High accuracy energy formulas for the attractive two-site Bose-Hubbard model
arXiv:1708.08696 · doi:10.1103/PhysRevA.97.023626
Abstract
The attractive two-site Bose-Hubbard model is studied within the framework of the analytical solution obtained by the application of Quantum Inverse Scattering Method. The structure of the ground and excited states is analyzed in terms of solutions of Bethe equations, and an approximate solution for the Bethe roots are given. This yields approximate formulas for the ground state and for the first excited state energies. The obtained formulas work with remarkable precision for a wide range of parameters of the model, and confirmed numerically. An expansion of the Bethe state vectors into a Fock space is also provided for evaluation of expectation values, although this does not have the similar accuracy to the energies.
Submitted to Physical Review A (11 pages, 8 figures)
References in corpus (15)
- Nonlinear atom interferometer surpasses classical precision limit
- Matter-wave interferometry in a double well on an atom chip
- Squeezing and entanglement in a Bose-Einstein condensate
- Exciton-polariton condensates
- Bose-Einstein condensation of photons in an optical microcavity
- The ODE/IM Correspondence
- Spin squeezing, entanglement and quantum metrology with Bose-Einstein condensates
- EPR entanglement strategies in two-well BEC
- Lectures on the Bethe Ansatz
- Macroscopic quantum information processing using spin coherent states
- Deformed strings in the Heisenberg model
- Solving the Richardson equations close to the critical points
- Two-site Bose-Hubbard model with nonlinear tunneling: classical and quantum analysis
- Exact solution for a random walk in a time-dependent 1D random environment: the point-to-point Beta polymer
- Bethe states for the two-site Bose-Hubbard model: a binomial approach