Fundamental noise in matter interferometers

These lecture notes discuss two effects which contribute to the reduction of the interference fringe contrast in matter interferometers. The first effect is the shot noise arising from a finite number of atoms used in experiments. Focusing on a single shot measurement we provide explicit calculations of the full distribution functions of the fringe contrast for the interference of either the coherent or the number states of atoms. Another mechanism of the suppression of the amplitude of interference fringes discussed in these lecture notes is the quantum and thermal fluctuations of the order parameter in low dimensional condensates. We summarize recent theoretical and experimental studies demonstrating that suppression of the interference fringe contrast and its shot to shot variations can be used to study correlation functions within individual condensates. We also discuss full distribution functions of the fringe amplitudes for one and two dimensional condensates and review their connection to high order correlation functions. We point out intriguing mathematical connections between the distribution functions of interference fringe amplitudes and several other problems in field theory, systems of correlated electrons, and statistical physics.