Spatial coherence and density correlations of trapped Bose gases

Abstract

We study first and second order coherence of trapped dilute Bose gases using appropriate correlation functions. Special attention is given to the discussion of second order or density correlations. Except for a small region around the surface of a Bose-Einstein condensate the correlations can be accurately described as those of a locally homogeneous gas with a spatially varying chemical potential. The degrees of first and second order coherence are therefore functions of temperature, chemical potential, and position. The second order correlation function is governed both by the tendency of bosonic atoms to cluster and by a strong repulsion at small distances due to atomic interactions. In present experiments both effects are of comparable magnitude. Below the critical temperature the range of the bosonic correlation is affected by the presence of collective quasi-particle excitations. The results of some recent experiments on second and third order coherence are discussed. It is shown that the relation between the measured quantities and the correlation functions is much weaker than previously assumed.Comment: RevTeX, 25 pages with 7 Postscript figure

Reversible and irreversible evolution of a condensed bosonic gas

“…Time is measured in units of the harmonic oscillator period T = 2π/ω. In contrast to these numbers that are genuine single-particle properties, the anomalous fluctuations are a physical measure of the degree of two-particle correlations or squeezing [49]. For example, the total particle number fluctuations (N − N ) 2 or, more specifically, the normally ordered density fluctuations :f (x, x),f (y, y) : would reflect the degree of squeezing of the quadrature components along certain directions x, y.…”

Coherence properties of the two-dimensional Bose-Einstein condensate

“…In order to study coherence properties, we calculate the normalized first order correlation, or coherence function, which can be written in terms of the field operators as [21] …”

Bose-Einstein condensation of correlated atoms in a trap

“…The NO's and the NON's have been calculated, in case 1, by diagonalizing the OBDM through Eq. (22). The NON n 1s , gives directly the condensation fraction n 0 as a result of the repulsive interaction between the atoms of the Bose gas at zero temperature.…”

“…Another quantity characterizing the atomic system is the OBDM ρ(r 1 , r ′ 1 ) [22,[38][39][40][41] which is defined as…”

“…Seventy years later, in a remarkable experiment, Anderson et al [9] have cooled magnetically trapped 87 Rb gas to nanokelvin temperatures, and observed the BEC. This discovery has generated a huge amount of theoretical investigations [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27].…”