27 research outputs found
Long Distance Transport of Ultracold Atoms using a 1D optical lattice
We study the horizontal transport of ultracold atoms over macroscopic
distances of up to 20 cm with a moving 1D optical lattice. By using an optical
Bessel beam to form the optical lattice, we can achieve nearly homogeneous
trapping conditions over the full transport length, which is crucial in order
to hold the atoms against gravity for such a wide range. Fast transport
velocities of up to 6 m/s (corresponding to about 1100 photon recoils) and
accelerations of up to 2600 m/s2 are reached. Even at high velocities the
momentum of the atoms is precisely defined with an uncertainty of less than one
photon recoil. This allows for construction of an atom catapult with high
kinetic energy resolution, which might have applications in novel collision
experiments.Comment: 15 pages, 8 figure
Tight polynomial bounds for Loop programs in polynomial space
We consider the following problem: given a program, find tight asymptotic
bounds on the values of some variables at the end of the computation (or at any given
program point) in terms of its input values. We focus on the case of polynomially-bounded
variables, and on a weak programming language for which we have recently shown that
tight bounds for polynomially-bounded variables are computable. These bounds are sets
of multivariate polynomials. While their computability has been settled, the complexity
of this program-analysis problem remained open. In this paper, we show the problem to
be PSPACE-complete. The main contribution is a new, space-efficient analysis algorithm.
This algorithm is obtained in a few steps. First, we develop an algorithm for univariate
bounds, a sub-problem which is already PSPACE-hard. Then, a decision procedure for
multivariate bounds is achieved by reducing this problem to the univariate case; this
reduction is orthogonal to the solution of the univariate problem and uses observations on
the geometry of a set of vectors that represent multivariate bounds. Finally, we transform
the univariate-bound algorithm to produce multivariate bounds
Both can be found at the ENTCS Macro Home Page. The Garland Measure and Computational Complexity of Stack Programs
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