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Chinese Physics Letters

Floquet Bound States in a Driven Two-Particle Bose–Hubbard Model with an Impurity

Honghua Zhong, Zheng Zhou, Bo Zhu, Yongguan Ke, Chaohong Lee

Published Jul 1, 2017• 11 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/34/7/070304

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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.
We study solutions to the Lippmann-Schwinger equation in systems where a slow subsystem is coupled to a fast subsystem via an impurity. Such situations appear when a high-frequency Floquet-driven impurity is introduced into a low-energy system, but the driving frequency is at resonance with a high-energy band. In contrast to the case of resonant bulk driving, where the particles in the low-energy system are excited into the high-energy band, we surprisingly find that these excitations are suppressed for resonantly driven impurities. Still, the transmission through the impurity is strongly affected by the presence of the high-energy band in a universal way that does not depend on the details of the high-energy band. We apply our general result to two examples and show the suppression of excitations from the low-energy band into the high-energy band: a) bound pairs in a Fermi-Hubbard chain scattering at a driven impurity, which is at resonance with the Hubbard interaction and b) particles in a deep optical lattice described by the tight-binding approximation, which scatter at a driven impurity, whose driving frequency equals the band gap between the two lowest energy bands.
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.
Periodic driving has emerged as a powerful tool in the quest to engineer new and exotic quantum phases. While driven many-body systems are generically expected to absorb energy indefinitely and reach an infinite-temperature state, the rate of heating can be exponentially suppressed when the drive frequency is large compared to the local energy scales of the system -- leading to long-lived 'prethermal' regimes. In this work, we experimentally study a bosonic cloud of ultracold atoms in a driven optical lattice and identify such a prethermal regime in the Bose-Hubbard model. By measuring the energy absorption of the cloud as the driving frequency is increased, we observe an exponential-in-frequency reduction of the heating rate persisting over more than 2 orders of magnitude. The tunability of the lattice potentials allows us to explore one- and two-dimensional systems in a range of different interacting regimes. Alongside the exponential decrease, the dependence of the heating rate on the frequency displays features characteristic of the phase diagram of the Bose-Hubbard model, whose understanding is additionally supported by numerical simulations in one dimension. Our results show experimental evidence of the phenomenon of Floquet prethermalization, and provide insight into the characterization of heating for driven bosonic systems.
The manipulation of many-body systems often involves time-dependent forces that cause unwanted heating. One strategy to suppress heating is to use time-periodic (Floquet) forces at large driving frequencies. For quantum spin systems with bounded spectra, it was shown rigorously that the heating rate is exponentially small in the driving frequency. Recently, such exponential suppression of heating has been observed in an experiment with ultracold atoms, realizing a periodically driven Bose-Hubbard model. This model has an unbounded spectrum and, hence, is beyond the reach of previous theoretical approaches. Here, we study this model with two semiclassical approaches valid, respectively, at large and weak interaction strengths. In both limits, we compute the heating rates by studying the statistical probability to encounter a many-body resonance, and obtain a quantitative agreement with the exact diagonalization of the quantum model. Our approach demonstrates the relevance of statistical arguments to Floquet perthermalization of interacting many-body quantum systems.
The manipulation of many-body systems often involves time-dependent forces that cause unwanted heating. One strategy to suppress heating is to use time-periodic (Floquet) forces at large driving frequencies. For quantum spin systems with bounded spectra, it was shown rigorously that the heating rate is exponentially small in the driving frequency. Recently, the exponential suppression of heating has also been observed in an experiment with ultracold atoms, realizing a periodically driven Bose-Hubbard model. This model has an unbounded spectrum and, hence, is beyond the reach of previous theoretical approaches. Here, we study this model with two semiclassical approaches valid, respectively, at large and weak interaction strengths. In both limits, we compute the heating rates by studying the statistical probability to encounter a many-body resonance, and obtain a quantitative agreement with the exact diagonalization of the quantum model. Our approach demonstrates the relevance of statistical arguments to Floquet perthermalization of interacting many-body quantum systems.