## Abstract

A formalism for describing the coherence and interference properties of two atomic clouds of Bose-Einstein condensates (BEC) is presented, which is applicable even in the opposite limits when the BEC clouds are initially coherent and when they are initially independent. First, we develop a mean-field theory wherein one mean-field mode is used, and then, for fragmented (i.e., independent) condensates, we use a mean-field theory with two modes. We then develop a full two-mode field theory, with a field operator composed of a sum of two terms containing matter wave mode functions φ_{1} and φ_{2}, that multiply the destruction operators of the modes, â_{1} and â_{2}. When atom-atom interactions are present and when the mode functions overlap, the matter wave mode functions φ_{1} and φ_{2} develop components moving to the right and left, and this results in interference fringes in the density. At the many-body level, another source of interference arises from expectation values of the form â_{i}?â_{j} with i ≠ j, which become nonzero due to tunneling and interactions. We detail how these two sources of interference affect the density profile and the density-density correlation functions of Bose-Einstein condensates in the coherent and in the fragmented regimes.

Original language | English |
---|---|

Pages (from-to) | 16097-16103 |

Number of pages | 7 |

Journal | Journal of Physical Chemistry B |

Volume | 112 |

Issue number | 50 |

DOIs | |

State | Published - 18 Dec 2008 |