Bose Atoms In Optical Lattices Research Articles

Topological magnon bound states in periodically modulated Heisenberg XXZ chains

Strongly interacting topological states in multi-particle quantum systems pose great challenges to both theory and experiment. Recently, bound states of elementary spin waves (magnons) in quantum magnets have been experimentally observed in quantum Heisenberg chains comprising ultracold Bose atoms in optical lattices. Here, we explore a strongly interacting topological state called topological magnon bound-state in the quantum Heisenberg chain under cotranslational symmetry. We find that the cotranslational symmetry is the key to the definition of a topological invariant for multi-particle quantum states, which enables us to characterize the topological features of multi-magnon excitations. We calculate energy spectra, density distributions, correlations and Chern numbers of the two-magnon bound-states and show the existence of topological protected edge bound-states. Our study not only opens a new prospect to pursue topological magnon bound-states, but also gives insights into the characterization and understanding of strongly interacting topological states.

Variational study of phase diagrams of spin–orbit coupled bosons

We use a variational order method to explore the ground state phase diagrams of spin–orbit coupled Bose atoms in optical lattices. By properly parameterizing the order with an ansatz function for each possible phase and comparing their energies which are minimized with respect to the variational parameters, we can effectively identify the lowest energy states and depict the phase diagram. While the Mott-insulator-superfluid phase boundary is computed by the usual Gutzwiller method, the spin-ordered phase structures of the deep Mott regime as well as the superfluid regime are studied by the variational order method. For the isotropic spin–orbit coupling, the phase diagram in the deep Mott insulator regime is qualitatively similar to results derived by the classical Monte-Carlo simulations or other numerical methods. The spiral phases with different spatial periods are discussed in detail. We find three new spin-ordered phases in the deep Mott insulator regime with anisotropic spin–orbit coupling. We also identify the uniform superfluid, stripe and checkerboard supersolid phases with exotic spin orders in the superfluid regime.

Phonon-like excitations in the two-state Bose-Hubbard model

The spectrum of phonon-like collective excitations in the system of Bose-atoms in optical lattice (more generally, in the system of quantum particles described by the Bose-Hubbard model) is investigated. Such excitations appear due to displacements of particles with respect to their local equilibrium positions. The two-level model taking into account the transitions of bosons between the ground state and the first excited state in potential wells, as well as interaction between them, is used. Calculations are performed within the random phase approximation in the hard-core boson limit. It is shown that excitation spectrum in normal phase consists of the one exciton-like band, while in the phase with BE condensate an additional band appears. The positions, spectral weights and widths of bands strongly depend on chemical potential of bosons and temperature. The conditions of stability of a system with respect to the lowering of symmetry and displacement modulation are discussed.

Self-consistent approach for Bose-condensed atoms in optical lattices

Bose atoms in optical lattices are considered at low temperatures and weak interactions, when Bose-Einstein condensate is formed. A self-consistent approach, based on the use of a representative statistical ensemble, is employed, ensuring a gapless spectrum of collective excitations and the validity of conservation laws. In order to show that the approach is applicable to both weak and tight binding, the problem is treated in the Bloch as well as in the Wannier representations. Both these ways result in similar expressions that are compared for the self-consistent Hartree-Fock-Bogolubov approximation. A convenient general formula for the superfluid fraction of atoms in an optical lattice is derived.

Efficiency for preforming molecules from mixtures of light Fermi and heavy Bose atoms in optical lattices: The strong-coupling-expansion method

We discuss the application of a strong-coupling expansion (perturbation theory in the hopping) for studying light-Fermi-heavy-Bose (like $^{40}$K-$^{87}$Rb) mixtures in optical lattices. We use the strong-coupling method to evaluate the efficiency for pre-forming molecules, the entropy per particle and the thermal fluctuations. We show that within the strong interaction regime (and at high temperature), the strong-coupling expansion is an economical way to study this problem. In some cases, it remains valid even down to low temperatures. Because the computational effort is minimal, the strong-coupling approach allows us to work with much larger system sizes, where boundary effects can be eliminated, which is particularly important at higher temperatures. Since the strong-coupling approach is so efficient and accurate, it allows one to rapidly scan through parameter space in order to optimize the pre-forming of molecules on a lattice (by choosing the lattice depth and interspecies attraction). Based on the strong-coupling calculations, we test the thermometry scheme based on the fluctuation-dissipation theorem and find the scheme gives accurate temperature estimation even at very low temperature. We believe this approach and the calculation results will be useful in the design of the next generation of experiments, and will hopefully lead to the ability to form dipolar matter in the quantum degenerate regime.

