Emptiness Formation Probability in 1D Bose Liquids

We study emptiness formation probability (EFP) in interacting 1D Bose liquids. That is the probability that a snapshot of its ground state reveals exactly zero number of particles within the interval $\mathrm{\mid }x\mathrm{\mid }<R$. For a weakly interacting liquid there is parametrically wide regime $n^{-1}<R<\xi$ (here $n$ is the average density and $\xi$ is the healing length), where EFP exhibits a non-trivial crossover from the Poisson to the Gaussian behavior. We employ the instanton technique [A. Abanov, 2004] to study quantitative details of these regime and compare it with previously reported limited cases.