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.     

Commensurability effects for fermionic atoms trapped in 1D optical lattices

Fermionic atoms in two different hyperfine states confined in optical lattices show strong commensurability effects due to the interplay between the atomic density wave ordering and the lattice potential. We show that spatially separated regions of commensurable and incommensurable phases can coexist. The commensurability between the harmonic trap and the lattice sites can be used to control the amplitude of the atomic density waves in the central region of the trap.     

Proposal for a chaotic ratchet using cold atoms in optical lattices

We investigate a new type of quantum ratchet which may be realized by cold atoms in a double-well optical lattice, pulsed with unequal periods. The classical dynamics is chaotic and we find the classical diffusion rate D is asymmetric in momentum up to a finite time t(r). The quantum behavior produces a corresponding asymmetry in the momentum distribution which is "frozen-in" by dynamical localization provided the break time t(*)>or=t(r). We conclude that the cold atom ratchets require Db/ variant Planck's over 2pi approximately 1, where b is a small deviation from period-one pulses.     

Quantum phase transition of cold atoms trapped in optical lattices

We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.     

Modified optical bloch equations in nonlocal systems of two-level atoms interacting with ultrashort light pulses

Modified optical Bloch equations for two-level atoms in the radiation field with the complex polarization vector, the complex amplitude, and the complex wave vector are derived. A specific case is considered in which a field of this kind acts on a separate atom of a nonlocal atomic system. The solution of the modified equations for the interaction of atoms with ultrashort light pulses is obtained.     

Echo responses of an ensemble of cold atoms in optical lattices

The dynamics of an ultracold dilute boson gas in an optical lattice is described in the framework of the Bose-Hubbard model in which the parameters of the system are controlled by light. Within this model, an ensemble of Bose-Einstein condensates trapped in cells of a double optical lattice generates an echo response in the quantum-mechanical probability current. The echo signal is excited by biharmonic radiation pulses under two-photon (Raman) resonance conditions. The time profile of the echo signal and the role played by the inhomogeneous broadening and the interaction of atoms in the formation of the boson echo are discussed.     

Two-dimensional novel optical lattices with multi-well traps for cold atoms or molecules

We propose some new schemes to constitute two-dimensional (2D) array of multi-well optical dipole traps for cold atoms (or molecules) by using an optical system consisting of a binary π-phase grating and a 2D array of rectangle microlens. We calculate the intensity distribution of each optical well in 2D array of multi-well traps and its geometric parameters and so on. The proposed 2D array of multi-well traps can be used to form novel 2D optical lattices with cold atoms (or molecules), and form various novel optical crystals with cold atoms (or molecules), or to perform quantum computing and quantum information processing on an atom chip, even to realize an array of all-optical multi-well atomic (or molecular) BoseEinstein condensates (BECs) on an all-optical integrated atom (or molecule) chip.     

Quantum insulating states of F=2 cold atoms in optical lattices

In this Letter we study various spin correlated insulating states of F=2 cold atoms in optical lattices. We find that the effective spin exchange interaction due to virtual hopping contains an octopole coupling between two neighboring lattice sites. Depending on scattering lengths and numbers of particles per site the ground states are either rotationally invariant dimer or trimer Mott insulators or insulating states with various spin orders. Three spin-ordered insulating phases are ferromagnetic, cyclic, and nematic Mott insulators. We estimate the phase boundaries for states with different numbers of atoms per lattice site.     

Edge transport in 2D cold atom optical lattices

We theoretically study the observable response of edge currents in two-dimensional cold atom optical lattices. As an example, we use Gutzwiller mean-field theory to relate persistent edge currents surrounding a Mott insulator in a slowly rotating trapped Bose-Hubbard system to time of flight measurements. We briefly discuss an application, the detection of the Chern number using edge currents of a topologically ordered optical lattice insulator.     

Localization of cold atoms in state-dependent optical lattices via a Rabi Pulse

We propose a novel realization of Anderson localization in nonequilibrium states of ultracold atoms in an optical lattice. A Rabi pulse transfers part of the population to a different internal state with infinite effective mass. These frozen atoms create a quantum superposition of different disorder potentials, localizing the mobile atoms. For weakly interacting mobile atoms, Anderson localization is obtained. The localization length increases with increasing disorder and decreasing interaction strength, contrary to the expectation for equilibrium localization.     

Simulating cyclotron-Bloch dynamics of a charged particle in a 2D lattice by means of cold atoms in driven quasi-1D optical lattices

Quantum dynamics of a charged particle in a two-dimensional (2D) lattice subject to magnetic and electric fields is a rather complicated interplay between cyclotron oscillations (the case of vanishing electric field) and Bloch oscillations (zero magnetic field), details of which has not yet been completely understood. In the present work we suggest to study this problem by using cold atoms in optical lattices. We introduce a one-dimensional (1D) model which can be easily realized in laboratory experiments with quasi-1D optical lattices and show that this model captures many features of the cyclotron-Bloch dynamics of the quantum particle in 2D square lattices.     

