Strongly interacting ultracold quantum gases

This article reviews recent progresses in ultracold quantum gases, and it includes three subjects which are the Fermi gases across a Feshbach resonance, quantum gases in the optical lattices and the fast rotating quantum gases. In this article, we discuss many basic physics pictures and concepts in quantum gases, for examples, the resonant interaction, universality and condensation in the lowest Landau level; we introduce fundamental theoretical tools for studying these systems, such as mean-field theory for BEC-BCS crossover and for the boson Hubbard model; also, we emphasize the important unsolved problems in the forefront of this field, for instance, the temperature effect in optical lattices.      

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.     

Quantum dynamics in ultracold atomic physics

We review recent developments in the theory of quantum dynamics in ultracold atomic physics, including exact techniques and methods based on phase-space mappings that are applicable when the complexity becomes exponentially large. Phase-space representations include the truncated Wigner, positive-P and general Gaussian operator representations which can treat both bosons and fermions. These phase-space methods include both traditional approaches using a phase-space of classical dimension, and more recent methods that use a non-classical phase-space of increased dimensionality. Examples used include quantum Einstein-Podolsky-Rosen (EPR) entanglement of a four-mode BEC, time-reversal tests of dephasing in single-mode traps, BEC quantum collisions with up to 106 modes and 105 interacting particles, quantum interferometry in a multi-mode trap with nonlinear absorption, and the theory of quantum entropy in phase-space. We also treat the approach of variational optimization of the sampling error, giving an elementary example of a nonlinear oscillator.     

超冷原子中的拉曼增益光栅

为提高光栅的衍射效率,提出了基于主动拉曼效应的超冷原子光栅系统。理论研究表明：通过拉曼增益的空间周期性调节,可有效地将沿垂直光栅方向传播的弱探测光衍射到一级方向,同时零级衍射光将被放大。当系统中引进微波场的原子相干效应时,可以进一步提高光栅的一级衍射效率。在一定的条件下,拉曼增益光栅的一级衍射效率可高于电磁诱导相位光栅的一级衍射效率。该系统可作为高效光开关用于全光网络。     

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.     

超冷原子系综的非高斯纠缠态与精密测量

量子精密测量是基于量子力学的基本原理对特定物理量实施测量,并利用量子效应提高测量精度的交叉科学.随着超冷原子实验技术的发展,超冷原子为量子精密测量提供了一个优异的研究平台.利用发展成熟的量子调控技术,人们可以基于超冷原子系综制备一些新奇的非高斯多粒子纠缠态.基于多体量子干涉,利用这些非高斯纠缠态作为输入,可以实现超越标准量子极限的高精度测量.本文简要综述这一研究领域的进展.     

Analytic calculation of high-order corrections to quantum phase transitions of ultracold Bose gases in bipartite superlattices

We clarify some technical issues in the present generalized effective-potential Landau theory (GEPLT) to make the GEPLT more consistent and complete. Utilizing this clarified GEPLT, we analytically study the quantum phase transitions of ultracold Bose gases in bipartite superlattices at zero temperature. The corresponding quantum phase boundaries are analytically calculated up to the third-order hopping, which are in excellent agreement with the quantum Monte Carlo (QMC) simulations.     

Slow light in ultra-cold atomic gases

We investigate the influence of slow light with an orbital angular momentum on the mechanical motion of ultra-cold atomic gases including both the atomic Bose–Einstein condensates and degenerate Fermi gases. We present a microscopic analysis of the interplay between light and matter and show how slow light can provide an effective magnetic field acting on the electrically neutral atoms.     

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.     

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.

Motto:     

超冷费米气体的膨胀动力学研究新进展

多体系统的非平衡动力学演化是当前物理学中最具挑战性的问题之一.超冷量子费米原子气体具有较强的可控性,是研究多体非平衡动力学的理想系统,可以用来模拟和理解大爆炸后的早期宇宙、重离子碰撞中产生的夸克-胶子以及核物理等动力学.一般多体系统演化是非常复杂的,往往需要利用对称性来研究.利用Feshbach共振可以制备标度不变的费米原子气体:无相互作用和幺正费米量子气体.当远离平衡态时,可利用普适的指数和函数来刻画,其动力学可以通过对系统的时空演化进行标度变换来识别.本文主要介绍近年来强相互作用超冷费米气体的膨胀动力学研究进展,包括原子气体的各向异性展开、标度动力学和Efimovian膨胀动力学.     

