Correlation of Position for the Ideal Quantum Gas

Prabhu L. Bhatnagar, K. S. Singwi

P. Durganandini

Isabelle Bouchoule, Maksims Arzamasovs, Karen V. Kheruntsyan +1 more

We analyze the two-body momentum correlation function for a uniform, weakly interacting, one-dimensional Bose gas. We show that the strong positive correlation between opposite momenta, expected in a Bose-Einstein condensate with a true long-range order, almost vanishes in a phase-fluctuating quasicondensate where the long-range order is destroyed. Using the Luttinger liquid approach, we derive an analytic expression for the momentum correlation function in the quasicondensate regime, showing (i) the reduction and broadening of the opposite-momentum correlations (compared to the singular behavior in a true condensate) and (ii) an emergence of anticorrelations at small momenta. We also numerically investigate the momentum correlations in the crossover between the quasicondensate and the ideal Bose-gas regimes using a classical field approach and show how the anticorrelations gradually disappear in the ideal-gas limit.

Marco Merkli

Julien Armijo, T. Jacqmin, Karen V. Kheruntsyan +1 more

We perform measurements of the third moment of atom number fluctuations in small slices of a very elongated weakly interacting degenerate Bose gas. We find a positive skewness of the atom number distribution in the ideal gas regime and a reduced skewness compatible with zero in the quasicondensate regime. For our parameters, the third moment is a thermodynamic quantity whose measurement constitutes a sensitive test of the equation of state, and our results are in agreement with a modified Yang-Yang thermodynamic prediction. Moreover, we show that the measured skewness reveals the presence of true three-body correlations in the system.

RAGNAR EKHOLM, Leonard D. Kohn, Seymour H. Wollman