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Matter-wave propagation in optical lattices: geometrical and flat-band effects

Metcalf, Mekena, Chern, Gia-Wei, Di Ventra, Massimiliano, Chien, Chih-Chun

Published Apr 14, 2016• 10 citations
OpenAlex

Abstract

The geometry of optical lattices can be engineered allowing the study of\natomic transport along paths arranged in patterns that are otherwise difficult\nto probe in the solid state. A question readily accessible to atomic systems is\nrelated to the speed of propagation of matter-waves as a function of the\nlattice geometry. To address this issue, we have investigated theoretically the\nquantum transport of non-interacting and weakly-interacting ultracold fermionic\natoms in several 2D optical lattice geometries. We find that the triangular\nlattice has a higher propagation velocity compared to the square lattice,\ndespite supporting longer paths. The body-centered square lattice has even\nlonger paths, nonetheless the propagation velocity is yet faster. This apparent\nparadox arises from the mixing of the momentum states which leads to different\ngroup velocities in quantum systems. Standard band theory provides an\nexplanation and allows for a systematic way to search and design systems with\ncontrollable matter-wave propagation. Moreover, the presence of a flat band\nsuch as in a two-leg ladder geometry leads to a dynamical density\ndiscontinuity, which contrasts the behavior of mobile and localized atoms in\nquantum transport. Our predictions are realizable with present experimental\ncapability.

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Matter-wave propagation in optical lattices: geometrical and flat-band effects

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Abstract Inspired by the growing interest in probing many-body phases in novel two-dimensional lattice geometries we investigate the properties of cold atoms as they could be observed in an optical Lieb lattice. We begin by computing Wannier functions localised at individual sites for a realistic experimental setup, and determining coefficients for a Hubbard-like model. Based on this, we show how experiments could probe the robustness of edge states in a Lieb lattice with diagonal boundary conditions to the effects of interactions and realise strongly correlated many-body phases in this geometry. We then generalise this to interacting particles in a half-filled 1D Lieb ladder, where excitations are dominated by flat band states. We show that for strong attractive interactions, pair correlations are enhanced even when there is strong mixing with the Dirac cone. These findings in 1D raise interesting questions about the phases in the full 2D Lieb lattice which we show can be explored in current experiments.

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arXiv:1409.5143•Physical Review A•Sep 17, 2014•6 citations
The geometry of optical lattices can be engineered allowing the study of\natomic transport along paths arranged in patterns that are otherwise difficult\nto probe in the solid state. A question readily accessible to atomic systems is\nrelated to the speed of propagation of matter-waves as a function of the\nlattice geometry. To address this issue, we have investigated theoretically the\nquantum transport of non-interacting and weakly-interacting ultracold fermionic\natoms in several 2D optical lattice geometries. We find that the triangular\nlattice has a higher propagation velocity compared to the square lattice,\ndespite supporting longer paths. The body-centered square lattice has even\nlonger paths, nonetheless the propagation velocity is yet faster. This apparent\nparadox arises from the mixing of the momentum states which leads to different\ngroup velocities in quantum systems. Standard band theory provides an\nexplanation and allows for a systematic way to search and design systems with\ncontrollable matter-wave propagation. Moreover, the presence of a flat band\nsuch as in a two-leg ladder geometry leads to a dynamical density\ndiscontinuity, which contrasts the behavior of mobile and localized atoms in\nquantum transport. Our predictions are realizable with present experimental\ncapability.
Abstract The geometry of optical lattices can be engineered, allowing the study of atomic transport along paths arranged in patterns that are otherwise difficult to probe in the solid state. A question feasible to atomic systems is related to the speed of matter-wave propagation as a function of the lattice geometry. To address this issue, we investigated, theoretically, the quantum transport of noninteracting and weakly-interacting ultracold fermionic atoms in several 2D optical lattice geometries. We find that the triangular lattice has a higher propagation velocity compared to the square lattice, and the cross-linked square lattice has an even faster propagation velocity. The increase results from the mixing of the momentum states which leads to different group velocities in quantum systems. Standard band theory provides an explanation and allows for a systematic way to search and design systems with controllable matter-wave propagation. Moreover, the presence of a flat band such as in a two-leg ladder geometry leads to a dynamical density discontinuity due to its localized atoms. Possible realizations of those dynamical phenomena are discussed.
Motivated by recent advances in the realization of complex two-dimensional optical lattices, we investigate theoretically the quantum transport of ultracold fermions in an optical kagome lattice. In particular, we focus on its extensively degenerate localized states (flat band). By loading fermions in a partial region of the lattice and depleting the mobile atoms at the far boundary of the initially unoccupied region, we find a dynamically generated flat-band insulator, which is also a population-inverted state. We further show that inclusion of weak repulsion leads to a dynamical stripe phase for two-component fermions in a similar setup. Finally, by preparing a topological insulating state in a partially occupied kagome lattice, we find that the topological chiral current decays but exhibits an interesting oscillating dynamics during the nonequilibrium transport. Given the broad variety of lattice geometries supporting localized or topological states, our work suggests new possibilities for using geometrical effects and their dynamics in atomtronic devices.
Inspired by the growing interest in probing many-body phases in novel two-dimensional lattice geometries we investigate the properties of cold atoms as they could be observed in an optical Lieb lattice. We begin by computing Wannier functions localised at individual sites for a realistic experimental setup, and determining coefficients for a Hubbard-like model. Based on this, we show how experiments could probe the robustness of edge states in a Lieb lattice with diagonal boundary conditions to the effects of interactions and realise strongly correlated many-body phases in this geometry. We then generalise this to interacting particles in a half-filled 1D Lieb ladder, where excitations are dominated by flat band states. We show that for strong attractive interactions, pair correlations are enhanced even when there is strong mixing with the Dirac cone. These findings in 1D raise interesting questions about the phases in the full 2D Lieb lattice which we show can be explored in current experiments.
Abstract Inspired by the growing interest in probing many-body phases in novel two-dimensional lattice geometries we investigate the properties of cold atoms as they could be observed in an optical Lieb lattice. We begin by computing Wannier functions localised at individual sites for a realistic experimental setup, and determining coefficients for a Hubbard-like model. Based on this, we show how experiments could probe the robustness of edge states in a Lieb lattice with diagonal boundary conditions to the effects of interactions and realise strongly correlated many-body phases in this geometry. We then generalise this to interacting particles in a half-filled 1D Lieb ladder, where excitations are dominated by flat band states. We show that for strong attractive interactions, pair correlations are enhanced even when there is strong mixing with the Dirac cone. These findings in 1D raise interesting questions about the phases in the full 2D Lieb lattice which we show can be explored in current experiments.
We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture of the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due to the atom-atom interaction are discussed in detail, such as atom-optical limiting and atom-optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties.
We present a general scheme to realize a cold-atom quantum simulator of bidimensional atomic crystals. Our model is based on the use of two independently trapped atomic species: the first one, subject to a strong in-plane confinement, constitutes a two-dimensional matter wave which interacts only with atoms of the second species, deeply trapped around the nodes of a two-dimensional optical lattice. By introducing a general analytic approach we show that the system Green function can be exactly determined, allowing for the investigation of the matter-wave transport properties. We propose some illustrative applications to both Bravais (square, triangular) and non-Bravais (graphene, kagom\'e) lattices, studying both ideal periodic systems and experimental-size and disordered ones. Some remarkable spectral properties of these atomic artificial lattices are pointed out, such as the emergence of single and multiple gaps, flat bands, and Dirac cones. All these features can be manipulated via the interspecies interaction, which proves to be widely tunable due to the interplay between scattering length and confinements.