17,190 research outputs found
Enhancing the area of a Raman atom interferometer using a versatile double-diffraction technique
IIn this paper we demonstrate a new scheme for Raman transitions which
realize a symmetric momentum-space splitting of , deflecting the
atomic wave-packets into the same internal state. Combining the advantages of
Raman and Bragg diffraction, we achieve a three pulse state labelled
interferometer, intrinsically insensitive to the main systematics and
applicable to all kind of atomic sources. This splitting scheme can be extended
to momentum transfer by a multipulse sequence and is implemented
on a interferometer. We demonstrate the area enhancement by
measuring inertial forces
Some q-analogues of supercongruences of Rodriguez-Villegas
We study different q-analogues and generalizations of the ex-conjectures of
Rodriguez-Villegas. For example, for any odd prime p, we show that the known
congruence \sum_{k=0}^{p-1}\frac{{2k\choose k}^2}{16^k} \equiv
(-1)^{\frac{p-1}{2}}\pmod{p^2} has the following two nice q-analogues with
[p]=1+q+...+q^{p-1}:
\sum_{k=0}^{p-1}\frac{(q;q^2)_k^2}{(q^2;q^2)_k^2}q^{(1+\varepsilon)k} &\equiv
(-1)^{\frac{p-1}{2}}q^{\frac{(p^2-1)\varepsilon}{4}}\pmod{[p]^2}, where
(a;q)_0=1, (a;q)_n=(1-a)(1-aq)...(1-aq^{n-1}) for n=1,2,..., and
\varepsilon=\pm1. Several related conjectures are also proposed.Comment: 14 pages, to appear in J. Number Theor
- …