Narrow Results

This work is devoted to Bloch oscillations (BO) of cold neutral atoms in optical lattices. After a general introduction to the phenomenon of BO and its realization in optical lattices, we study different extentions of this problem, which account for recent developments in this field. These are two-dimensional BO, decoherence of BO, and BO in correlated systems. Although these problems are discussed in relation to the system of cold atoms in optical lattices, many of the results are of general validity and can be well applied to other systems showing the phenomenon of BO.

Within a mean-field treatment of the Bose–Hubbard model for an optical lattice, we have derived a self-consistent equation for the order parameter of possible phases in the optical lattice at finite temperatures. From the solutions to the self-consistent equation, we have inferred the temperature dependence of the order parameter and transition temperatures of Mott-insulator and superfluid phases into the normal phase. The condensation fraction in the superfluid phase has been deduced from the one-body density matrix and its temperature dependence has been given. In terms of the normalized correlation function of quasiparticles, strong coherence in the superfluid phase and its loss in Mott-insulator phases are demonstrated.

Boson lattices are theoretically well described by the Hubbard model. The basic model and its variants can be effectively simulated using Monte Carlo techniques. We describe two newly developed approaches, the Stochastic Series Expansion (SSE) with directed loop updates and continuous–time Diffusion Monte Carlo (CTDMC). SSE is a formulation of the finite temperature partition function as a stochastic sampling over product terms. Directed loops is a general framework to implement this stochastic sampling in a non–local fashion while maintaining detailed balance. CTDMC is well suited to finding exact ground–state properties, applicable to any lattice model not suffering from the sign problem; for a lattice model the evolution of the wave function can be performed in continuous time without any time discretization error. Both the directed loop algorithm and the CTDMC are important recent advances in development of computational methods. Here we present results for a Hubbard model for anti–ferromagnetic spin–1 bosons in one dimensions, and show evidence for a dimerized ground state in the lowest Mott lobe.

Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subjected to a harmonic trapping potential exhibit interesting compound phases in which fluid regions coexist with local Mott-insulator and/or band-insulator regions. Motivated by experiments on cold atoms inside disordered optical lattices, we present a theoretical study of the effects of a correlated random potential on these ground-state phases. We employ a lattice version of density-functional theory within the local-density approximation to determine the density distribution of fermions in these phases. The exchange-correlation potential is obtained from the Lieb-Wu exact solution of Fermi-Hubbard model. On-site disorder (with and without Gaussian correlations) and harmonic trap are treated as external potentials. We find that disorder has two main effects: (i) it destroys the local insulating regions if it is sufficiently strong compared with the on-site atom-atom repulsion, and (ii) it induces an anomaly in the inverse compressibility at low density from quenching of percolation. For sufficiently large disorder correlation length the enhancement in the inverse compressibility diminishes.

Experimental realizations of a two-qubit quantum logic gate based on cold atom collisions have been elusive mainly due to the decoherence effects introduced during the quantum gate operation, which cause transitions out of the two-qubit space and lead to a decreased gate operation fidelity. This type of decoherence effects, due to the non closeness of the interacting two-qubit system, are characteristic of the electromagnetic interaction, since the electromagnetic vacuum acts as a reservoir whose eigenmodes might become active during the gate operation. To describe the cold-atom collision we consider the quantum non-Hermitian dipole-dipole interaction instead of the less realistic s-scattering approach widely used in the literature. By adding an ancillary qubit, we take advantage of the spatial modulation of the non-Hermitian part of the interaction potential to obtain a "resonant" condition that should be satisfied to achieve lossless operation of a specific two-qubit quantum phase-gate. We demonstrate that careful engineering of the collision is required to obtain a specific truth table and to suppress the effects inherent in the openness of the system arising from the electromagnetic interaction.

We show that stable surface fundamental defect solitons can exist in different gaps of an optical lattice with focusing nonlocal Kerr nonlinearity. For positive defect, solitons stably exist in the semi-infinite gap. For negative defect, solitons are stable in the semi-infinite gap and the first gap. Increasing the negative defect depth, the existent regions of defect solitons in the semi-infinite gap and in the first gap will be changed. The degree of the nonlocality will affect the profiles of these solitons.