Quasi-equilibrium mixture of itinerant and localized bose atoms in optical lattice

Conditions are studied under which there can exist a quasi-equilibrium mixture of itinerant and localized bosonic atoms in an optical lattice, even at zero temperature and at integer filling factor, when such a coexistence is impossible for an equilibrium lattice. The consideration is based on a model having the structure of a two-band, or two-component, boson Hubbard Hamiltonian. The minimal value for the ratio of onsite repulsion to tunneling parameter, necessary for the occurrence of such a mixture, is found.

Cold bosons in optical lattices

Basic properties of cold Bose atoms in optical lattices are reviewed. The main principles of correct self-consistent description of arbitrary systems with Bose-Einstein condensate are formulated. Theoretical methods for describing regular periodic lattices are presented. A special attention is paid to the discussion of Bose-atom properties in the frame of the boson Hubbard model. Optical lattices with arbitrary strong disorder, induced by random potentials, are treated. Possible applications of cold atoms in optical lattices are discussed, with an emphasis of their usefulness for quantum information processing and quantum computing. An important feature of the present review article, distinguishing it from other review works, is that theoretical fundamentals here are not just mentioned in brief, but are thoroughly explained. This makes it easy for the reader to follow the principal points without the immediate necessity of resorting to numerous publications in the field.

Entanglement production with Bose atoms in optical lattices

A method of entanglement production is suggested, based on the resonant generation of topological modes in systems with Bose-Einstein condensates trapped in optical or magnetic lattices. The method makes it possible to regulate the strength of entanglement production as well as to govern its time variation. This method can serve as a practical tool for quantum information processing and quantum computing.

Finite-temperature effects on the number fluctuation of ultracold atoms across the superfluid–to–Mott-insulator transition

We study the thermodynamics of ultracold Bose atoms in optical lattices by numerically diagonalizing the mean-field Hamiltonian of the Bose-Hubbard model. This method well describes the behavior of long-range correlations and therefore is valid deep in the superfluid phase. For the homogeneous Bose-Hubbard model, we draw the finite-temperature phase diagram and calculate the superfluid density at unity filling. We evaluate the finite-temperature effects in a recent experiment probing number fluctuation [Phys. Rev. Lett. \textbf{96}, 090401 (2006)], and find that our finite-temperature curves give a better fitting to the experimental data, implying non-negligible temperature effects in this experiment.

Localized excitations at the Mott insulator–superfluid interfaces for confined Bose atoms in optical lattices

In this paper, we consider a cloud of Bose atoms in an optical lattice subjected to a confinement. The equilibrium state of the system can show the coexistence of superfluid and Mott-insulating domains. We consider the surface waves at the interfaces between Mott-insulating and superfluid regions and derive their dispersion. Then, we calculate their contribution to the heat capacity of the system, showing how its low-temperature scaling is qualitatively affected by the presence/absence of the domain structure. This allows for an experimental test of the existence and properties of Mott insulator–superfluid domains, a currently open issue.

Phase diagram of ultracold atoms in optical lattices: Comparative study of slave fermion and slave boson approaches to Bose-Hubbard model

We perform a comparative study of the finite temperature behavior of ultracold Bose atoms in optical lattices by the slave fermion and the slave boson approaches to the Bose-Hubbard model. The phase diagram of the system is presented. Although both approaches are equivalent without approximations, the mean field theory based on the slave fermion technique is quantitatively more appropriate. Conceptually, the slave fermion approach automatically excludes the double occupancy of two identical fermions on the same lattice site. By comparing to known results in limiting cases, we find the slave fermion approach better than the slave boson approach. For example, in the non-interacting limit, the critical temperature of the superfluid-normal liquid transition calculated by the slave fermion approach is closer to the well-known ideal Bose gas result. At zero-temperature limit of the critical interaction, strength from the slave fermion approach is also closer to that from the direct calculation using a zero-temperature mean field theory.