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 spinorbit 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.

Unconventional Energy Bands and Chirality of Ultracold Atoms in Trilayer Honeycomb Lattice

We investigate ultracold fermionic atoms in the trilayer honeycomb lattice. In the low energy approximation, we derive an effective Hamiltonian for pseudospins. The energy spectrum shows a cubic form of the wavevector and is gapless. The quasiparticles and quasiholes are ehiral and show Berry＇s phase π when the wavevector adiabatically evolves along a closed circle, Furthermore, the experimental detection of the energy spectrum is proposed with Bragg scattering techniques.

Enhancement of the photoassociation of ultracold atoms via a non-resonant magnetic field

We report an effective method for enhancing the photoassociation of ultracold atoms using a non-resonant magnetic field,which enables the manipulation of the coupling between the wavefunctions of the colliding atomic pairs and the excited molecules.A series of photoassociation spectra are measured for different magnetic fields.We show that the photoassociation rate is significantly dependent on the non-resonant magnetic field.A qualitatively theoretical explanation is provided,and shows a good agreement with the experimental result.

Electric-field-modified Feshbach resonances in ultracold atom–molecule collision

We present a detailed analysis of near zero-energy Feshbach resonances in ultracold collisions of atom and molecule,taking the He–PH system as an example, subject to superimposed electric and magnetic static fields. We find that the electric field can induce Feshbach resonance which cannot occur when only a magnetic field is applied, through couplings of the adjacent rotational states of different parities. We show that the electric field can shift the position of the magnetic Feshbach resonance, and change the amplitude of resonance significantly. Finally, we demonstrate that, for narrow magnetic Feshbach resonance as in most cases of ultracold atom–molecule collision, the electric field may be used to modulate the resonance, because the width of resonance in electric field scale is relatively larger than that in magnetic field scale.

Controlling the Directed Quantum Transport of Ultracold Atoms in an Optical Lattice with a Periodic Driving Field

We propose a new method to control the directed quantum transport of ultracold atoms in a one-dimensional optical lattice. In this proposal, the effective tunneling between the neighboring sites can be adjusted via coherent destruction of tunneling by tuning the phase of the external field, instead of using the driving field intensity or the frequency, thus the directed quantum transport of ultracold atoms can be coherently controlled in a nmch easier manner. Our proposal overcomes the major drawback of the method used by Creffield et al [Phys. Rev. Lett. 99 （2007） 110501], and can be implemented, in principle, in any one-dimensional optical lattice. Some potential applications of the scheme are also discussed.

Observation of Atomic Dynamic Behaviors in the Evaporative Cooling by In-Situ Imaging the Plugged Hole of Ultracold Atoms

We experimentally observe the dynamic evolution of atoms in the evaporative cooling, by in-situ imaging the plugged hole of ultracold atoms. Ultracold rubidium atoms confined in a magnetic trap are plugged using a blue-detuned laser beam with a waist of 20 m at a wavelength of 767 nm. We probe the variation of the atomic temperature and width versus the radio frequency in the evaporative cooling. Both the behaviors are in good agreement with the calculation of the trapping potential dressed by the rf signal above the threshold temperature,while deviating from the calculation near the phase transition. To accurately obtain the atomic width, we use the plugged hole as the reference to optimize the optical imaging system by precisely minimizing the artificial structures due to the defocus effect.

An introduction to dressed-atom adiabatic potentials for ultracold atoms

We give a simple introduction to the theoretical treatment of atoms interacting strongly w ith electromagnetic fields in the radiofrequency,microw ave and laser domains. In particular,w e discuss the concept of dressed atoms,w hich considers the combination of the atom and photons as a composite physical system. This pow erful concept has a w ide range of applications in atomic physics and w e give a few examples of its use in the manipulation of ultracold atoms in adiabatic potentials. These examples are selected from experimental w ork conducted by our research team in Oxford but there are numerous other applications and w e outline some future possibilities.

