45 research outputs found
Bogoliubov theory for atom scattering into separate regions
We review the Bogoliubov theory in the context of recent experiments, where
atoms are scattered from a Bose-Einstein Condensate into two well-separated
regions. We find the full dynamics of the pair-production process, calculate
the first and second order correlation functions and show that the system is
ideally number-squeezed. We calculate the Fisher information to show how the
entanglement between the atoms from the two regions changes in time. We also
provide a simple expression for the lower bound of the useful entanglement in
the system in terms of the average number of scattered atoms and the number of
modes they occupy. We then apply our theory to a recent "twin-beam" experiment
[R. B\"ucker {\it et al.}, Nat. Phys. {\bf 7}, 608 (2011)]. The only numerical
step of our semi-analytical description can be easily solved and does not
require implementation of any stochastic methods.Comment: 11 pages, 6 figure
Genericity of Fr\'echet smooth spaces
If a separable Banach space contains an isometric copy of every separable
reflexive Fr\'echet smooth Banach space, then it contains an isometric copy of
every separable Banach space. The same conclusion holds if we consider
separable Banach spaces with Fr\'echet smooth dual space. This improves a
result of G. Godefroy and N. J. Kalton.Comment: 34 page
Self-consistent field theory of polarized BEC: dispersion of collective excitation
We suggest the construction of a set of the quantum hydrodynamics equations
for the Bose-Einstein condensate (BEC), where atoms have the electric dipole
moment. The contribution of the dipole-dipole interactions (DDI) to the Euler
equation is obtained. Quantum equations for the evolution of medium
polarization are derived. Developing mathematical method allows to study effect
of interactions on the evolution of polarization. The developing method can be
applied to various physical systems in which dynamics is affected by the DDI.
Derivation of Gross-Pitaevskii equation for polarized particles from the
quantum hydrodynamics is described. We showed that the Gross-Pitaevskii
equation appears at condition when all dipoles have the same direction which
does not change in time. Comparison of the equation of the electric dipole
evolution with the equation of the magnetization evolution is described.
Dispersion of the collective excitations in the dipolar BEC, either affected or
not affected by the uniform external electric field, is considered using our
method. We show that the evolution of polarization in the BEC leads to the
formation of a novel type of the collective excitations. Detailed description
of the dispersion of collective excitations is presented. We also consider the
process of wave generation in the polarized BEC by means of a monoenergetic
beam of neutral polarized particles. We compute the possibilities of the
generation of Bogoliubov and polarization modes by the dipole beam.Comment: 16 pages, 15 figures. arXiv admin note: substantial text overlap with
arXiv:1106.082
Surprising results of soliton collisions in a three component Bose Einstein condensate
We investigate binary soliton collisions in three component BECs with spin exchange
interactions and FÂ =Â 1. For very special values of the coupling
constants, these collisions are known to be elastic. We find that, for a further narrow
range of parameters, collisions are almost elastic in the sense that a small amount of
energy is lost in the process. Emergent solitons are almost identical to the original
ones. However, the generic behaviour, found for most values of the two coupling constants,
is very different. We observed the creation of spin component oscillations in both
emerging entities. We therefore call these entities oscillatons. They are robust and fit
an exact solution of the equations. Thus colliding two solitons can in general, somewhat
unexpectedly, result in one of two very different outcomes