6,775 research outputs found
Combinatorial theorems relative to a random set
We describe recent advances in the study of random analogues of combinatorial
theorems.Comment: 26 pages. Submitted to Proceedings of the ICM 201
`St\"uckelberg interferometry' with ultracold molecules
We report on the realization of a time-domain `St\"uckelberg interferometer',
which is based on the internal state structure of ultracold Feshbach molecules.
Two subsequent passages through a weak avoided crossing between two different
orbital angular momentum states in combination with a variable hold time lead
to high-contrast population oscillations. This allows for a precise
determination of the energy difference between the two molecular states. We
demonstrate a high degree of control over the interferometer dynamics. The
interferometric scheme provides new possibilities for precision measurements
with ultracold molecules.Comment: 4 pages, 5 figure
A sharp threshold for random graphs with a monochromatic triangle in every edge coloring
Let be the set of all finite graphs with the Ramsey property that
every coloring of the edges of by two colors yields a monochromatic
triangle. In this paper we establish a sharp threshold for random graphs with
this property. Let be the random graph on vertices with edge
probability . We prove that there exists a function with
, as tends to infinity
Pr[G(n,(1-\eps)\hat c/\sqrt{n}) \in \R ] \to 0 and Pr [ G(n,(1+\eps)\hat
c/\sqrt{n}) \in \R ] \to 1. A crucial tool that is used in the proof and is
of independent interest is a generalization of Szemer\'edi's Regularity Lemma
to a certain hypergraph setting.Comment: 101 pages, Final version - to appear in Memoirs of the A.M.
Production of cold molecules via magnetically tunable Feshbach resonances
Magnetically tunable Feshbach resonances were employed to associate cold
diatomic molecules in a series of experiments involving both atomic Bose as
well as two spin component Fermi gases. This review illustrates theoretical
concepts of both the particular nature of the highly excited Feshbach molecules
produced and the techniques for their association from unbound atom pairs.
Coupled channels theory provides the rigorous formulation of the microscopic
physics of Feshbach resonances in cold gases. Concepts of dressed versus bare
energy states, universal properties of Feshbach molecules, as well as the
classification in terms of entrance- and closed-channel dominated resonances
are introduced on the basis of practical two-channel approaches. Their
significance is illustrated for several experimental observations, such as
binding energies and lifetimes with respect to collisional relaxation.
Molecular association and dissociation are discussed in the context of
techniques involving linear magnetic field sweeps in cold Bose and Fermi gases
as well as pulse sequences leading to Ramsey-type interference fringes. Their
descriptions in terms of Landau-Zener, two-level mean field as well as beyond
mean field approaches are reviewed in detail, including the associated ranges
of validity.Comment: 50 pages, 26 figures, to be published in Reviews of Modern Physics,
final version with updated reference
Feshbach resonances in Cesium at Ultra-low Static Magnetic Fields
We have observed Feshbach resonances for 133Cs atoms in two different
hyperfine states at ultra-low static magnetic fields by using an atomic
fountain clock. The extreme sensitivity of our setup allows for high
signal-to-noise-ratio observations at densities of only 2*10^7 cm^{-3}. We have
reproduced these resonances using coupled-channels calculations which are in
excellent agreement with our measurements. We justify that these are s-wave
resonances involving weakly-bound states of the triplet molecular Hamiltonian,
identify the resonant closed channels, and explain the observed multi-peak
structure. We also describe a model which precisely accounts for the
collisional processes in the fountain and which explains the asymmetric shape
of the observed Feshbach resonances in the regime where the kinetic energy
dominates over the coupling strength.Comment: 5 pages, 4 figures, 1 tabl
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