Efficient loading of cesium atoms in a magnetic levitated dimple trap

We report a detailed study of magnetically levitated loading of ultracold ^(133)Cs atoms in a dimple trap.The atomic sample was produced in a combined red-detuned optical dipole trap and dimple trap formed by two small waist beams crossing a horizontal plane.The magnetic levitation for the ^(133)Cs atoms forms an effective potential for a large number of atoms in a high spatial density.Dependence of the number of atoms loaded and trapped in the dimple trap on the magnetic field gradient and bias field is in good agreement with the theoretical analysis.This method has been widely used to obtain the Bose–Einstein condensation atoms for many atomic species.

Relativistic quantum effects of Dirac particles simulated by ultracold atoms

Quantum simulation is a powerful tool to study a variety of problems in physics, ranging from high-energy physics to condensed-matter physics. In this article, we review the recent theoretical and experimental progress in quantum simulation of Dirac equation with tunable parameters by using ultracold neutral atoms trapped in optical lattices or subject to light-induced synthetic gauge fields. The effective theories for the quasiparticles become relativistic under certain conditions in these systems, making them ideal platforms for studying the exotic relativistic effects. We focus on the realization of one, two, and three dimensional Dirac equations as well as the detection of some relativistic effects, including particularly the well-known Zitterbewegung effect and Klein tunneling. The realization of quantum anomalous Hall effects is also briefly discussed.

Systematically investigating the polarization gradient cooling in an optical molasses of ultracold cesium atoms

We systematically investigate the polarization gradient cooling （PGC） process in an optical molasses of ultracold cesium atoms. The SR mode for changing the cooling laser, which means that the cooling laser frequency is stepped to the setting value while its intensity is ramped, is found to be the best for the PGC, compared with other modes studied. We verify that the heating effect of the cold atoms, which appears when the cooling laser intensity is lower than the saturation intensity, arises from insufficient polarization gradient cooling. Finally, an exponential decay function with a statistical explanation is introduced to explain the dependence of the cold atom temperature on the PGC interaction time.

Magnetic lattices for ultracold atoms and degenerate quantum gases

We review recent developments in the use of magnetic lattices as a complementary tool to optical lattices for trapping periodic arrays of ultracold atoms and degenerate quantum gases. Recent advances include the realisation of Bose–Einstein condensation in multiple sites of a magnetic lattice of one-dimensional microtraps, the trapping of ultracold atoms in square and triangular magnetic lattices,and the fabrication of magnetic lattice structures with submicron period suitable for quantum tunnelling experiments.Finally, we describe a proposal to utilise long-range interacting Rydberg atoms in a large spacing magnetic lattice to create interactions between atoms on neighbouring sites.

Coherent Assembly of Ultracold Polyatomic Molecules: Two-Channel Interference

The evidences of three-body and four-body bound states have been reported in a series of very recent experiments with ultracold atoms.Here we study coherent creation of polyatomic molecules via a generalized atom-molecule dark-state technique.By keeping the intermediate trimer or tetramer state essentially unpopulated,the constructive quantum two-channel interference is shown to play an important role in,e.g.coherent atom-pentamer conversion at ultracold temperature.

Tight-binding models for ultracold atoms in optical lattices：general formulation and applications

Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients—one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum—are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between s and p orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented.

Gain/loss effects on spin-orbit coupled ultracold atoms in two-dimensional optical lattices

Due to the fundamental position of spin-orbit coupled ultracold atoms in the simulation of topological insulators, the gain/loss effects on these systems should be evaluated when considering the measurement or the coupling to the environment. Here, incorporating the mature gain/loss techniques into the experimentally realized spin-orbit coupled ultracold atoms in two-dimensional optical lattices, we investigate the corresponding non-Hermitian tight-binding model and evaluate the gain/loss effects on various properties of the system, revealing the interplay of the non-Hermiticity and the spin-orbit coupling. Under periodic boundary conditions, we analytically obtain the topological phase diagram, which undergoes a non-Hermitian gapless interval instead of a point that the Hermitian counterpart encounters for a topological phase transition. We also unveil that the band inversion is just a necessary but not sufficient condition for a topological phase in two-level spin-orbit coupled non-Hermitian systems. Because the nodal loops of the upper or lower two dressed bands of the Hermitian counterpart can be split into exceptional loops in this non-Hermitian model, a gauge-independent Wilson-loop method is developed for numerically calculating the Chern number of multiple degenerate complex bands. Under open boundary conditions, we find that the conventional bulk-boundary correspondence does not break down with only on-site gain/loss due to the lack of non-Hermitian skin effect, but the dissipation of chiral edge states depends on the boundary selection, which may be used in the control of edge-state dynamics. Given the technical accessibility of state-dependent atom loss, this model could be realized in current cold-atom experiments.

