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.
Highlights
In weakly interacting ultracold Bose gas, the mean-field approach given by a single particle non-linear Schrodinger equation, which is known as the Gross-Pitaevski equation (GPE), has explained and predicted a large swathe of phenomena [1]
We present the excitation energy being the total energy of the GPE (6) or the Lieb-Liniger Gross-Pitaevski equation (LLGPE) (17) soliton reduced by the energy of the ground state5
The purpose of this work has been to benchmark the generalization of GPE, called here the LLGPE on the well-studied case of gas with solely contact interactions trapped in a 1D box with the periodic boundary conditions
Summary
In weakly interacting ultracold Bose gas, the mean-field approach given by a single particle non-linear Schrodinger equation, which is known as the Gross-Pitaevski equation (GPE), has explained and predicted a large swathe of phenomena [1]. The dark solitons predicted by the GPE correspond to hole excitations in the many-body system described by the linear Lieb-Liniger model [5]. We will benchmark the ground state and its elementary excitations inferred from the effective non-linear approach [23, 31, 34], called here the Lieb-Liniger Gross-Pitaevski equation (LLGPE), against the corresponding solutions of the LL model [26, 27] to test the validity range of the former. We will discuss the interpretation of solitons as the many-body excitations for strong and intermediate interaction strength In this way, we will test the scope of the non-linear model, which is the cornerstone of the quantum droplet description employed in [23] and an analysis of breathing modes in [40].
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