Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rotational spectroscopy of cold, trapped molecular ions in the
  Lamb-Dicke regime   Sympathetic cooling of trapped ions has been established as a powerful
technique for manipulation of non-laser-coolable ions
(Raizen1992,Waki1992,Bowe1999,Barrett2003). For molecular ions, it promises
vastly enhanced spectroscopic resolution and accuracy. However, this potential
remains untapped so far, with the best resolution achieved being not better
than $5\times10^{-8}$ fractionally, due to residual Doppler broadening being
present in ion clusters even at the lowest achievable translational
temperatures (Bressel2012). Here we introduce a general and accessible approach
that enables Doppler-free rotational spectroscopy. It makes use of the strong
radial spatial confinement of molecular ions when trapped and crystallized in a
linear quadrupole trap, providing the Lamb-Dicke regime for rotational
transitions. We achieve a line width of $1\times10^{-9}$ fractionally and
$1.3~\textrm{kHz}$ absolute, an improvement by $50$ and nearly $3\times10^{3}$,
respectively, over other methods. The systematic uncertainty is
$2.5\times10^{-10}$. As an application, we demonstrate the most precise test of
$\textit{ab initio}$ molecular theory and the most precise ($1.3~\textrm{PPB}$)
spectroscopic determination of the proton mass. The results represent the long
overdue extension of Doppler-free microwave spectroscopy of laser-cooled atomic
ion clusters (Berkeland1998) to higher spectroscopy frequencies and to
molecules. This approach enables a vast range of high-precision measurements on
molecules, both on rotational and, as we project, vibrational transitions.

15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg