Coherence Properties of a Continuous Atom Laser

We investigate the coherence properties of an atomic beam evaporatively cooled in a magnetic guide, assuming thermal equilibrium in the quantum degenerate regime. The gas experiences two-dimensional, transverse Bose-Einstein condensation rather than a full three-dimensional condensation because of the very elongated geometry of the magnetic guide. First order and second order correlation functions of the atomic field are used to characterize the coherence properties of the gas along the axis of the guide. The coherence length of the gas is found to be much larger than the thermal de Broglie wavelength in the strongly quantum degenerate regime. Large intensity fluctuations present in the ideal Bose gas model are found to be strongly reduced by repulsive atomic interactions; this conclusion is obtained with a one-dimensional classical field approximation valid when the temperature of the gas is much higher than its chemical potential, k B T ≫ |µ|. The first experimental achievements of Bose-Einstein condensates in atomic vapors [1, 2, 3, 4] have opened promising perspectives for atom optics: condensates constitute indeed atomic waves sources of much better coherence properties than the usual 'thermal' sources like the standard magneto-optical trap. These coherence properties have already been demonstrated experimentally: interferences experiments between two condensates have been performed at MIT [5] and at JILA [6], the first order correlation function of the atomic field has been measured in Münich [7], and suppression of density fluctuations (that is fluctuations in the intensity of the atomic field) has been revealed by a measurement of the mean-field energy [8] and of three-body losses [9]. By inducing a coherent leak of atoms out of trapped condensates several groups have succeeded in creating pulsed or quasi-continuous 'atom-lasers' [10]. For future applications the already realized 'atom-lasers' may suffer from the handicap of a low mean flux of atoms: the condensates were not experiencing any continuous loading of atoms, so that the coherent output of atoms terminated once the ∼ 10 6 atoms of the condensate were leaked out. As the repetition rate of the whole sequence is limited by the time required to form a condensate by evaporative cooling (on the order of seconds) the resulting mean flux of atoms is < 10 6 atoms/s. Several proposals have been made to refill the condensates with atoms in a continuous way [11] but they have to our knowledge not been realized yet. Recently we proposed a different scheme, based on the …