Dynamic Critical Phenomena in Trapped Bose Gases

Nonlinear dynamics of a trapped Bose-Einstein condensate, subject to the action of a resonant external field, is studied. This field produces a spatio-temporal modulation of the trapping potential with the frequency close to the transition frequency between the ground state and a higher energy level. The evolution equations of fractional populations display a kind of critical phenomena at a critical line on the manifold of the system parameters. It is demonstrated that there exists a direct analogy between dynamical instability at this line and critical phenomena at a critical line of a related averaged system.Comment: Latex file, 7 pages, no figure

Tkachenko polarons in vortex lattices

We analyze the properties of impurities immersed in a vortex lattice formed by ultracold bosons in the mean field quantum Hall regime. In addition to the effects of a periodic lattice potential, the impurity is dressed by collective modes with parabolic dispersion (Tkachenko modes). We derive the effective polaron model, which contains a marginal impurity-phonon interaction. The polaron spectral function exhibits a Lorentzian broadening for arbitrarily small wave vectors even at zero temperature, in contrast with the result for optical or acoustic phonons. The anomalous damping of Tkachenko polarons could be detected experimentally using momentum-resolved spectroscopy.Comment: 10 pages, 2 figure