2014/01/31 by Luca Barbiero, Luca Salasnich
Mathematics · Physics and Astronomy · #Boson #Cold Atom Physics and Bose-Einstein Condensates #Density matrix renormalization group #Ground state #Hamiltonian (control theory) #Hubbard model #Mathematics #Optical lattice #Physics #Quantum #Quantum electrodynamics #Quantum mechanics #Quantum, superfluid, helium dynamics #Strong Light-Matter Interactions #Superfluidity #cond-mat.quant-gas
paper · pdf · doi:10.1103/physreva.89.063605
published as Phys. Rev. A 89 063605 (2014)
arxiv created 2014/06/04 · openalex publication_date 2014/06/04 · arxiv updated 2014/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study a quasi-one-dimensional attractive Bose gas confined in an optical lattice with a superimposed harmonic potential by analyzing the one-dimensional Bose-Hubbard Hamiltonian of the system. Starting from the three-dimensional many-body quantum Hamiltonian, we derive strong inequalities involving the transverse degrees of freedom under which the one-dimensional Bose-Hubbard Hamiltonian can be safely used. To have a reliable description of the one-dimensional ground state, which we call a quantum bright soliton, we use the density-matrix-renormalization-group (DMRG) technique. By comparing DMRG results with mean-field (MF) ones, we find that beyond-mean-field effects become relevant by increasing the attraction between bosons or by decreasing the frequency of the harmonic confinement. In particular, we find that, contrary to the MF predictions based on the discrete nonlinear Schr"odinger equation, average density profiles of quantum bright solitons are not shape-invariant. We also use the time-evolving-block-decimation method to investigate the dynamical properties of bright solitons when the frequency of the harmonic potential is suddenly increased. This quantum quench induces a breathing mode whose period crucially depends on the final strength of the superimposed harmonic confinement.