Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear Phonon Interferometry at the Heisenberg Limit   Interferometers operating at or close to quantum limits of precision have
found wide application in tabletop searches for physics beyond the standard
model, the study of fundamental forces and symmetries of nature and
foundational tests of quantum mechanics. The limits imposed by quantum
fluctuations and measurement backaction on conventional interferometers
($\delta \phi \sim 1/\sqrt{N}$) have spurred the development of schemes to
circumvent these limits through quantum interference, multiparticle
interactions and entanglement. A prominent example of such schemes, the
so-called $SU(1,1)$ interferometer, has been shown to be particularly robust
against particle loss and inefficient detection, and has been demonstrated with
photons and ultracold atoms. Here, we realize a $SU(1,1)$ interferometer in a
fundamentally new platform in which the interfering arms are distinct flexural
modes of a millimeter-scale mechanical resonator. We realize up to 15.4(3) dB
of noise squeezing and demonstrate the Heisenberg scaling of interferometric
sensitivity ($\delta \phi \sim 1/N$), corresponding to a 6-fold improvement in
measurement precision over a conventional interferometer. Our work extends the
optomechanical toolbox for the quantum manipulation of macroscopic mechanical
motion and presents new avenues for studies of optomechanical sensing and the
nonequilibrium dynamics of multimode optomechanical systems.

23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol