Cold Bose atoms around the crossing of quantum waveguides

Abstract

We show that massive low-energy particles traversing a branching zone or a crossing of quantum waveguides may experience a nonstandard trapping force that can not be derived from a potential. For interacting cold Bose atoms, we report on the formation of a localized Hartree ground state for three prototype waveguide geometries with broken translational symmetry: a cranked L-shaped waveguide $\mathcal{L}$, a T-shaped waveguide $\mathcal{T}$, and the crossing $\mathcal{C}$ of two quantum waveguides. The phenomenon is kinetic energy driven and can not be described within the Thomas-Fermi approximation. Depending on the ratio ${\ensuremath{\kappa}}^{(\ensuremath{\Gamma})}$ of joining lateral tube diameters of the respective waveguides $\ensuremath{\Gamma}\ensuremath{\in}{\mathcal{C},\mathcal{L},\mathcal{T}}$, delocalization commences when the particle number $N$ approaches a critical value ${N}_{c}^{(\ensuremath{\Gamma})}$. For the case of a binary mixture of two different Bose atom species $A$ and $B$, we observe nonstandard trapping of both atom species for subcritical particle numbers. A sudden demixing quantum transition takes place as the total particle number $N={N}_{A}+{N}_{B}$ is increased at fixed mixing ratio ${N}_{A}/{N}_{B}$. Depending on the mass ratio ${m}_{A}/{m}_{B}$, the heavier atom species delocalizes first for a wide range of interaction parameters. The numerical calculations are based on a splitting scheme involving an analytic approximation to the short-time asymptotics of the imaginary-time quantum propagator of a single particle obeying Dirichlet boundary conditions at the walls inside the respective waveguides.