Beyond Gross-Pitaevskii equation for 1D gas: quasiparticles and solitons

Abstract

Describing properties of a strongly interacting quantum many-body system poses a serious challenge both for theory and experiment. In this work, we study excitations of one-dimensional repulsive Bose gas for arbitrary interaction strength using a hydrodynamic approach. We use linearization to study particle (type-I) excitations and numerical minimization to study hole (type-II) excitations. We observe a good agreement between our approach and exact solutions of the Lieb-Liniger model for the particle modes and discrepancies for the hole modes. Therefore, the hydrodynamical equations find to be useful for long-wave structures like phonons and of a limited range of applicability for short-wave ones like narrow solitons. We discuss potential further applications of the method.

Ultrawide dark solitons and droplet-soliton coexistence in a dipolar Bose gas with strong contact interactions

“…For the weak contact interactions the subsequent terms of µ LL expanded in the Taylor series give rise to the GPE and eGPE (that is GPE with LHY terms). Keeping in (1) the full µ LL , without cutting the Taylor series, makes the equation useful for strong short-range interactions [34] and a tool to study the 1D quantum droplets [38].…”

“…The equation in question was used to investigate BECs in Refs. [29][30][31][32][33][34][35][36][37], including the prediction of dipolar quantum droplets in a quasi-1D configuration [38]. Some attention was given to the Bogoliubov-like droplet excitations [39,40], and the subsequent effects like self-cooling and matter-wave emissions [17] in threedimensional droplets.…”

“…There are no reports about solitonic excitations, though. Typically, these waves due their existence to nonlinear effects and have been already studied in various physical systems [41][42][43][44][45][46][47][48][49], including BECs with contact interactions [50][51][52], dipolar interactions [53,54], and also beyond the mean-field description [19,34,55]. Dark solitons are routinely produced via phase imprinting [56,57], but they are predicted to appear spontaneously during heating as well [58].…”

Dynamics of quantum double dark-solitons and an exact finite-size scaling of Bose–Einstein condensation

“…Finally, we mention some potentially relevant results in the following. For strong and intermediate interaction strengths, the Lieb-Liniger Gross-Pitaevski equation is introduced, which is an extension of the GP equation [29]. Associated with the quantum states of dark solitons, bound states of dark solitons are numerically studied by solving the GP equation [30], dynamics of a bright soliton in the quasi-BEC with time-dependent atomic scattering length in a repulsive parabolic potential [31], quantized quasi-two-dimensional Bose-Einstein condensates with spatially modulated nonlinearity [32], matter rogue wave in Bose-Einstein condensates with attractive atomic interaction [33], exact soliton solutions, and nonlinear modulation instability in spinor Bose-Einstein condensates [34].…”