Density profile of a semi-infinite one-dimensional Bose gas and bound states of the impurity

Abstract

We study the effect of the boundary on a system of weakly interacting bosons in one dimension. It strongly influences the boson density which is completely suppressed at the boundary position. Away from it, the density is depleted over the distances on the order of the healing length at the mean-field level. Quantum fluctuations modify the density profile considerably. The local density approaches the average one as an inverse square of the distance from the boundary. We calculate an analytic expression for the density profile at arbitrary separations from the boundary. We then consider the problem of localization of a foreign quantum particle (impurity) in the potential created by the inhomogeneous boson density. At the mean-field level, we find exact results for the energy spectrum of the bound states, the corresponding wave functions, and the condition for interaction-induced localization. The quantum contribution to the boson density gives rise to small corrections of the bound state energy levels. However, it is fundamentally important for the existence of a long-range Casimir-like interaction between the impurity and the boundary.

arXiv comment10 pages, 5 figures

References in corpus (34)

• Bose-Einstein condensation of atoms in a uniform potential
• Interacting one dimensional electron gas with open boundaries
• Emergence of coherence in a uniform quasi-two-dimensional Bose gas
• Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction
• Small polarons in dilute gas Bose-Einstein condensates
• Fermi-Bose mapping for one-dimensional Bose gases
• Bipolarons in a Bose-Einstein Condensate
• Friedel oscillations for interacting fermions in one dimension
• Impurities in S=1/2 Heisenberg Antiferromagnetic Chains: Consequences for Neutron Scattering and Knight Shift
• Fermion-Mediated Interactions Between Bosonic Atoms
• Recurrences in an isolated quantum many-body system
• Interaction-Induced Localization of an Impurity in a Trapped Bose Condensate
• Self-trapping of impurities in Bose-Einstein condensates: Strong attractive and repulsive coupling
• Self-localized impurities embedded in a one dimensional Bose-Einstein condensate and their quantum fluctuations
• Casimir forces between defects in one-dimensional quantum liquids
• Boundary Effects on Spectral Properties of Interacting Electrons in One Dimension
• Coalescence of Two Impurities in a Trapped One-dimensional Bose Gas
• Ground-state properties of one-dimensional ultracold Bose gases in a hard-wall trap
• Two impurities in a Bose-Einstein condensate: from Yukawa to Efimov attracted polarons
• Self-Trapping of Bosons and Fermions in Optical Lattices
• Phonon-mediated Casimir interaction between mobile impurities in one-dimensional quantum liquids
• Observation of spin-spin fermion-mediated interactions between ultracold bosons
• Drag force on an impurity below the superfluid critical velocity in a quasi-one-dimensional Bose-Einstein condensate
• Exact form of the Bogoliubov excitations in one-dimensional nonlinear Schrödinger equation
• Strong coupling Bose polarons in a two-dimensional gas
• Low-Energy Properties of a One-dimensional System of Interacting bosons with Boundaries
• The Casimir-like effect in a one-dimensional Bose gas
• From single-particle excitations to sound waves in a box-trapped atomic Bose-Einstein condensate
• Induced pairing of fermionic impurities in a one-dimensional strongly correlated Bose gas
• Field-theoretical approach to the Casimir-like interaction in a one-dimensional Bose gas
• Exact Results for the Boundary Energy of One-Dimensional Bosons
• In-medium bound states of two bosonic impurities in a one-dimensional Fermi gas
• Phonon-mediated Casimir interaction between finite mass impurities
• Fluctuation-induced potential for an impurity in a semi-infinite one-dimensional Bose gas

Cited by in corpus (7)

• Polaron Interactions and Bipolarons in One-Dimensional Bose Gases in the Strong Coupling Regime
• Mediated interaction between polarons in a one-dimensional Bose gas
• Impurities in a one-dimensional Bose gas: the flow equation approach
• Impurities in a trapped 1D Bose gas of arbitrary interaction strength: localization-delocalization transition and absence of self-localization
• Local spectral density of an interacting one-dimensional Bose gas with an impurity
• Friedel oscillations in one-dimensional 4He
• The density of a one-dimensional Bose gas far from an impurity