Decay of super-currents in condensates in optical lattices

In this paper we discuss decay of superfluid currents in boson lattice systems due to quantum tunneling and thermal activation mechanisms. We derive asymptotic expressions for the decay rate near the critical current in two regimes, deep in the superfluid phase and close to the superfluid-Mott insulator transition. The broadening of the transition at the critical current due to these decay mechanisms is more pronounced at lower dimensions. We also find that the crossover temperature below which quantum decay dominates is experimentally accessible in most cases. Finally, we discuss the dynamics of the current decay and point out the difference between low and high currents.Comment: Contribution to the special issue of Journal of Superconductivity in honor of Michael Tinkham's 75th birthda

Dynamical instability of a spin spiral in an interacting Fermi gas as a probe of the Stoner transition

We propose an experiment to probe ferromagnetic phenomena in an ultracold Fermi gas, while alleviating the sensitivity to three-body loss and competing many-body instabilities. The system is initialized in a small pitch spin spiral, which becomes unstable in the presence of repulsive interactions. To linear order the exponentially growing collective modes exhibit critical slowing down close to the Stoner transition point. Also, to this order, the dynamics are identical on the paramagnetic and ferromagnetic sides of the transition. However, we show that scattering off the exponentially growing modes qualitatively alters the collective mode structure. The critical slowing down is eliminated and in its place a new unstable branch develops at large wave vectors. Furthermore, long-wavelength instabilities are quenched on the paramagnetic side of the transition. We study the experimental observation of the instabilities, specifically addressing the trapping geometry and how phase-contrast imaging will reveal the emerging domain structure. These probes of the dynamical phenomena could allow experiments to detect the transition point and distinguish between the paramagnetic and ferromagnetic regimes

Phase Diagram of the Bose-Hubbard Model with T_3 symmetry

In this paper we study the quantum phase transition between the insulating and the globally coherent superfluid phases in the Bose-Hubbard model with T_3 structure, the "dice lattice". Even in the absence of any frustration the superfluid phase is characterized by modulation of the order parameter on the different sublattices of the T_3 structure. The zero-temperature critical point as a function of a magnetic field shows the characteristic "butterfly" form. At fully frustration the superfluid region is strongly suppressed. In addition, due to the existence of the Aharonov-Bohm cages at f=1/2, we find evidence for the existence of an intermediate insulating phase characterized by a zero superfluid stiffness but finite compressibility. In this intermediate phase bosons are localized due to the external frustration and the topology of the T_3 lattice. We name this new phase the Aharonov-Bohm (AB) insulator. In the presence of charge frustration the phase diagram acquires the typical lobe-structure. The form and hierarchy of the Mott insulating states with fractional fillings, is dictated by the particular topology of the T_3 lattice. The results presented in this paper were obtained by a variety of analytical methods: mean-field and variational techniques to approach the phase boundary from the superconducting side, and a strongly coupled expansion appropriate for the Mott insulating region. In addition we performed Quantum Monte Carlo simulations of the corresponding (2+1)D XY model to corroborate the analytical calculations with a more accurate quantitative analysis. We finally discuss experimental realization of the T_3 lattice both with optical lattices and with Josephson junction arrays.Comment: 16 pages, 17 figure