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arXiv:1906.11132 · Physical Review A

Perfect transmission of Higgs modes via antibound states

Takeru Nakayama, Shunji Tsuchiya

Published Dec 5, 2019• 4 citations
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Abstract

We study tunneling properties of Higgs modes in superfluid Bose gases in optical lattices in the presence of a potential barrier introduced by local modulation of hopping amplitude. Solving the time-dependent Ginzburg-Landau equation, Higgs modes are found to exhibit perfect transmission through a potential barrier if the barrier strength is weak. There exists, on the other hand, localized Higgs bound states in the presence of a strong potential barrier. We find that the perfect transmission disappears at the critical barrier strength above which one of the odd antibound states turns into a true bound state. We demonstrate that the perfect transmission of Higgs modes is mediated by resonance with the antibound states of Higgs modes.

DOI
10.1103/physreva.100.063612

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We study tunneling properties of Higgs modes in superfluid Bose gases in optical lattices in the presence of a potential barrier introduced by local modulation of hopping amplitude. Solving the time-dependent Ginzburg-Landau equation, Higgs modes are found to exhibit perfect transmission through a potential barrier if the barrier strength is weak. There exists, on the other hand, localized Higgs bound states in the presence of a strong potential barrier. We find that the perfect transmission disappears at the critical barrier strength above which one of the odd antibound states turns into a true bound state. We demonstrate that the perfect transmission of Higgs modes is mediated by resonance with the antibound states of Higgs modes.
We study effects of a potential barrier on collective modes of superfluid Bose gases in optical lattices. We assume that the barrier is created by local suppression of the hopping amplitude. When the system is in a close vicinity of the Mott transition at commensurate fillings, where an approximate particle-hole symmetry emerges, there exist bound states of Higgs amplitude mode that are localized around the barrier. By applying the Gutzwiller mean-field approximation to the Bose-Hubbard model, we analyze properties of normal modes of the system with a special focus on the Higgs bound states. We show that when the system moves away from the Mott transition point, the Higgs bound states turn into quasibound states due to inevitable breaking of the particle-hole symmetry. We use a stabilization method to compute the resonance energy and linewidth of the quasibound states. We compare the results obtained by the Gutzwiller approach with those by the Ginzburg-Landau theory. We find that the Higgs bound states survive even in a parameter region far from the Mott transition, where the Ginzburg-Landau theory fails.
We study collective modes of superfluid Bose gases in optical lattices combined with potential barriers. 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. In the presence of the former barrier, we find Higgs bound states that have binding energies lower than the bulk Higgs gap and are localized around the barrier. We analyze tunneling properties of the NG mode incident to both barriers to show that the latter barrier couples the Higgs bound states with the NG mode, leading to Fano resonance mediated by the bound states. Thanks to the universality of the underlying field theory, it is expected that Higgs bound states may be present also in other condensed-matter systems with a particle-hole symmetry and spontaneous breaking of a continuous symmetry, such as quantum dimer antiferromagnets, superconductors, and charge-density-wave materials.
We study the Higgs mode of superfluid Bose gases in a three-dimensional optical lattice, which emerges near the quantum phase transition to the Mott insulator at commensurate fillings. Specifically, we consider responses of the Higgs mode to temporal modulations of the onsite interaction and the hopping energy. In order to calculate the response functions including the effects of quantum and thermal fluctuations, we map the Bose-Hubbard model onto an effective pseudospin-1 model and use a perturbative expansion based on the imaginary-time Green's function theory. We also include the effects of an inhomogeneous trapping potential by means of a local density approximation. We find that the response function for the hopping modulation is equal to that for the interaction modulation within our approximation. At the unit filling rate and in the absence of a trapping potential, we show that the Higgs mode can exist as a sharp resonance peak in the dynamical susceptibilities at typical temperatures. However, the resonance peak is significantly broadened due to the trapping potential when the modulations are applied globally to the entire system. We suggest that the Higgs mode can be detected as a sharp resonance peak by partial modulations around the trap center.
We investigate the tunneling properties of collective excitations in the ferromagnetic phase of a spin-1 spinor Bose-Einstein condensate (BEC). In addition to the Bogoliubov mode, this superfluid phase has two spin excitations, namely, the gapless transverse spin wave and the quadrupolar mode with a finite excitation gap. In the mean-field theory at T=0T=0T=0, we examine how these collective modes tunnel through a barrier potential that couples to the local density of particles. In the presence of supercurrent with a finite momentum qqq, while the Bogoliubov mode shows the so-called anomalous tunneling behavior (which is characterized by perfect transmission) in the low-energy limit, the transverse spin wave transmits perfectly only when the momentum kkk of this mode coincides with $\ifmmode\pm\else\textpm\fi{}q$. At $k=\ifmmode\pm\else\textpm\fi{}q$, the wave function of this spin wave has the same form as the condensate wave function in the current-carrying state, so that the mechanism of this perfect transmission is found to be the same as tunneling of the supercurrent. Using this fact, the perfect transmission of the spin wave is proved for a generic barrier potential. We show that such perfect transmission does not occur in the quadrupolar mode. Further, we consider the effects of potentials breaking U(1) and spin-rotation symmetries on the transmission properties of excitations. Our results would be useful for understanding excitation properties of spinor BEC's, as well as the anomalous tunneling phenomenon in Bose superfluids.
We derive the exact solution of low energy limit of Bogoliubov equations for excitations of Bose-Einstein condensate in the presence of arbitrary potential barrier and maximum current of condensate. Using this solution, we give the explicit expression for the transmission coefficient against the potential barrier, which shows partial transmission in the low energy limit. The wavefunctions of excitations in the low energy limit do not coincide with that of the condensate. The absence of the perfect transmission in the critical current state originates from local enhancement of density fluctuations around the potential barrier.
We study collective modes of superfluid Bose gases in optical lattices at commensurate fillings.We focus on the vicinity of the quantum phase transition to the Mott insulator, where there exists the Higgs amplitude mode in addition to the Nambu-Goldstone phase mode associated with the spontaneous U(1) symmetry breaking.We analyze finite-temperature effects on the damping of the collective modes by using an effective spin-1 model and field-theoretical methods based on the finite-temperature Green's function.We calculate the damping rates up to 1-loop order and evaluate them analytically and numerically.We show that the damping rate of the Higgs mode increases with increasing temperature but it remains underdamped up to the typical temperature achieved in experiments.Moreover, we find that the Nambu-Goldstone mode attenuates via a Landau damping process resulting from interactions with the Higgs mode and it can be overdamped at the typical temperature in a certain parameter region..............