Artificial atoms from cold bosons in one dimension

TL;DR

This paper studies the ground-state behavior of weakly repulsive one-dimensional bosons with an attractive impurity, deriving mean-field solutions, critical conditions for binding, and validating results with advanced computational methods.

Contribution

It introduces a mean-field framework for artificial atoms formed by bosons bound to an impurity in 1D and confirms the robustness of the critical binding number beyond mean-field approximations.

Findings

Derived the critical line for boson binding in the thermodynamic limit.

Validated mean-field results with flow equation and multi-layer MCTDH methods.

Found that beyond-mean-field effects do not alter the maximum bound boson number.

Abstract

We investigate the ground-state properties of weakly repulsive one-dimensional bosons in the presence of an attractive zero-range impurity potential. First, we derive mean-field solutions to the problem on a finite ring for the two asymptotic cases: (i) all bosons are bound to the impurity and (ii) all bosons are in a scattering state. Moreover, we derive the critical line that separates these regimes in the parameter space. In the thermodynamic limit, this critical line determines the maximum number of bosons that can be bound by the impurity potential, forming an artificial atom. Second, we validate the mean-field results using the flow equation approach and the multi-layer multi-configuration time-dependent Hartree method for atomic mixtures. While beyond-mean-field effects destroy long-range order in the Bose gas, the critical boson number is unaffected. Our findings are important for understanding such artificial atoms in low-density Bose gases with static and mobile impurities.