Novel Quantum Phases of Ultracold Bosonic Atoms in Honeycomb Optical Lattice

We study the quantum phase transition of ultracold atoms in the honeycomb optical lattice. The Hamiltonian of ultracold bosonic atoms in the honeycomb optical lattice is derived. We take the mean-field approximation and further solve the Hamiltonian with the numerical diagonalization method. We obtain the phase diagram and find that the Mort-insulator （MI）, density wave （DW） and modulated superfluid （MS） phases appear. Furthermore, the phase diagram is analyzed according to the order parameter and the average number of particles.

Unconventional Landau Levels of Ultracold Fermionic Atoms on Two-Dimensional Honeycomb Lattice

We investigate the unconventional Landau levels of ultracold fermionic atoms on the two-dimensionalhoneycomb optical lattice subjected to an effective magnetic field,which is created with optical means.In the presenceof the effective magnetic field,the energy spectrum of the unconventional Landau levels is calculated.Furthermore,wepropose to detect the unconventional Landau levels with Bragg scattering techniques.

Measurement of quantum defects of nS and nD states using field ionization spectroscopy in ultracold cesium atoms

This paper reports that ultracold atoms are populated into different nS and nD Rydberg states （n=25-52） by two-photon excitation. The ionization spectrum of an ultracold Rydberg atom is acquired in a cesium magneto-optical trap by using the method of pulse field ionization. This denotes nS and nD states in the ionization spectrum and fits the data of energy levels of different Rydberg states to obtain quantum defects of nS and nD states.

Soliton Trains Induced by Adaptive Shaping with Periodic Traps in Four-Level Ultracold Atom Systems

It is well known that an optical trap can be imprinted by a light field in an ultracold-atom system embedded in an optical cavity, and driven by three different coherent fields. Of the three felds coexisting in the optical cavity there is an intense control field that induces a giant Kerr nonlinearity via electromagnetically-induced transparency, and another feld that creates a periodic optical grating of strength proportional to the square of the associated Rabi frequency. In this work elliptic-soliton solutions to the nonlinear equation governing the propagation of the probe field are considered, with emphasis on the possible generation of optical soliton trains forming a discrete spectrum with well defined quantum numbers. The problem is treated assuming two distinct types of periodic optical gratings and taking into account the negative and positive signs of detunings （detuning above or below resonance）. Results predict that the competition between the self-phase and cross-phase modulation nonlinearities gives rise to a rich family of temporal soliton train modes characterized by distinct quantum numbers.

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.

周期驱动拉曼晶格系统中的动力学拓扑现象

基于目前超冷原子系统中模拟能带拓扑和动力学量子相变的有关实验进展,设计出一个时间周期驱动的一维拉曼晶格系统来模拟动力学拓扑现象.利用振幅周期调制的拉曼光束耦合类碱土^(171)Yb原子的{^(1)S_(0),^(3)P_(1)}能级可以实现所需要的周期驱动拉曼晶格系统.时间周期系统的单带紧束缚近似哈密顿量通过特定变换可以解析求得有效Floquet哈密顿量和微动算符(micromotion operator),从而可以在一维晶格系统中研究任意驱动频率下Floquet动力学量子相变和动力学斯格明子结构出现的条件.结果表明,拓扑非平庸的有效Floquet哈密顿量是系统出现Floquet动力学量子相变的充分不必要条件,并且可以保护Floquet微动过程中的动力学斯格明子结构.