Quantum bright solitons in a quasi-one-dimensional optical lattice

Year: 2014

Authors: Barbiero L., Salasnich L.

Autors Affiliation: Dipartimento di Fisica e Astronomia “Galileo Galilei” and CNISM, Università di Padova, Via Marzolo 8, 35131 Padova, Italy;
Istituto Nazionale di Ottica (INO) del Consiglio Nazionale delle Ricerche (CNR), Sezione di Sesto Fiorentino, Via Nello Carrara, 1-50019 Sesto Fiorentino, Italy

Abstract: 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 Schrodinger 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.

Journal/Review: PHYSICAL REVIEW A

Volume: 89 (6)      Pages from: 63605-1  to: 63605-5

More Information: The authors acknowledge partial support from the Universita di Padova (Grant No. CPDA118083), the Cariparo Foundation (Eccellenza Grant No. 11/12), and MIUR (PRIN Grant No. 2010LLKJBX). The authors thank L. D. Carr, B. Malomed, S. Manmana, A. Parola, V. Penna, and F. Toigo for fruitful discussions, and S. Saha for useful suggestions.
KeyWords: Superfluid; Insulator
DOI: 10.1103/PhysRevA.89.063605

Citations: 13
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