RKKY interaction in three-dimensional tilted Dirac and Weyl semimetals

We theoretically investigate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities of the tilted Dirac and Weyl semimetals in three dimensions. In accordance with the untilted scenario, the RKKY interaction contains three terms, namely the Heisenberg term, the Ising term, and the Dzyaloshinsky-Moriya term. The main influence of tilt on the RKKY Hamiltonian is a modulation to the oscillation frequencies of range functions. Our results enrich the knowledge of the magnetic properties of materials with tilted Dirac cones and may see an important application in spintronics.     

Virial expansion for a strongly correlated Fermi system and its application to ultracold atomic Fermi gases

A strongly correlated Fermi system plays a fundamental role in very different areas of physics, from neutron stars, quark–gluon plasmas, to high temperature superconductors. Despite the broad applicability, it is notoriously difficult to be understood theoretically because of the absence of a small interaction parameter. Recent achievements of ultracold trapped Fermi atoms near a Feshbach resonance have ushered in enormous changes. The unprecedented control of interaction, geometry and purity in these novel systems has led to many exciting experimental results, which are to be urgently understood at both low and finite temperatures. Here we review the latest developments of virial expansion for a strongly correlated Fermi gas and their applications on ultracold trapped Fermi atoms. We show remarkable, quantitative agreements between virial predictions and various recent experimental measurements at about the Fermi degenerate temperature. For equations of state, we discuss a practical way of determining high-order virial coefficients and use it to calculate accurately the long-sought third-order virial coefficient, which is now verified firmly in experiments at ENS and MIT. We discuss also virial expansion of a new many-body parameter—Tan’s contact. We then turn to less widely discussed issues of dynamical properties. For dynamic structure factors, the virial prediction agrees well with the measurement at the Swinburne University of Technology. For single-particle spectral functions, we show that the expansion up to the second order accounts for the main feature of momentum-resolved rf-spectroscopy for a resonantly interacting Fermi gas, as recently reported by JILA. In the near future, more practical applications with virial expansion are possible, owing to the ever-growing power in computation.     

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.     

Matter wave interference of dilute Bose gases in the critical regime

Ultra-cold atomic gases provide a new chance to study the universal critical behavior of phase transition. We study theoretically the matter wave interference for ultra-cold Bose gases in the critical regime. We demonstrate that the interference in the momentum distribution can be used to extract the correlation in the Bose gas. A simple relation between the interference visibility and the correlation length is found and used to interpret the pioneering experiment about the critical behavior of dilute Bose gases [Science 315 1556(2007)]. Our theory paves the way to experimentally study various types of ultra-cold atomic gases with the means of matter wave interference.     

Nonequilibrium phase transition in stochastic lattice gases: Simulation of a three-dimensional system

We report results of computer simulations of a three-dimensional lattice gas of interacting particles subject to a uniform external fieldE. The dynamics of the system is given by hoppings of particles to nearby empty sites with rates biased for jumps in the direction ofE. As for the two-dimensional system we find that here too there exists a critical temperature,T _c (E) such that forT < T _c (E) the systems orders in a very anisotropic phase with striplike typical configurations parallel to the field.T _c (E) increases withE but substantially less strongly than in two dimensions. There is a break in the slope of the saturation current atT _c (E). Our data are consistent with the critical exponent being mean field.     

On the derivation of the entropy of ideal quantum gases confined in a three-dimensional harmonic potential

In this work,the entropy functions of ideal quantum gases in a three-dimensional harmonic trap are analytically calculated using temperature as an explicit variable.Afterward,the applicability of the analytical formulas is validated by comparison with the numerical calculation.The results illustrate that the obtained functions could be applied for the whole temperature regime with a maximum relative deviation of less than 7.5%in the vicinity of the critical temperature Tcin the case of Bose gases.Meanwhile,for Fermi gases,although the analytical formula fits well at very low-and high-temperature regimes,it cannot be applied at temperature in the range[0.3-0.5]T_F,where T_F is the Fermi temperature.In addition,the consistency between our formulas and classical ones at significantly high temperatures is also discussed.     

Molecular ions in ultracold atomic gases: computed electronic interactions for MgH<Superscript>+</Superscript>(X<Superscript>1</Superscript>Σ<Superscript>+</Superscript>) with Rb

The electronic structures of the manifold of potential energy surfaces generated in the lower energy range by the interaction of the MgH⁺(X¹Σ⁺)  cationic molecule with Rb(²S)  neutral atom are obtained over a broad range of Jacobi coordinates from strongly correlated ab initio calculations which use a Multireference (MR) wavefunction within a Complete Active Space (CAS) approach. The relative features of the lowest five surfaces are analyzed in terms of possible collisional outcomes when employed to model the ultracold dynamics of ionic molecular partners.