Random on-site interactions versus random potential in ultra cold atoms in optical lattices

We consider the physics of lattice bosons in the presence of either disordered on-site chemical potential or disordered on-site interparticle interactions. By means of analytical results using strong-coupling expansion, and numerical results based on quantum Monte Carlo calculations, we show that important qualitative changes in the zero temperature phase diagram are observed when comparing both cases. Although for both types of disorder superfluid, Mott-insulator and Bose-glass phases may be found, we show that in the case of random interactions the Mott-insulating regions shrink and eventually vanish for any finite disorder strength beyond a sufficiently large filling factor. Furthermore, at low values of the chemical potential both the superfluid and Mott insulator are stable towards the formation of a Bose-glass, leading to a possibly non-trivial tricritical point. We discuss possible experimental realizations of both types of disorder in the context of ultra cold atomic gases in optical lattices. PACS 03.75.Lm; 03.75.Ss; 05.30.Jp; 32.80.Pj     

用光晶格模拟狄拉克、外尔和麦克斯韦方程

相对论性量子力学波动方程,如狄拉克、外尔和麦克斯韦方程,是描述微观粒子运动的基石.最近的实验和理论研究表明,冷原子系统中几乎所有参数都可精确调控,因此冷原子系统被认为是实现量子模拟的理想平台,可以用来研究高能和凝聚态物理中的一些基本问题.本文介绍了设计原子光晶格哈密顿量的思路和方法,主要涉及激光辅助跳跃的理论.基于这些方法,物理学界提出了利用光晶格体系模拟相对论性量子力学波动方程,包括狄拉克、外尔和麦克斯韦方程等,并且预言了一些在基本粒子物理中很难观察到,但在冷原子体系可能观察到的物理现象.本文综述了国际上此领域的研究进展.     

Zoo of quantum phases and excitations of cold bosonic atoms in optical lattices

Quantum phases and phase transitions of weakly to strongly interacting bosonic atoms in deep to shallow optical lattices are described by a single multiorbital mean-field approach in real space. For weakly interacting bosons in one dimension, the critical value of the superfluid to Mott insulator (MI) transition found is in excellent agreement with many-body treatments of the Bose-Hubbard model. For strongly interacting bosons, (i) additional MI phases appear, for which two (or more) atoms residing in each site undergo a Tonks-Girardeau-like transition and localize, and (ii) on-site excitation becomes the excitation lowest in energy. Experimental implications are discussed.     

Bose-Einstein condensates in 1D optical lattices

We discuss the Bloch-state solutions of the stationary Gross-Pitaevskii equation and of the Bogoliubov equations for a Bose-Einstein condensate in the presence of a one-dimensional optical lattice. The results for the compressibility, effective mass and velocity of sound are analysed as a function of the lattice depth and of the strength of the two-body interaction. The band structure of the spectrum of elementary excitations is compared with the one exhibited by the stationary solutions (Bloch bands). Moreover, the numerical calculations are compared with the analytic predictions of the tight binding approximation. We also discuss the role of quantum fluctuations and show that the condensate exhibits 3D, 2D or 1D features depending on the lattice depth and on the number of particles occupying each potential well. We finally show how, using a local density approximation, our results can be applied to study the behaviour of the gas in the presence of harmonic trapping.Received: 15 July 2003, Published online: 8 October 2003PACS: 03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow - 03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices and topological excitations     

Delocalized entanglement of atoms in optical lattices

We show how to detect and quantify entanglement of atoms in optical lattices in terms of correlation functions of the momentum distribution. These distributions can be measured directly in the experiments. We introduce two kinds of entanglement measures related to the position and the spin of the atoms.     

Mixtures of strongly interacting bosons in optical lattices

We investigate the properties of strongly interacting heteronuclear boson-boson mixtures loaded in realistic optical lattices, with particular emphasis on the physics of interfaces. In particular, we numerically reproduce the recent experimental observation that the addition of a small fraction of 41K induces a significant loss of coherence in 87Rb, providing a simple explanation. We then investigate the robustness against the inhomogeneity typical of realistic experimental realizations of the glassy quantum emulsions recently predicted to occur in strongly interacting boson-boson mixtures on ideal homogeneous lattices.     

Diffusion and localization of cold atoms in 3D optical speckle

In this work we re-formulate and solve the self-consistent theory for localization to a Bose-Einstein condensate expanding in a 3D optical speckle. The long-range nature of the fluctuations in the potential energy, treated in the self-consistent Born approximation, make the scattering strongly velocity dependent, and its consequences for mobility edge and fraction of localized atoms have been investigated numerically.