Signatures of the quantum fluctuations of cold atoms in an optical lattice in the three-body loss rate

Abstract

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 ${b}_{i}$ is the annihilation operator of the $i\mathrm{th}$ 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 ${G}_{3}^{i}$ 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.