Internal structure of a quantum soliton and classical excitations due to trap opening

Abstract

We analytically solve two problems that may be useful in the context of the recent observation of matter wave bright solitons in a one-dimensional attractive atomic Bose gas. The first problem is strictly beyond mean field: From the Bethe ansatz solution we extract the internal correlation function of the particle positions in the quantum soliton, that is for a fixed center of mass position. The second problem is solved in the limit of a large number of particles, where the mean field theory is asymptotically correct: It deals with the number of excitations created by the opening of the trap, starting from a pure soliton in a weakly curved harmonic potential.

12 pages; 2 figures added ; a few typos corrected

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• Quantum theory of bright matter wave solitons in harmonic confinement
• Attractive Bose-Einstein condensates in anharmonic traps: Accurate numerical treatment and the intriguing physics of the variance
• Elastic scattering of a quantum matter-wave bright soliton on a barrier
• From short-time diffusive to long-time ballistic dynamics: the unusual center-of-mass motion of quantum bright solitons
• A liquid-gas transition for bosons with attractive interaction in one dimension
• Progress towards quantum-enhanced interferometry with harmonically trapped quantum matter-wave bright solitons
• Localization of solitons: linear response of the mean-field ground state to weak external potentials
• Superballistic center-of-mass motion in one-dimensional attractive Bose gases: Decoherence-induced Gaussian random walks in velocity space
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• Massive particle interferometry with lattice solitons
• Gravity Dual of Two-Dimensional $\mathcal{N}=(2,2{)}^{\ast }$ Supersymmetric Yang-Mills Theory and Integrable Models
• Shape of a sound wave in a weakly-perturbed Bose gas
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• The single-particle density matrix of a quantum bright soliton from the coordinate Bethe ansatz