Quantum dark solitons in Bose gas confined in a hard wall box

Abstract

Schrödinger equation for Bose gas with repulsive contact interactions in one-dimensional space may be solved analytically with the help of the Bethe ansatz if we impose periodic boundary conditions. It was shown that in such a system there exist many-body eigenstates directly corresponding to dark soliton solutions of the mean-field equation. The system is still integrable if one switches from the periodic boundary conditions to an infinite square well potential. The corresponding eigenstates were constructed by M. Gaudin. We analyze weak interaction limit of Gaudin's solutions and identify parametrization of eigenstates strictly connected with single and multiple dark solitons. Numerical simulations of detection of particle's positions reveal dark solitons in the weak interaction regime and their quantum nature in the presence of strong interactions.

7 pages, 4 figures, version accepted for publication in Phys. Rev. A

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• Quantum dark solitons in ultracold one-dimensional Bose and Fermi gases
• Beyond Gross-Pitaevskii equation for 1D gas: quasiparticles and solitons
• Emergence of dark soliton signatures in a one-dimensional unpolarized attractive Fermi gas on a ring
• Measurement of one-dimensional matter-wave quantum breather
• Exact crystalline solution for a one-dimensional few-boson system with point interaction
• Nonuniform Bose-Einstein condensate. II. Doubly coherent states
• Generating nonequilibrium stationary state from ground state condensate through an almost-adiabatic cycle
• Drag-induced dynamical formation of dark solitons in Bose mixture on a ring
• Correlated many-body quantum dynamics of the Peregrine soliton