We have studied the thermodynamic properties of noninteracting gases in periodic lattice potential at arbitrary integer fillings and compared them with that of ideal homogeneous gases. By deriving explicit expressions for the thermodynamic quantities and performing exact numerical calculations, we have found that the dependence of e.g., entropy and energy on the temperature in the normal phase is rather weak especially at large filling factors. In the Bose condensed phase, their power dependence on the reduced temperature is nearly linear, which is in contrast to that of ideal homogeneous gases. We evaluated the discontinuity in the slope of the specific heat which turned out to be approximately the same as that of the ideal homogeneous Bose (IHB) gas for filling factor ν = 1. The discontinuity i.e. the jump in the heat capacity per particle linearly decreases with increasing ν. These results may serve as a checkpoint for various experiments on optical lattices as well as theoretical studies of weakly interacting Bose systems in periodic potentials being a starting point for perturbative calculations.

A self-consistent equation is derived for the order parameter of quantum phases in an optical lattice within a mean-field approximation to the Bose–Hubbard model. Analyzing the solutions of the self-consistent equation in terms of the number fluctuations of quasiparticles, the one-body density matrix of atoms, and the normalized correlation function of quasiparticles, we have identified two types of Mott-insulator phases that are characterized by different values of the order parameter, quasiparticle fluctuations, and correlations. We have also identified the quantum critical points separating these two types of Mott-insulator phases and the corresponding quantum critical lines on the phase diagram.

We propose a model that includes itinerant and localized states to study Bose–Einstein condensation of ultracold atoms in optical lattices (Bose–Anderson model). It is found that the original itinerant and localized states intermix to give rise to a new energy band structure with two quasiparticle energy bands. We have computed the critical temperature T_c of the Bose–Einstein condensation of the quasiparticles in the Bose–Anderson model using our newly developed numerical algorithm and found that T_c increases as na³ (the number density times the lattice constant cubed) increases according to the power law T_c≈18.93(na³)^0.59nK for na³<0.125 and according to the linear relation T_c≈8.75+10.53na³nK for 1.25<na³<12.5 for the given model parameters. With the self-consistent equations for the condensation fractions obtained within the Bogoliubov mean-field approximation, the effects of the on-site repulsion U on the quasiparticle condensation are investigated. We have found that, for values up to several times the zeroth-order critical temperature, U enhances the zeroth-order condensation fraction at intermediate temperatures and effectively raises the critical temperature, while it slightly suppresses the zeroth-order condensation fraction at very low temperatures.

Feynman's "no-node" theorem states that the conventional many-body ground state wavefunctions of bosons in the coordinate representation are positive definite. This implies that time-reversal symmetry cannot be spontaneously broken. In this article, we review our progress in studying a class of new states of unconventional Bose–Einstein condensations beyond this paradigm. These states can either be the long-lived metastable states of ultracold bosons in high orbital bands in optical lattices as a result of the "orbital Hund's rule" interaction, or the ground states of spinful bosons with spin-orbit coupling linearly dependent on momentum. In both cases, Feynman's argument does not apply. The resultant many-body wavefunctions are complex-valued and thus break time-reversal symmetry spontaneously. Exotic phenomena in these states include the Bose–Einstein condensation at nonzero momentum, the ordering of orbital angular momentum moments, the half-quantum vortex, and the spin texture of skyrmions.

In this paper, we study the ultracold atoms in optical lattice with a weak random external potential by an extended Bose–Hubbard model. When the on-site interaction is strong enough, the model can be mapped to the XXZ model. Then the mean-field theory is applied and we get the zero- and finite-temperature phase diagrams in different optical parameters. The differences between the systems with and without disorder were found, and the Bose-glass phase may exist in the system with disorder.

In this paper, we systematically analyze the properties of the bosonic t–J model simulated in optical superlattices. In particular, by using a slave-particle approach, we show the emergence of a strange topological Fermi liquid with Fermi surfaces from a purely bosonic system. We also discuss the possibility of observing these phenomena in ultracold atom experiments. The result may provide some crucial insights into the origin of high-T_c superconductivity.

