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Journal of Physics B Atomic Molecular and Optical Physics

Effect of next-nearest-neighbour hopping on Bose–Einstein condensation in optical lattices

T. A. Zaleski, T. K. Kopeć

Published Apr 6, 2010• 9 citations
Publisher

Abstract

We study the influence of the various hopping elements on the ground state properties of the bosons in the 2D optical square lattice. Using the quantum rotor approach for the Bose–Hubbard model with nearest t and next-nearest-neighbour t ' hopping, we quantify to what extent changing the ratio t '/ t affects the superfluid to Mott-insulator transition.

DOI
10.1088/0953-4075/43/8/085303

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We study the influence of the various hopping elements on the ground state properties of the bosons in the 2D optical square lattice. Using the quantum rotor approach for the Bose–Hubbard model with nearest t and next-nearest-neighbour t ' hopping, we quantify to what extent changing the ratio t '/ t affects the superfluid to Mott-insulator transition.
We study the influence of the restricted geometry of a cubic lattice confined within a finite slab of L layers (i.e. of the form ∞ × ∞ × L ) on the ground-state properties of interacting bosons in the optical lattice. Using the quantum rotor approach for the Bose–Hubbard model, we quantify how the restricted slab geometry affects the superfluid-to-Mott-insulator transition. For increasing values of L , both the analytical approach for large L and the direct calculation using lattice density of states for any arbitrary L show that the behavior of the system becomes indistinguishable from the cubic bulk case ( L = ∞ ) even for relatively small values of L ( L ≈ 10). This may be an important justification for treating bosons in optical lattices using methods of statistical physics pertinent for infinite systems.
Introducing the next-nearest-neighbor hopping t′ into the Bose–Hubbard model, we study its effects on the phase diagram, on the ground-state energy, and on the quasiparticle and quasihole dispersion relations of the Mott insulating phase in optical lattices. We have found that a negative value of t′ enlarges the Mott-insulating region on the phase diagram, while a positive value of t′ acts oppositely. We have also found that the effects of t′ are dependent on the dimensionality of optical lattices with its effects largest in three-dimensional optical lattices.
We study an extended Bose-Hubbard model with next-nearest-neighbor (NNN) hopping in a shaken optical lattice. We show how mean-field phase diagram evolves with the change of NNN hopping amplitude t2{t}_{2}t2​, which can be easily tuned via shaking amplitude. As t2{t}_{2}t2​ increases, a Z2{Z}_{2}Z2​-symmetry-breaking superfluid (Z2SF)({Z}_{2}\mathrm{SF})(Z2​SF) phase emerges at the bottom of the Mott lobs. The tricritical points between normal superfluid, Z2SF{Z}_{2}\mathrm{SF}Z2​SF, and Mott insulator (MI) phases are identified. We further demonstrate the tricritical point can be tuned to the tip of the Mott lobe, in which case a new critical behavior has been predicted. Within random-phase approximation, excitation spectra in the three phases are obtained, which indicate how the phase transitions occur.
We study the superfluid to Mott-insulator transition of bosons in an optical anizotropic lattice by employing the Bose-Hubbard model living on a two-dimensional lattice with anizotropy parameter κ.The compressible superfluid state and incompressible Mott-insulator (MI) lobes are efficiently described analytically, using the quantum U(1) rotor approach.The ground state phase diagram showing the evolution of the MI lobes is quantified for arbitrary values of κ, corresponding to various kind of lattices: from square, through rectangular to almost one-dimensional.
We consider ultracold bosons in a two-dimensional square optical lattice described by the Bose-Hubbard model. In addition, an external time-dependent sinusoidal force is applied to the system, which shakes the lattice along one of the diagonals. The effect of the shaking is to renormalize the nearest-neighbor-hopping coefficients, which can be arbitrarily reduced, can vanish, or can even change sign, depending on the shaking parameter. Therefore, it is necessary to account for higher-order-hopping terms, which are renormalized differently by the shaking, and to introduce anisotropy into the problem. We show that the competition between these different hopping terms leads to finite-momentum condensates with a momentum that may be tuned via the strength of the shaking. We calculate the boundaries between the Mott insulator and the different superfluid phases and present the time-of-flight images expected to be observed experimentally. Our results open up possibilities for the realization of bosonic analogs of the Fulde, Ferrel, Larkin, and Ovchinnikov phase describing inhomogeneous superconductivity.