Bose-Hubbard Hamiltonian: Quantum Chaos approach

Abstract

We discuss applications of the theory of Quantum Chaos to one of the paradigm models of many-body quantum physics -- the Bose-Hubbard model, which describes, in particular, interacting ultracold Bose atoms in an optical lattice. After preliminary, pure quantum analysis of the system we introduce the classical counterpart of the Bose-Hubbard model and the governing semiclassical equations of motion. We analyze these equations for the problem of Bloch oscillations of cold atoms where a number of experimental results are available. The review is written for non-experts and can be viewed as an introduction to the field.

Conference proceeding, 18 pages, 11 figures

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• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Precision measurement of gravity with cold atoms in an optical lattice and comparison with a classical gravimeter
• Mott insulators in strong electric fields
• Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model
• Semiclassical quantization of the Bogoliubov spectrum
• Periodic Mean-Field Solutions and the Spectra of Discrete Bosonic Fields: Trace Formula for Bose-Hubbard Models
• Persistent current of atoms in a ring optical lattice

Cited by in corpus (26)

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• Phase separation can be stronger than chaos
• Chaos in the three-site Bose-Hubbard model -- classical vs quantum
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• Quantum metrology via chaos in a driven Bose-Josephson system
• Quantum entanglement and the Born-Markov approximation for an open quantum system
• Caustics in quantum many-body dynamics
• Bogoliubov depletion of the fragmented condensate in the bosonic flux ladder
• Complex saddle trajectories for multidimensional quantum wave packet/coherent state propagation: application to a many-body system
• Probing Quantum Chaos in many-body quantum systems by the induced dissipation
• Eigenstate thermalization scaling in approaching the classical limit
• Monodromy and chaos for condensed bosons in optical lattices
• Quantum information scrambling in two-dimensional Bose-Hubbard lattices
• Exact variational dynamics of the multimode Bose-Hubbard model based on SU(M) coherent states
• Chaos-induced depletion of a Bose-Einstein condensate
• Coherence Times of Bose-Einstein Condensates beyond the Shot-Noise Limit via Superfluid Shielding
• Quasistatic transfer protocols for atomtronic superfluid circuits
• Chaotic and regular dynamics in the three-site Bose-Hubbard model
• Many-body adiabatic passage: Instability, chaos, and quantum classical correspondence
• Quantum irreversibility of quasistatic protocols for finite-size quantized systems
• Chaos, Metastability and Ergodicity in Bose-Hubbard Superfluid Circuits
• Characterization of the chaotic phase in the tilted Bose-Hubbard model
• Chaos and anomalous transport in a semiclassical Bose-Hubbard chain
• Simplifying higher-order perturbation theory for ring-shaped Bose-Hubbard systems
• Metastability, chaos and spectrum tomography for Bose-Hubbard rings and chains
• Stochastic modeling of spreading and dissipation in mixed-chaotic systems that are driven quasistatically