6,721 research outputs found
Large rainbow matchings in large graphs
A \textit{rainbow subgraph} of an edge-colored graph is a subgraph whose
edges have distinct colors. The \textit{color degree} of a vertex is the
number of different colors on edges incident to . We show that if is
large enough (namely, ), then each -vertex graph with
minimum color degree at least contains a rainbow matching of size at least
Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit
Squeezing of quantum fluctuations by means of entanglement is a well
recognized goal in the field of quantum information science and precision
measurements. In particular, squeezing the fluctuations via entanglement
between two-level atoms can improve the precision of sensing, clocks,
metrology, and spectroscopy. Here, we demonstrate 3.4 dB of metrologically
relevant squeezing and entanglement for ~ 10^5 cold cesium atoms via a quantum
nondemolition (QND) measurement on the atom clock levels. We show that there is
an optimal degree of decoherence induced by the quantum measurement which
maximizes the generated entanglement. A two-color QND scheme used in this paper
is shown to have a number of advantages for entanglement generation as compared
to a single color QND measurement.Comment: 6 pages+suppl, PNAS forma
Short proofs of some extremal results
We prove several results from different areas of extremal combinatorics,
giving complete or partial solutions to a number of open problems. These
results, coming from areas such as extremal graph theory, Ramsey theory and
additive combinatorics, have been collected together because in each case the
relevant proofs are quite short.Comment: 19 page
Space-time sensors using multiple-wave atom levitation
The best clocks to date control the atomic motion by trapping the sample in
an optical lattice and then interrogate the atomic transition by shining on
these atoms a distinct laser of controlled frequency. In order to perform both
tasks simultaneously and with the same laser field, we propose to use instead
the levitation of a Bose-Einstein condensate through multiple-wave atomic
interferences. The levitating condensate experiences a coherent localization in
momentum and a controlled diffusion in altitude. The sample levitation is bound
to resonance conditions used either for frequency or for acceleration
measurements. The chosen vertical geometry solves the limitations imposed by
the sample free fall in previous optical clocks using also atomic
interferences. This configuration yields multiple-wave interferences enabling
levitation and enhancing the measurement sensitivity. This setup, analogous to
an atomic resonator in momentum space, constitutes an attractive alternative to
existing atomic clocks and gravimeters.Comment: 5 pages, 4 figures.Final versio
- âŠ