We consider an optical lattice potential loaded with a Bose-Einstein condensate in the presence of three-body loss. The dynamics of the atoms in the lattice realizes the Bose-Hubbard model of condensed-matter physics, where on-site number fluctuations are reduced by the atomic repulsion energy but increase with increased tunneling between lattice sites. A range of quantum states with different number fluctuations can therefore be created by varying the amplitude of the optical potential, and will be reflected in the values of the on-site correlation functions ${G}_{n}^{i}=〈{b}_{i}^{\ifmmode\dagger\else\textdagger\fi{}n}{b}_{i}^{n}〉,$ where
bi is the annihilation operator of the
ith lattice site. The three-body loss rate is shown to be proportional to a sum of the on-site three-body correlation functions and therefore acts as a natural probe of the number fluctuations. The three-body correlation function
G3i is a sensitive measure of the number fluctuations when site occupation is low. In particular, when the average number at each site is less than
3, the number fluctuations in the superfluid phase result in ${G}_{3}^{i}\ensuremath{\approx}{n}_{i}^{3}$ and give rise to a finite three-body loss, whereas in the insulator phase, ${G}_{3}^{i}{=n}_{i}{(n}_{i}\ensuremath{-}{1)(n}_{i}\ensuremath{-}2)$ and three-body loss ceases to occur.
Abstract It is shown that the extended one-dimensional dimer Bose–Hubbard model with multi-body interactions can be solved exactly by using the algebraic Bethe ansatz mainly due to the site-permutation S 2 symmetry. The solution for the model with up to three-particle hopping and three-body on-site interaction is explicitly shown. As an example of the application, lower part of the excitation energy levels and the ground-state entanglement measure of the standard Bose–Hubbard Hamiltonian with the attractive two-body on-site interaction plus the three-body on-site interaction for 100 bosons with variation of the control parameter are calculated by using the exact solution. It is shown that the attractive three-body on-site interaction reinforces the critical point entanglement of the system, which may be helpful for design of an optical lattice for ultracold atoms or a tuneable superconducting quantum interference device with maximal entanglement.
The introduction of disorder in Bose-Hubbard model gives rise to new glassy quantum phases, namely the Bose-glass (BG) and disordered solid (DS) phases. In this work, we present the rich phase diagram of interacting bosons in disordered two-dimensional optical lattice, modelled by the disordered Bose-Hubbard model. We systematically probe the effect of long-range interaction truncated to the nearest neighbors and next-nearest neighbors on the phase diagram. We investigate the zero-temperature ground-state quantum phases using the single-site Gutzwiller mean field (SGMF) theory. We also employ strong-coupling perturbative expansion to identify the nature of ground-state solid phases analytically. At sufficiently high disorder strength, we observe a quantum phase transition between the DS and BG phases. We have investigated this transition in greater detail using cluster Gutzwiller mean field theory to study the effect of inter-site correlations which is absent in the SGMF method. We have also studied this phase transition from the perspective of percolation theory.