Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase Estimation from Atom Position Measurements   We study the measurement of the position of atoms as a means to estimate the
relative phase between two Bose-Einstein condensates. First, we consider $N$
atoms released from a double-well trap, forming an interference pattern, and
show that a simple least-squares fit to the density gives a shot-noise limited
sensitivity. The shot-noise limit can instead be overcome by using correlation
functions of order $\sqrt{N}$ or larger. The measurement of the
$N\mathrm{th}$-order correlation function allows to estimate the relative phase
at the Heisenberg limit. Phase estimation through the measurement of the
center-of-mass of the interference pattern can also provide sub-shot-noise
sensitivity. Finally, we study the effect of the overlap between the two clouds
on the phase estimation, when Mach-Zehnder interferometry is performed in a
double-well.

32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom