300 research outputs found
A nonlinear dynamics approach to Bogoliubov excitations of Bose-Einstein condensates
We assume the macroscopic wave function of a Bose-Einstein condensate as a
superposition of Gaussian wave packets, with time-dependent complex width
parameters, insert it into the mean-field energy functional corresponding to
the Gross-Pitaevskii equation (GPE) and apply the time-dependent variational
principle. In this way the GPE is mapped onto a system of coupled equations of
motion for the complex width parameters, which can be analyzed using the
methods of nonlinear dynamics. We perform a stability analysis of the fixed
points of the nonlinear system, and demonstrate that the eigenvalues of the
Jacobian reproduce the low-lying quantum mechanical Bogoliubov excitation
spectrum of a condensate in an axisymmetric trap.Comment: 7 pages, 3 figures, Proceedings of the "8th International Summer
School/Conference Let's Face Chaos Through Nonlinear Dynamics", CAMTP,
University of Maribor, Slovenia, 26 June - 10 July 201
Multimode analysis of non-classical correlations in double well Bose-Einstein condensates
The observation of non-classical correlations arising in interacting two to
size weakly coupled Bose-Einstein condensates was recently reported by Esteve
et al. [Nature 455, 1216 (2008)]. In order to observe fluctuations below the
standard quantum limit, they utilized adiabatic passage to reduce the thermal
noise to below that of thermal equilibrium at the minimum realizable
temperature. We present a theoretical analysis that takes into account the
spatial degrees of freedom of the system, allowing us to calculate the expected
correlations at finite temperature in the system, and to verify the hypothesis
of adiabatic passage by comparing the dynamics to the idealized model.Comment: 12 pages, 7 figure
Time-resolved density correlations as probe of squeezing in toroidal Bose-Einstein condensates
I study the evolution of mean field and linear quantum fluctuations in a
toroidal Bose-Einstein condensate, whose interaction strength is quenched from
a finite (repulsive) value to zero. The azimuthal equal-time density-density
correlation function is calculated and shows temporal oscillations with twice
the (final) excitation frequencies after the transition. These oscillations are
a direct consequence of positive and negative frequency mixing during
non-adiabatic evolution. I will argue that a time-resolved measurement of the
equal-time density correlator might be used to calculate the moduli of the
Bogoliubov coefficients and thus the amount of squeezing imposed on a mode,
i.e., the number of atoms excited out of the condensate.Comment: 18 pages, IOP styl
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