Ultracold bosons with short-range interaction in regular optical lattices

Abstract

During the last decade, many exciting phenomena have been experimentally observed and theoretically predicted for ultracold atoms in optical lattices. This paper reviews these rapid developments concentrating mainly on the theory. Different types of the bosonic systems in homogeneous lattices of different dimensions as well as in the presence of harmonic traps are considered. An overview of the theoretical methods used for these investigations as well as of the obtained results is given. Available experimental techniques are presented and discussed in connection with theoretical considerations. Eigenstates of the interacting bosons in homogeneous lattices and in the presence of harmonic confinement are analysed. Their knowledge is essential for understanding of quantum phase transitions at zero and finite temperature.

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• Chaos and ergodicity across the energy spectrum of interacting bosons
• Many-body Multifractality throughout Bosonic Superfluid and Mott Insulator Phases
• Gap-type dark localized modes in a Bose-Einstein condensate with optical lattices
• Interaction-induced topological bound states and Thouless pumping in a one-dimensional optical lattice
• One-dimensional Bose gas in optical lattices of arbitrary strength
• Superfluid density and quasi-long-range order in the one-dimensional disordered Bose-Hubbard model
• Quantum phase transitions of interacting bosons on hyperbolic lattices
• Producing and storing spin-squeezed states and Greenberger-Horne-Zeilinger states in a one-dimensional optical lattice
• Dynamical quantum phase transitions in collapse and revival oscillations of a quenched superfluid
• Tensor-network study of correlation-spreading dynamics in the two-dimensional Bose-Hubbard model
• Lattice polarons across the superfluid to Mott insulator transition
• Superfluidity in the 1D Bose-Hubbard Model
• Quantum Gutzwiller approach for the two-component Bose-Hubbard model
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• Optimal route to quantum chaos in the Bose-Hubbard model
• Tensor network simulation of the quantum Kibble-Zurek quench from the Mott to superfluid phase in the two-dimensional Bose-Hubbard model
• Doublons, topology and interactions in a one-dimensional lattice
• Experimental Determination of Bose-Hubbard Energies
• Quantum droplets with particle imbalance in one-dimensional optical lattices
• Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures
• Magnetic phase transitions of spin-1 ultracold bosons in a cubic optical lattice
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• Many-body interference at the onset of chaos
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• Optical lattices as a tool to study defect-induced superfluidity
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• Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition
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