01204nas a2200181 4500008004100000245007100041210006900112260001500181490000800196520064500204100002700849700001900876700001900895700002700914700002000941700002500961856003600986 2018 eng d00aSpectrum estimation of density operators with alkaline-earth atoms0 aSpectrum estimation of density operators with alkalineearth atom c2018/01/090 v1203 aWe show that Ramsey spectroscopy of fermionic alkaline-earth atoms in a square-well trap provides an efficient and accurate estimate for the eigenspectrum of a density matrix whose *n *copies are stored in the nuclear spins of *n *such atoms. This spectrum estimation is enabled by the high symmetry of the interaction Hamiltonian, dictated, in turn, by the decoupling of the nuclear spin from the electrons and by the shape of the square-well trap. Practical performance of this procedure and its potential applications to quantum computing, quantum simulation, and time-keeping with alkalineearth atoms are discussed.

1 aBeverland, Michael, E.1 aHaah, Jeongwan1 aAlagic, Gorjan1 aCampbell, Gretchen, K.1 aRey, Ana, Maria1 aGorshkov, Alexey, V. uhttp://arxiv.org/abs/1608.0204501945nas a2200205 4500008004100000245007600041210006900117260001500186300001100201490000700212520133700219100001901556700001901575700001901594700002401613700002701637700001801664700001901682856003801701 2015 eng d00aSelf-heterodyne detection of the {\it in-situ} phase of an atomic-SQUID0 aSelfheterodyne detection of the it insitu phase of an atomicSQUI c2015/09/03 a0336020 v923 a We present theoretical and experimental analysis of an interferometric
measurement of the {\it in-situ} phase drop across and current flow through a
rotating barrier in a toroidal Bose-Einstein condensate (BEC). This experiment
is the atomic analog of the rf-superconducting quantum interference device
(SQUID). The phase drop is extracted from a spiral-shaped density profile
created by the spatial interference of the expanding toroidal BEC and a
reference BEC after release from all trapping potentials. We characterize the
interferometer when it contains a single particle, which is initially in a
coherent superposition of a torus and reference state, as well as when it
contains a many-body state in the mean-field approximation. The single-particle
picture is sufficient to explain the origin of the spirals, to relate the
phase-drop across the barrier to the geometry of a spiral, and to bound the
expansion times for which the {\it in-situ} phase can be accurately determined.
Mean-field estimates and numerical simulations show that the inter-atomic
interactions shorten the expansion time scales compared to the single-particle
case. Finally, we compare the mean-field simulations with our experimental data
and confirm that the interferometer indeed accurately measures the {\it
in-situ} phase drop.
1 aMathew, Ranchu1 aKumar, Avinash1 aEckel, Stephen1 aJendrzejewski, Fred1 aCampbell, Gretchen, K.1 aEdwards, Mark1 aTiesinga, Eite uhttp://arxiv.org/abs/1506.09149v2