We review the recent developments in the field of photonic lattices emphasizing their unique properties for controlling linear and nonlinear propagation of light. We draw some important links between optical lattices and photonic crystals pointing towards practical applications in optical communications and computing, beam shaping, and biosensing.

We address the propagation dynamics of two-dimensional multi-peak solitons in the optical lattices based on the fractional Schrödinger equation. The effect of Lévy index and lattice depth on the band-gap structure of optical lattices are presented. Two-, three-, four-, six- and eight-peak solitons all can exist in the first gap and be stable in a wide region of their existence domain. The effective width, maximal peak value and the power of soliton are also studied. It indicates that the Lévy index plays a significant role on the properties of solitons.

The entanglement properties of some novel quantum systems are studied that are inspired by recent developments in cold-atom technology. A triangular optical lattice of two atomic species can be employed to generate a variety of spin-1/2 Hamiltonians including effective three-spin interactions. A variety of one- or two-dimensional systems can thus be realized that possess multi-degenerate ground states or non-vanishing chirality. The properties of these ground states and their phase transitions are probed with appropriate measures such as the entropic entanglement and the spin chirality.

We will review the realization of magnetic microtraps for ultracold atoms. Such devices combine experimental simplicity with unsurpassed versatility in designing confining potentials. We will show how combining magnetic microtraps with optical lattices one can realize many possible quantum systems of interest in many fields ranging from solid state physics to condensed matter. We will also illustrate new possibilities in the quantum simulation of different physical systems.

Matter waves can be coherently and adiabatically loaded and controlled in strongly driven optical lattices. This coherent control is used in order to modify the modulus and the sign of the tunneling matrix element in the tunneling Hamiltonian. Our findings pave the way for studies of driven quantum systems and new methods for engineering Hamiltonians that are impossible to realize with static techniques.

In this paper, we propose to directly detect Mott lobes, i.e. the order parameter 〈a〉, describing the Mott insulator (MI) to superfluid (SF) quantum phase transition of the Bose–Hubbard (BH) model. By weakly coupling the system to an environment in the SF phase, the U(1) symmetry breaking of the system is simulated, and the order parameter can be read from the AC Josephson current between the system and the environment. The relation between the order parameter and the Josephson current is obtained from both the mean-field theory approach and an exact numerical simulation of a finite-size example. Our numerical simulations show that the profile of the order parameter read from the Josephson current is different from it predicted by the mean-field theory, but similar to it in a system whose U(1) symmetry is broken by a weak field proportional to a + a^†. This proposal is feasible in optical lattices.

Boson lattices are theoretically well described by the Hubbard model. The basic model and its variants can be effectively simulated using Monte Carlo techniques. We describe two newly developed approaches, the Stochastic Series Expansion (SSE) with directed loop updates and continuous–time Diffusion Monte Carlo (CTDMC). SSE is a formulation of the finite temperature partition function as a stochastic sampling over product terms. Directed loops is a general framework to implement this stochastic sampling in a non–local fashion while maintaining detailed balance. CTDMC is well suited to finding exact ground–state properties, applicable to any lattice model not suffering from the sign problem; for a lattice model the evolution of the wave function can be performed in continuous time without any time discretization error. Both the directed loop algorithm and the CTDMC are important recent advances in development of computational methods. Here we present results for a Hubbard model for anti–ferromagnetic spin–1 bosons in one dimensions, and show evidence for a dimerized ground state in the lowest Mott lobe.

In this paper we deal with the general subject of realizing disordered states in optical lattices by using an unequal mixture of fast and slow (or frozen) particles. We discuss the onset of Anderson localization of fast hardcore bosons when brought into interaction with the random potential created by secondary hardcore bosons frozen in a superfluid state. In the case of softcore bosons we discuss how localization phenomena, in the form of fragmentation of the mixture into many metastable droplets, intervene when trying to reach the equilibrium ground state of the system.