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Optics Express

Characterizing the coherence of Bose-Einstein condensates and atom lasers

R. J. Dodd, Charles W. Clark, Mark Edwards, Keith R. Burnett

Published Nov 10, 1997• 25 citations
Publisher

Abstract

For a dilute, interacting Bose gas of magnetically-trapped atoms at temperatures below the critical temperature T0 for Bose-Einstein condensation, we determine the second-order coherence function g (2) (r1 ; r2) within the framework of a finite-temperature quantum field theory. We show that, because of the different spatial distributions of condensate and thermal atoms in the trap, g (2) (r1 ; r2) does not depend on jr1 r2j alone. This means that the experimental determinations of g (2) reported to date give only its spatial average. Such an average may underestimate the degree of coherence attainable in an atom laser by judicious engineering of the output coupler.

DOI
10.1364/oe.1.000284

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For a dilute, interacting Bose gas of magnetically-trapped atoms at temperatures below the critical temperature T0 for Bose-Einstein condensation, we determine the second-order coherence function g (2) (r1 ; r2) within the framework of a finite-temperature quantum field theory. We show that, because of the different spatial distributions of condensate and thermal atoms in the trap, g (2) (r1 ; r2) does not depend on jr1 r2j alone. This means that the experimental determinations of g (2) reported to date give only its spatial average. Such an average may underestimate the degree of coherence attainable in an atom laser by judicious engineering of the output coupler.
For a dilute, interacting Bose gas of magnetically-trapped atoms at temperatures below the critical temperature T0 for Bose-Einstein condensation, we determine the second-order coherence function g(2)(r1, r2) within the framework of a finite-temperature quantum field theory. We show that, because of the different spatial distributions of condensate and thermal atoms in the trap, g(2)(r1, r2) does not depend on |r1 - r2| alone. This means that the experimental determinations of g(2) reported to date give only its spatial average. Such an average may underestimate the degree of coherence attainable in an atom laser by judicious engineering of the output coupler.
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, kBT ≫ |µ|. Pacs: 03.75.Fi, 42.50.-p 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
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.
Summary form only given.Our treatment is based on a straightforward application of the quantum-field theory of atoms. Although the key result is obtained within the Hartree-Fock-Bogoliubov-Popov (HFB-Popov) approximation we believe it will be found to be valid in a wider context. The essential aspects of this result are as follows. First, current BEC systems are produced in atom traps, and so they are intrinsically inhomogeneous. Second, the condensed and noncondensed (thermal) fractions of the atomic gas are distributed differently over the trap, and they make separate and distinct contributions to the local coherence function.
We develop a general theory of adiabatic output coupling from trapped, weakly interacting, atomic Bose-Einstein condensates at finite temperatures. For weak coupling, the output rate from the condensate and the excited levels in the trap settles in a time proportional to the inverse of the spectral width of the coupling to the output modes. We discuss the properties of the output atoms in the quasi-steady-state, where the population inside the trap is not appreciably depleted. We show how the composition of the output beam, containing the condensate and the thermal component, may be controlled by changing the frequency of the output coupling lasers. This composition determines the first- and second-order coherence of the output beam. We discuss the changes in the composition of the Bose gas left in the trap, and show how nonresonant output coupling can stimulate either the evaporation of the thermal excitations in the trap or the growth of the nonthermal excitations, when pairs of correlated atoms leave the condensate.
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|.