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

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_nⁱ=〈b_i^†nb_iⁿ〉, where b_i 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 G₃ⁱ≈n_i³ and give rise to a finite three-body loss, whereas in the insulator phase, G₃ⁱ=n_i(n_i-1)(n_i-2) and three-body loss ceases to occur.