a 2D array of coupled finite size 1D Bose gases. It is shown that the momentum distribution in the lattice plane is very sensitive to the interaction regime in the 1D tubes. In particular, we find that the disappearance of the interference pattern in time-of-flight experiments is a clear consequence of the strongly interacting Tonks-Girardeau regime along the tubes.     

Classification of quantum degenerate regimes in one-dimensional Bose gases

In this paper we address the different regimes of quantum degeneracy in a one-dimensional Bose gas taking into consideration some parameters that are readily accessible in the experiment. We pay particular attention to the tunability of the trap anisotropy and the number of particles in the system.     

冷原子物理中的一维少体问题

作为构成量子多体系统的基本单元,一维少体系统的研究不仅可以在理论上为多体系统的量子关联及动力学等性质提供更为基本的理解,也可以为实验上制备多体系统提供更加方便和功能更加全面的方法.本文回顾了冷原子物理中一维少体系统最新的实验和理论进展.首先介绍了少体实验中实现的谐振子势阱中确定原子数的精确制备,亚稳态势阱和双阱系统中原子的隧穿,以及强相互作用下等效自旋链的实验结果.然后深度解析了理论研究方面,特别是基于精确可解模型的一些重要结果,包括亚稳态势阱中相互作用原子的隧穿概率,以及相应实验上常见势阱的能谱分析、密度分布、隧穿动力学以及强相互作用极限下的有效自旋链模型等.     

光学微腔中一维费米气的磁性关联特性

对于准一维两组分费米气与光学微腔耦合的系统,证明了微腔光子的超辐射可以驱动原子系统的磁性转变,该磁性转变与原子的失谐以及费米子的填充数密切相关.对于无相互作用原子气,在超辐射相区内平均场近似合理.基于该近似,分析了不同的填充和失谐情况下体系的静态自旋结构因子,由此刻画出腔光子协助的磁性关联转变,并得到了依赖于微腔参数的相图.最后,对可行的实验参数做了相关讨论.     

Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in “artificial” magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed.

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