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Physical Review B

Floquet-Hubbard bound states in the continuum

Giuseppe Della Valle, Stefano Longhi

Published Mar 19, 2014• 29 citations
Publisher

Abstract

We theoretically demonstrate that a type of robust two-particle bound state embedded in the continuum (BIC), which we call Floquet-Hubbard (FH) BIC, can be induced in a homogeneous (i.e., defect-free) Hubbard semilattice by an intense oscillating electric field. While single-particle BIC states are fragile states that exist solely for specially tailored potentials, FH BIC states are found in a wide range of parameter space, do not require fulfillment of resonance conditions, and are thresholdless. Analytical results are derived in the high-frequency limit of field modulation by a multiple-time-scale asymptotic analysis of the ac-driven Hubbard Hamiltonian in the two-particle sector. A FH BIC mode basically corresponds to a molecular state, in which the two particles bind together, undergoing correlated tunneling on the lattice. Localization of the molecular state is induced by the external oscillating field, which effectively attracts the molecular state at the edge of the semi-infinite lattice. Our results can pave the way for the study and interpretation of strong-field phenomena in correlated-particles physics.

DOI
10.1103/physrevb.89.115118

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We theoretically demonstrate that a type of robust two-particle bound state embedded in the continuum (BIC), which we call Floquet-Hubbard (FH) BIC, can be induced in a homogeneous (i.e., defect-free) Hubbard semilattice by an intense oscillating electric field. While single-particle BIC states are fragile states that exist solely for specially tailored potentials, FH BIC states are found in a wide range of parameter space, do not require fulfillment of resonance conditions, and are thresholdless. Analytical results are derived in the high-frequency limit of field modulation by a multiple-time-scale asymptotic analysis of the ac-driven Hubbard Hamiltonian in the two-particle sector. A FH BIC mode basically corresponds to a molecular state, in which the two particles bind together, undergoing correlated tunneling on the lattice. Localization of the molecular state is induced by the external oscillating field, which effectively attracts the molecular state at the edge of the semi-infinite lattice. Our results can pave the way for the study and interpretation of strong-field phenomena in correlated-particles physics.
In the framework of the Bose-Hubbard model, we show that two-particle surface bound states embedded in the continuum (BIC) can be sustained at the edge of a semi-infinite one-dimensional tight-binding lattice for any infinitesimally-small impurity potential V at the lattice boundary. Such thresholdless surface states, which can be referred to as Tamm-Hubbard BIC states, exist provided that the impurity potential V is attractive (repulsive) and the particle-particle Hubbard interaction U is repulsive (attractive), i.e. for UV < 0.
Bound states in the continuum (BICs) are localized modes residing in the radiation continuum. They were first predicted for single-particle states, and became a general feature of many wave systems. In many-body quantum physics, it is still unclear what would be a close analog of BICs, and whether interparticle interaction may induce BICs. Here, we predict a novel type of multiparticle states in the interaction-modulated Bose-Hubbard model that can be associated with the BIC concept. Under periodic boundary conditions, a so-called quasi-BIC appears as a bound pair residing in a standing wave formed by the third particle. Under open boundary conditions, such a hybrid state becomes an eigenstate of the system. We demonstrate that the Thouless pumping of the quasi-BICs can be realized by modulating the onsite interactions in space and time. Surprisingly, while the center of mass of the quasi-BIC is shifted by a unit cell in one cycle, the bound pair moves in the opposite direction with the standing wave.
A bound state in the continuum (BIC) is a spatially localized energy eigenstate embedded in a continuous spectrum of extended eigenstates. While diverse types of single-particle BICs have been reported in the literature, understanding how such localization persists in interacting many-body systems remains a fundamental problem. Here, we present numerical evidence and a perturbative analysis supporting the existence of many-body BICs in a one-dimensional Bose-Hubbard chain with an attractive impurity potential, a system previously known to host a BIC in the two-particle sector. Furthermore, we demonstrate that the Bethe-type construction of the known two-particle BIC breaks down already for three particles even for arbitrary finite superpositions of Bethe waves. The resulting BICs violate the eigenstate thermalization hypothesis for several local one- and two-body observables, leading to nonthermal dynamics from experimentally accessible initial states.
We investigate how the driving field affects the bound states in the one-dimensional two-particle Bose–Hubbard model with an impurity. In the high-frequency regime, compared with the static lattice [Phys. Rev. Lett. 109 (2012) 116405], a new type of Floquet bound state can be obtained even for a weak particle–particle interaction by tuning the driving amplitude. Moreover, the localization degree of the Floquet bound molecular state can be adjusted by tuning the driving frequency, and even the Floquet bound molecular state can be changed into the Floquet extended state when the driving frequency is below a critical value. Our results provide an efficient way to manipulate bound states in the many-body systems.
We investigate scattering phenomena in a one-dimensional attractive Bose-Hubbard model with a time-periodically modulated impurity. We analyze both single-particle and pair (doublon) transmission, exploring a range of interaction strengths and drive amplitudes. Our exact numerical results reveal excellent quantitative agreement with analytical predictions in the high-frequency limit. At intermediate and weak attractive interactions, we observe significant pair dissociation and the emergence of dynamically localized single-particle modes. These features are reminiscent of Floquet Bound States in the Continuum (BICs). These findings provide new avenues for engineering controllable quantum transport and localized states in ultracold atom experiments.
Abstract Bound states in the continuum (BICs), referring to spatially localized bound states with energies falling within the range of extended modes, have been extensively investigated in single-particle systems, leading to diverse applications in photonics, acoustics, and other classical-wave systems. Recently, there has been theoretical interest in exploring many-body BICs in interacting quantum systems, which necessitate the careful design of impurity potentials or spatial profiles of interaction. Here, we propose a type of many-body BICs localized at boundaries, which can be purely induced by the uniform onsite interaction without requiring any specific design of impurity potential or nonlocal interaction. We numerically show that three or more interacting bosons can concentrate on the boundary of a homogeneous one-dimensional lattice, which is absent at single- and two-particle counterparts. Moreover, the eigenenergy of multi-boson bound states can embed within the continuous energy spectra of extended scattering states, thereby giving rise to interaction-induced boundary many-body BICs. Furthermore, by mapping Fock states of three and four bosons to nonlinear circuit networks, we experimentally simulate boundary many-body BICs. Our findings enrich the comprehension of correlated BICs beyond the single-particle level, and have the potential to inspire future investigations on exploring many-body BICs.