## Bound states of Higgs modes in a superfluid

**Speaker:**Ippei Danshita

**When:**September 16, 2015 (Wed), 11:30AM to 12:30PM (add to my calendar)

**Location:**SCI 328

*This event is part of the Condensed Matter Theory Seminar Series. *

We study collective modes of superfluid Bose gases in optical lattices combined with potential barriers [1]. We assume that the system is in the vicinity of the quantum phase transition to a Mott insulator at a commensurate filling, where emergent particle-hole symmetry gives rise to two types of collective mode, namely, a gapless Nambu-Goldstone (NG) phase mode and a gapful Higgs amplitude mode. We consider two kinds of potential barrier: one does not break the particle-hole symmetry while the other does. Including effects of both kinds of barrier, we derive the Ginzburg-Landau equation for the superfluid order parameter. In the presence of the former barrier, we find bound states of Higgs mode that have binding energies lower than the gap of the Higgs mode in bulk and are localized around the barrier. We also analyze tunneling properties of the NG mode incident to both barriers. It is shown that the latter barrier couples the Higgs bound states with the NG mode, leading to Fano resonance mediated by the bound states. Finally, we present a quantum field theoretical description of the collective modes, including the Higgs bound states, in the presence of both types of barriers. [1] T. Nakayama, I. Danshita, T. Nikuni, and S. Tsuchiya, arXiv:1503.01516v2 (2015).