Anomalous Fluctuations of Bose-Einstein Condensates in Optical Lattices

Fluctuations are fundamental in physics and important for understanding and characterizing phase transitions. In this spirit, the phase transition to the Bose-Einstein condensate (BEC) is of specific importance. Whereas fluctuations of the condensate particle number in atomic BECs have been studied in continuous systems, experimental and theoretical studies for lattice systems were so far missing. Here, we explore the condensate particle number fluctuations in an optical lattice BEC across the phase transition in a combined experimental and theoretical study. We present both experimental data using ultracold ^{87}Rb atoms and numerical simulations based on a hybrid approach combining the Bogoliubov quasiparticle framework with a master equation analysis for modeling the system. We find strongly anomalous fluctuations, where the variance of the condensate number δN_{BEC}^{2} scales with the total atom number as N^{1+γ} with an exponent around γ_{theo}=0.74(10) and γ_{exp}=0.62(9), which we attribute to the 2D/3D crossover geometry. Our Letter highlights the importance of the trap geometry on the character of fluctuations and on fundamental quantum mechanical properties.