5,003 research outputs found
A nonlinear Ramsey interferometer operating beyond the Heisenberg limit
We show that a dynamically evolving two-mode Bose-Einstein condensate (TBEC)
with an adiabatic, time-varying Raman coupling maps exactly onto a nonlinear
Ramsey interferometer that includes a nonlinear medium. Assuming a realistic
quantum state for the TBEC, namely the SU(2) coherent spin state, we find that
the measurement uncertainty of the ``path-difference'' phase shift scales as
the standard quantum limit (1/N^{1/2}) where N is the number of atoms, while
that for the interatomic scattering strength scales as 1/N^{7/5}, overcoming
the Heisenberg limit of 1/N.Comment: 4 figures. Submitted for publicatio
Ehrenfest Dynamics and Frictionless Cooling Methods
Recently introduced methods which result in shortcuts to adiabaticity,
particularly in the context of frictionless cooling, are rederived and
discussed in the framework of an approach based on Ehrenfest dynamics. This
construction provides physical insights into the emergence of the Ermakov
equation, the choice of its boundary conditions, and the use of minimum
uncertainty states as indicators of the efficiency of the procedure.
Additionally, it facilitates the extension of frictionless cooling to more
general situations of physical relevance, such as optical dipole trapping
schemes. In this context, we discuss frictionless cooling in the short-time
limit, a complementary case to the one considered in the literature, making
explicit the limitations intrinsic to the technique when the full
three-dimensional case is analyzed.Comment: 9 pages, 4 figures, v2: To appear in Physical Review A. (some minor
typos corrected and some references added
Idiopathic arterial calcification of infancy : a case report
Idiopathic arterial calcification of infancy is a rare condition characterized by
extensive calcification and stenosis of large and medium sized arteries. A ten day old
female baby developed sudden shortness of breath and was treated with oxygen and
antibiotics. Antenatal echocardiography showed calcification of the aorta and
pulmonary arteries. Autopsy examination revealed extensive calcification in the walls
of major arteries and vessels of several organs. The baby was found to have a
karyotype of 47 chromosomes.peer-reviewe
Squeezing and robustness of frictionless cooling strategies
Quantum control strategies that provide shortcuts to adiabaticity are
increasingly considered in various contexts including atomic cooling. Recent
studies have emphasized practical issues in order to reduce the gap between the
idealized models and actual ongoing implementations. We rephrase here the
cooling features in terms of a peculiar squeezing effect, and use it to
parametrize the robustness of frictionless cooling techniques with respect to
noise-induced deviations from the ideal time-dependent trajectory for the
trapping frequency. We finally discuss qualitative issues for the experimental
implementation of this scheme using bichromatic optical traps and lattices,
which seem especially suitable for cooling Fermi-Bose mixtures and for
investigating equilibration of negative temperature states, respectively.Comment: 9 pages, 7 figures; To appear in Physical Review
An Atom Laser is not monochromatic
We study both numerically and analytically the possibility of using an
adiabatic passage control method to construct a Mach-Zehnder interferometer
(MZI) for Bose-Einstein condensates (BECs) in the time domain, in exact
one-to-one correspondence with the traditional optical MZI that involves two
beam splitters and two mirrors. The interference fringes one obtains from such
a minimum-disturbance set up clearly demonstrates that, fundamentally, an atom
laser is not monochromatic due to interatomic interactions. We also consider
how the amount of entanglement in the system correlates to the interference
fringes.Comment: 4 figures. Submitted for publicatio
Hook-content formulae for symplectic and orthogonal tableaux
By considering the specialisation of the
Schur function, Stanley was able to describe a formula for the number of
semistandard Young tableaux of shape in terms of two properties of
the boxes in the diagram for . Using specialisations of symplectic and
orthogonal Schur functions, we derive corresponding formulae, first given by El
Samra and King, for the number of semistandard symplectic and orthogonal
-tableaux.Comment: Withdrawn; paper is outdate
Spanning trees short or small
We study the problem of finding small trees. Classical network design
problems are considered with the additional constraint that only a specified
number of nodes are required to be connected in the solution. A
prototypical example is the MST problem in which we require a tree of
minimum weight spanning at least nodes in an edge-weighted graph. We show
that the MST problem is NP-hard even for points in the Euclidean plane. We
provide approximation algorithms with performance ratio for the
general edge-weighted case and for the case of points in the
plane. Polynomial-time exact solutions are also presented for the class of
decomposable graphs which includes trees, series-parallel graphs, and bounded
bandwidth graphs, and for points on the boundary of a convex region in the
Euclidean plane. We also investigate the problem of finding short trees, and
more generally, that of finding networks with minimum diameter. A simple
technique is used to provide a polynomial-time solution for finding -trees
of minimum diameter. We identify easy and hard problems arising in finding
short networks using a framework due to T. C. Hu.Comment: 27 page
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