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arXiv:cond-mat/9806362 · Physical Review A

Spatial coherence and density correlations of trapped Bose gases

M. Naraschewski, Roy J. Glauber

Published Jun 1, 1999• 276 citations
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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 quasiparticle 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.

DOI
10.1103/physreva.59.4595

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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 quasiparticle 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.
We develop a computationally tractable method for calculating correlation functions of the finite temperature trapped Bose gas that includes the effects of sss-wave interactions. Our approach uses a classical field method to model the low energy modes and treats the high energy modes using a Hartree-Fock description. We present results of first and second order correlation functions, in position and momentum space, for an experimentally realistic system in the temperature range of 0.6Tc0.6{T}_{c}0.6Tc​ to 1.0Tc1.0{T}_{c}1.0Tc​. We also characterize the spatial coherence length of the system. Our theory should be applicable in the critical region where experiments are now able to measure first and second order correlations.
Trapped bosonic gases have been shown to exhibit enhanced first-order coherence in various interferometric measurements when cooled below the critical temperature of Bose–Einstein condensation. However, first-order coherence does not reveal many-atom features for which higher-order atomic correlations must be explored. Here the second-order coherence is studied in the context of classicality of atom-atom correlations. To lowest order with respect to the inverse atom number an inequality for the condensate mode is derived that should hold for purely classical atom-atom correlations. A possible violation of this classical inequality is shown to be hardly possible, so that below the critical temperature the atomic gas should be considered as classical.
The dependence of the three lowest order spatial correlation functions of a harmonically confined Bose gas on temperature and interaction strength is presented at equilibrium. Our analysis is based on a stochastic Langevin equation for the order parameter of a weakly interacting gas. Comparison of the predicted first order correlation functions to those of appropriate mean field theories demonstrates the potentially crucial role of density fluctuations on the equilibrium coherence length. Furthermore, the change in both coherence length and shape of the correlation function, from Gaussian to exponential, with increasing temperature is quantified. Moreover, the presented results for higher order correlation functions are shown to be in agreement with existing predictions. Experimentalists often define a 'quasi-condensate' via bimodal density fits, and this work reveals how consideration of local density-density correlations provides an alternative determination of this quantity.
The dependence of the three lowest order spatial correlation functions of a harmonically confined Bose gas on temperature and interaction strength is presented at equilibrium. Our analysis is based on a stochastic Langevin equation for the order parameter of a weakly interacting gas. Comparison of the predicted first order correlation functions to those of appropriate mean field theories demonstrates the potentially crucial role of density fluctuations on the equilibrium coherence length. Furthermore, the change in both coherence length and shape of the correlation function, from Gaussian to exponential, with increasing temperature is quantified. Moreover, the presented results for higher order correlation functions are shown to be in agreement with existing predictions. Experimentalists often define a ``quasi-condensate'' via bimodal density fits, and this work reveals how consideration of local density-density correlations provides an alternative determination of this quantity.
The dependence of the three lowest order spatial correlation functions of a harmonically confined Bose gas on temperature and interaction strength is presented at equilibrium. Our analysis is based on a stochastic Langevin equation for the order parameter of a weakly interacting gas. Comparison of the predicted first order correlation functions to those of appropriate mean field theories demonstrates the potentially crucial role of density fluctuations on the equilibrium coherence length. Furthermore, the change in both coherence length and shape of the correlation function, from Gaussian to exponential, with increasing temperature is quantified. Moreover, the presented results for higher order correlation functions are shown to be in agreement with existing predictions. Experimentalists often define a 'quasi-condensate' via bimodal density fits, and this work reveals how consideration of local density-density correlations provides an alternative determination of this quantity. © 2006 The American Physical Society.
For some time, the theoretical result for the transition temperature of a dilute three-dimensional Bose gas in an arbitrarily wide harmonic trap has been known to first order in the interaction strength. We extend that result to second order. The first-order result for a gas trapped in a harmonic potential can be computed in mean-field theory (in contrast to the first-order result for a uniform gas, which cannot). We show that, at second order, perturbation theory suffices for relating the transition temperature to the chemical potential at the transition, but the chemical potential is nonperturbative at the desired order. The necessary information about the chemical potential can be extracted, however, from recent lattice simulations of uniform Bose gases.