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We study collective modes of superfluid Bose gases in optical latticescombined with potential barriers. We assume that the system is in the vicinityof the quantum phase transition to a Mott insulator at a commensurate filling,where emergent particle-hole symmetry gives rise to two types of collectivemode, namely a gapless Nambu-Goldstone (NG) phase mode and a gapful Higgsamplitude mode. We consider two kinds of potential barrier: One does not breakthe particle-hole symmetry while the other does. In the presence of the formerbarrier, we find Higgs bound states that have binding energies lower than thebulk Higgs gap and are localized around the barrier. We analyze tunnelingproperties of the NG mode incident to both barriers to show that the latterbarrier couples the Higgs bound states with the NG mode, leading to Fanoresonance mediated by the bound states. Thanks to the universality of theunderlying field theory, it is expected that Higgs bound states may be presentalso in other condensed matter systems with a particle-hole symmetry andspontaneous breaking of a continuous symmetry, such as quantum dimerantiferromagnets, superconductors, and charge-density-wave materials.

Fano resonance through Higgs bound states in tunneling of Nambu-Goldstone modes