31,979 research outputs found
Ramsey interferometry with an atom laser
We present results on a free-space atom interferometer operating on the first
order magnetically insensitive |F=1,mF=0> -> |F=2,mF=0> transition of
Bose-condensed 87Rb atoms. A pulsed atom laser is output-coupled from a
Bose-Einstein condensate and propagates through a sequence of two internal
state beam splitters, realized via coherent Raman transitions between the two
interfering states. We observe Ramsey fringes with a visibility close to 100%
and determine the current and the potentially achievable interferometric phase
sensitivity. This system is well suited to testing recent proposals for
generating and detecting squeezed atomic states.Comment: published version, 8 pages, 3 figure
Seconds-scale coherence in a tweezer-array optical clock
Optical clocks based on atoms and ions achieve exceptional precision and
accuracy, with applications to relativistic geodesy, tests of relativity, and
searches for dark matter. Achieving such performance requires balancing
competing desirable features, including a high particle number, isolation of
atoms from collisions, insensitivity to motional effects, and high duty-cycle
operation. Here we demonstrate a new platform based on arrays of ultracold
strontium atoms confined within optical tweezers that realizes a novel
combination of these features by providing a scalable platform for isolated
atoms that can be interrogated multiple times. With this tweezer-array clock,
we achieve greater than 3 second coherence times and record duty cycles up to
96%, as well as stability commensurate with leading platforms. By using optical
tweezer arrays --- a proven platform for the controlled creation of
entanglement through microscopic control --- this work further promises a new
path toward combining entanglement enhanced sensitivities with the most precise
optical clock transitions
Cycles are strongly Ramsey-unsaturated
We call a graph H Ramsey-unsaturated if there is an edge in the complement of
H such that the Ramsey number r(H) of H does not change upon adding it to H.
This notion was introduced by Balister, Lehel and Schelp who also proved that
cycles (except for ) are Ramsey-unsaturated, and conjectured that,
moreover, one may add any chord without changing the Ramsey number of the cycle
, unless n is even and adding the chord creates an odd cycle.
We prove this conjecture for large cycles by showing a stronger statement: If
a graph H is obtained by adding a linear number of chords to a cycle ,
then , as long as the maximum degree of H is bounded, H is either
bipartite (for even n) or almost bipartite (for odd n), and n is large.
This motivates us to call cycles strongly Ramsey-unsaturated. Our proof uses
the regularity method
Designing Networks with Good Equilibria under Uncertainty
We consider the problem of designing network cost-sharing protocols with good
equilibria under uncertainty. The underlying game is a multicast game in a
rooted undirected graph with nonnegative edge costs. A set of k terminal
vertices or players need to establish connectivity with the root. The social
optimum is the Minimum Steiner Tree. We are interested in situations where the
designer has incomplete information about the input. We propose two different
models, the adversarial and the stochastic. In both models, the designer has
prior knowledge of the underlying metric but the requested subset of the
players is not known and is activated either in an adversarial manner
(adversarial model) or is drawn from a known probability distribution
(stochastic model).
In the adversarial model, the designer's goal is to choose a single,
universal protocol that has low Price of Anarchy (PoA) for all possible
requested subsets of players. The main question we address is: to what extent
can prior knowledge of the underlying metric help in the design? We first
demonstrate that there exist graphs (outerplanar) where knowledge of the
underlying metric can dramatically improve the performance of good network
design. Then, in our main technical result, we show that there exist graph
metrics, for which knowing the underlying metric does not help and any
universal protocol has PoA of , which is tight. We attack this
problem by developing new techniques that employ powerful tools from extremal
combinatorics, and more specifically Ramsey Theory in high dimensional
hypercubes.
Then we switch to the stochastic model, where each player is independently
activated. We show that there exists a randomized ordered protocol that
achieves constant PoA. By using standard derandomization techniques, we produce
a deterministic ordered protocol with constant PoA.Comment: This version has additional results about stochastic inpu
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