Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Multi-path Interferometer with Ultracold Atoms Trapped in an Optical
  Lattice   We study an ultra-cold gas of $N$ bosons trapped in a one dimensional
$M$-site optical lattice perturbed by a spatially dependent potential $g\cdot
x^j$, where the unknown coupling strength $g$ is to be estimated. We find that
the measurement uncertainty is bounded by $\Delta g\propto\frac1{N (M^j-1)}$.
For a typical case of a linear potential, the sensitivity improves as $M^{-1}$,
which is a result of multiple interferences between the sites -- an advantage
of multi-path interferometers over the two-mode setups. Next, we calculate the
estimation sensitivity for a specific measurement where, after the action of
the potential, the particles are released from the lattice and form an
interference pattern. If the parameter is estimated by a least-square fit of
the average density to the interference pattern, the sensitivity still scales
like $M^{-1}$ for linear potentials and can be further improved by preparing a
properly correlated initial state in the lattice.

20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph