Cold Bose Atoms Around the Crossing of Quantum Waveguides

TL;DR

This paper investigates how cold Bose atoms behave around complex quantum waveguide crossings, revealing non-potential trapping forces, localized ground states, and quantum transitions in binary mixtures driven by kinetic energy effects.

Contribution

It introduces a new kinetic energy driven trapping phenomenon in waveguide crossings and analyzes localized ground states and demixing transitions in Bose mixtures.

Findings

Localized Hartree ground states form in waveguide crossings.

Delocalization occurs at a critical particle number depending on geometry.

Binary mixtures exhibit a quantum demixing transition with mass-dependent delocalization.

Abstract

We show that massive low energy particles traversing a branching zone or a crossing of quantum waveguides may experience a non standard trapping force that cannot be derived from a potential. For interacting cold Bose atoms we report on the formation of a localised Hartree ground state for three prototype waveguide geometries with broken translational symmetry: a cranked L-shaped waveguide L, a T-shaped waveguide T, and the crossing C of two quantum waveguides. The phenomenon is kinetic energy driven and cannot be described within the Thomas-Fermi approximation. Depending on the ratio of joining lateral tube diameters of the respective waveguides C,L,T delocalisation commences when the particle number N approaches a critical value. For the case of a binary mixture of two different Bose atom species A and B we observe non standard 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 delocalises 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 to Dirichlet boundary conditions at the walls inside the respective waveguides.