60 research outputs found
Continuous Observation of Interference Fringes from Bose Condensates
We use continuous measurement theory to describe the evolution of two Bose
condensates in an interference experiment. It is shown how the system evolves
in a single run of the experiment into a state with a fixed relative phase,
while the total gauge symmetry remains unbroken. Thus, an interference pattern
is exhibited without violating atom number conservation.Comment: 4 pages, Postscrip
Spatial coherence and density correlations of trapped Bose gases
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
Phase dynamics in a binary-collisions atom laser scheme
Various aspects of the phase dynamics of an atom laser scheme based on binary
collisions are investigated. Analytical estimates of the influence of elastic
atom-atom collisions on the laser linewidth are given, and linewidths
achievable in a recently proposed atom laser scheme [Phys. Rev. A 56, 2989
(1997)] are evaluated explicitly. The extent to which a relative phase can be
established between two interfering atom lasers, as well as the properties of
that phase, are also investigated.Comment: Revtex, 10 pages, 6 figure
Precision Monte Carlo Test of the Hartree-Fock Approximation for a trapped Bose Gas
We compare the semiclassical Hartree-Fock approximation for a trapped Bose
gas to a direct Path Integral Quantum Monte Carlo simulation. The chosen
parameters correspond to current Rb experiments. We observe corrections to the
mean-field density profile. The Path Integral calculation reveals an increase
of the number of condensed particles, which is of the same order as a
previously computed result for a homogeneous system. We discuss the
experimental observability of the effect and propose a method to analyze data
of in-situ experiments.Comment: 4 pages, 3 figures, revte
Spatial fragmentation of a Bose-Einstein condensate in a double-well potential
We present a theoretical study of the ground state of a Bose-Einstein
condensate with repulsive inter-particle interactions in a double-well
potential, using a restricted variational principle. Within such an approach,
there is a transition from a single condensate to a fragmented condensate as
the strength of the central barrier of the potential is increased. We determine
the nature of this transition through approximate analytic as well as numerical
solutions of our model in the regime where the inter-particle interactions can
be treated perturbatively. The degree of fragmentation of the condensate is
characterized by the degrees of first-order and second-order spatial coherence
across the barrier.Comment: 10 pages, 2 figures, submitted to Phys. Rev.
Quantum Kinetic Theory VI: The Growth of a Bose-Einstein Condensate
A detailed analysis of the growth of a BEC is given, based on quantum kinetic
theory, in which we take account of the evolution of the occupations of lower
trap levels, and of the full Bose-Einstein formula for the occupations of
higher trap levels, as well as the Bose stimulated direct transfer of atoms to
the condensate level introduced by Gardiner et al. We find good agreement with
experiment at higher temperatures, but at lower temperatures the experimentally
observed growth rate is somewhat more rapid. We also confirm the picture of the
``kinetic'' region of evolution, introduced by Kagan et al., for the time up to
the initiation of the condensate. The behavior after initiation essentially
follows our original growth equation, but with a substantially increased rate
coefficient.
Our modelling of growth implicitly gives a model of the spatial shape of the
condensate vapor system as the condensate grows, and thus provides an
alternative to the present phenomenological fitting procedure, based on the sum
of a zero-chemical potential vapor and a Thomas-Fermi shaped condensate. Our
method may give substantially different results for condensate numbers and
temperatures obtained from phenomentological fits, and indicates the need for
more systematic investigation of the growth dynamics of the condensate from a
supersaturated vapor.Comment: TeX source; 29 Pages including 26 PostScript figure
Continuous stochastic Schrodinger equations and localization
The set of continuous norm-preserving stochastic Schrodinger equations
associated with the Lindblad master equation is introduced. This set is used to
describe the localization properties of the state vector toward eigenstates of
the environment operator. Particular focus is placed on determining the
stochastic equation which exhibits the highest rate of localization for wide
open systems. An equation having such a property is proposed in the case of a
single non-hermitian environment operator. This result is relevant to numerical
simulations of quantum trajectories where localization properties are used to
reduce the number of basis states needed to represent the system state, and
thereby increase the speed of calculation.Comment: 18 pages in LaTeX + 6 figures (postscript), uses ioplppt.sty. To
appear in J. Phys.
Phase preparation by atom counting of Bose-Einstein condensates in mixed states
We study the build up of quantum coherence between two Bose-Einstein
condensates which are initially in mixed states. We consider in detail the two
cases where each condensate is initially in a thermal or a Poisson distribution
of atom number. Although initially there is no relative phase between the
condensates, a sequence of spatial atom detections produces an interference
pattern with arbitrary but fixed relative phase. The visibility of this
interference pattern is close to one for the Poisson distribution of two
condensates with equal counting rates but it becomes a stochastic variable in
the thermal case, where the visibility will vary from run to run around an
average visibility of In both cases, the variance of the phase
distribution is inversely proportional to the number of atom detections in the
regime where this number is large compared to one but small compared with the
total number of atoms in the condensates.Comment: 9 pages, 6 PostScript figure, submitted to PR
The validity of the Landau-Zener model for output coupling of Bose condensates
We investigate the validity of the Landau-Zener model in describing the
output coupling of Bose condensates from magnetic traps by a chirped
radiofrequency field. The predictions of the model are compared with the
numerical solutions of the Gross-Pitaevskii equation. We find a dependence on
the chirp direction, and also quantify the role of gravitation.Comment: 4 pages, Late
Phase resolution limit in macroscopic interference between Bose-Einstein condensates
We study the competition between phase definition and quantum phase
fluctuations in interference experiments between independently formed Bose
condensates. While phase-sensitive detection of atoms makes the phase
progressively better defined, interactions tend to randomize it faster as the
uncertainty in the relative particle number grows. A steady state is reached
when the two effects cancel each other. Then the phase resolution saturates to
a value that grows with the ratio between the interaction strength and the atom
detection rate, and the average phase and number begin to fluctuate
classically. We discuss how our study applies to both recently performed and
possible future experiments.Comment: 4 pages, 5 figure
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