102 research outputs found
Operator ordering and causality
It is shown that causality violations [M. de Haan, Physica 132A, 375, 397
(1985)], emerging when the conventional definition of the time-normal operator
ordering [P.L.Kelley and W.H.Kleiner, Phys.Rev. 136, A316 (1964)] is taken
outside the rotating wave approximation, disappear when the amended definition
[L.P. and S.S., Annals of Physics, 323, 1989 (2008)] of this ordering is used.Comment: References update
Quantum-field-theoretical approach to phase-space techniques: Symmetric Wick theorem and multitime Wigner representation
In this work we present the formal background used to develop the methods
used in earlier works to extend the truncated Wigner representation of quantum
and atom optics in order to address multi-time problems. The truncated Wigner
representation has proven to be of great practical use, especially in the
numerical study of the quantum dynamics of Bose condensed gases. In these
cases, it allows for the simulation of effects which are missed entirely by
other approximations, such as the Gross-Pitaevskii equation, but does not
suffer from the severe instabilities of more exact methods. The numerical
treatment of interacting many-body quantum systems is an extremely difficult
task, and the ability to extend the truncated Wigner beyond single-time
situations adds another powerful technique to the available toolbox. This
article gives the formal mathematics behind the development of our "time-Wigner
ordering" which allows for the calculation of the multi-time averages which are
required for such quantities as the Glauber correlation functions which are
applicable to bosonic fields.Comment: Submitted to PR
Occupation number and fluctuations in the finite-temperature Bose-Hubbard model
We study the occupation numbers and number fluctuations of ultra-cold atoms
in deep optical lattices for finite temperatures within the Bose-Hubbard model.
Simple analytical expressions for the mean occupation number and number
fluctuations are obtained in the weak-hopping regime using an interpolation
between results from different perturbation approaches in the Mott-insulator
and superfluid phases. These analytical results are compared to exact one
dimensional numerical calculations using a finite temperature variant of the
Density-Matrix Renormalisation Group (DMRG) method and found to have a high
degree of accuracy. We also find very good agreement in the crossover
``thermal'' region. With the present approach the magnitude of number
fluctuations under realistic experimental conditions can be estimated and the
properties of the finite temperature phase diagram can be studied.Comment: 4 pages, 1 eps figure, submitted to PR
Phase-space analysis of bosonic spontaneous emission
We present phase-space techniques for the modelling of spontaneous emission
in two-level bosonic atoms. The positive-P representation is shown to give a
full and complete description and can be further developed to give exact
treatments of the interaction of degenerate bosons with the electromagnetic
field in a given experimental situation. The Wigner representation, even when
truncated at second order, is shown to need a doubling of the phase-space to
allow for a positive-definite diffusion matrix in the appropriate Fokker-Planck
equation and still fails to agree with the full quantum results of the
positive-P representation. We show that quantum statistics and correlations
between the ground and excited states affect the dynamics of the emission
process, so that it is in general non-exponential.Comment: 16 pages, 6 figure
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