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arXiv:2106.10215 · Physica D Nonlinear Phenomena

Arnold web and dynamical tunneling in a four-site Bose–Hubbard model

Sourav Karmakar, Srihari Keshavamurthy

Published Sep 3, 2021• 6 citations
arXivHTMLPDF
DOI
10.1016/j.physd.2021.133006

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In this work, we present a four-site integrable model that describes the interaction and tunneling of ultracold dipolar bosons trapped in a rotating, tetrahedral site arrangement. The model is derived from an extension of the Bose-Hubbard model in a rotating frame where the interaction and tunneling parameters have been appropriately selected to produce four independent and conserved quantities, establishing integrability. Two of these conserved quantities – related to the two nonzero circulation modes found in the system – are used to derive an effective Hamiltonian dynamically equivalent to the system for large interactions, allowing for the analytical prediction of its quantum dynamics. By analyzing the site population dynamics in this large interaction regime, we find that rotation induces population imbalance in a manner akin to the Sagnac effect. This is exploited to design a simple rotation sensing protocol capable of estimating reference frame rotation through population imbalance measurements. We calculate the sensitivity of the proposed protocol and demonstrate it has a scaling advantage due to a nontrivial manifestation of the system’s nonlinearity, enabled by integrability. The findings presented here open further investigations into the effects of rotation in multi-site integrable models, highlighting their great potential for modeling quantum devices and quantum sensors.
We report on the experimental implementation of tunable occupation-dependent tunneling in a Bose-Hubbard system of ultracold atoms via time-periodic modulation of the on-site interaction energy. The tunneling rate is inferred from a time-resolved measurement of the lattice site occupation after a quantum quench. We demonstrate coherent control of the tunneling dynamics in the correlated many-body system, including full suppression of tunneling as predicted within the framework of Floquet theory. We find that the tunneling rate explicitly depends on the atom number difference in neighboring lattice sites. Our results may open up ways to realize artificial gauge fields that feature density dependence with ultracold atoms.
The Bose-Hubbard model is used to study bosons in optical lattices. In this thesis we will use an extended Bose-Hubbard model to study a type of completely localized solutions, called compactons. The compactons are a special case of the much studied solitons. The soliton is a familiar concept in non-linear physics. It is a stable, localized wave-solution, found in a range of different systems; from DNA-molecules to optical fibers. The compacton is a soliton that is completely localized, i.e. strictly zero outside a given area. The dynamics of the (extended) Bose-Hubbard model is based on the tunneling of particles between the lattice sites. The ordinary Bose-Hubbard model only accounts for one-particle tunneling processes. We will consider a model that also takes some two-particle tunneling processes into account, basically by considering long-range effects of the particle interaction. The aim of this thesis is to find and study the quantum analog of the compactons found in an extended Discrete Non-Linear Schrödinger equation. We will study analytical solutions and try to find if and under which conditions specific compactons exist. Numerical calculations are made to study the properties of the compactons and to study how compacton solutions arise in the classical limit.