2008/04/30 by A. L. Shelankov, J. Rammer · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #Boson #Characteristic function (probability theory) #Cold Atom Physics and Bose-Einstein Condensates #Interference (communication) #Joint probability distribution #Mathematics #Physics #Probability density function #Probability distribution #Quantum mechanics #Quantum, superfluid, helium dynamics #Spectroscopy and Laser Applications #Statistical physics #Statistics #Symmetric probability distribution #cond-mat.mes-hall #quant-ph
paper · pdf · doi:10.1209/0295-5075/83/60002
published as EPL, 83, (2008) 60002 · Some changes in presentation, as published, 6 pages, LaTeX
openalex publication_date 2008/09/01 · arxiv created 2008/09/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A method is presented that is able to predict the probability of outcomes of snapshot measurements, such as the images of the instantaneous particle density distribution in a quantum many-body system. It is shown that a gauge-like transformation of the phase of the many-body wave function allows one to construct a probability generating functional, the Fourier transform of which with respect to the "gauge" field returns the joint probability distribution to detect any given number of particles at various locations. The method is applied to the problem of interference of two independent clouds of Bose-Einstein condensates, where the initially separated clouds with fixed boson numbers expand and the density profile image of the overlapping clouds is registered. In the limit of large particle numbers, the probability to observe a particular image of the density profile is shown to be given by a sum of partial probability distributions, each of which corresponds to a noisy image of interference of two matter waves with definite phase difference. In agreement with earlier theoretical arguments, interference fringes are, therefore, expected in any single shot measurement, the fringe pattern randomly varying from run to run. These results conform to the physical picture where the Bose-Einstein clouds are in spontaneously symmetry broken states, the hidden phases of which are revealed by the density profile measurement via the position of the interference fringes.