Breakdown of Integrability in a Quasi-1D Ultracold Bosonic Gas

We demonstrate that virtual excitations of higher radial modes in an atomic Bose gas in a tightly confining waveguide result in effective three-body collisions that violate integrability in this quasi-one-dimensional quantum system and give rise to thermalization. The estimated thermalization rates are consistent with recent experimental results in quasi-1D dynamics of ultracold atoms.

Figure 1

Ratio between the scattering rates for the two routes to thermalization and breakdown of integrability in 1D systems: ${\Gamma }_{2b}$ for two-body collisions leading to excited transverse states, and ${\Gamma }_{3b}$ for the effective three-body collisions. Units on the axes are dimensionless. $\zeta =0.002$ (dashed curve), 0.007 (solid curve), and 0.02 (dot-dashed curve). The points represent the predicted ratios for various sets of experimental parameters from [6] (points), [7] (crosses), and [8] (triangle). Inset: Feynman diagrams for the effective three-body processes in the second (a) and third (b) orders of perturbation theory. Solid and dashed lines correspond to atoms in the ground and excited states of the radial trapping Hamiltonian, respectively.

Figure 2

Dependence of the rate ${\Gamma }_{[4]}^{3b}$ of thermalization induced by effective three-body collisions on the radial trapping frequency. $n_{1\mathrm{D}}=30\mu {\mathrm{m}}^{-1}$ (dashed curve), $40\mu {\mathrm{m}}^{-1}$ (solid curve), and $50\mu {\mathrm{m}}^{-1}$ (dot-dashed curve).