%0 Journal Article
%J Physical Review A
%D 2015
%T Self-heterodyne detection of the \it in-situ phase of an atomic-SQUID
%A Ranchu Mathew
%A Avinash Kumar
%A Stephen Eckel
%A Fred Jendrzejewski
%A Gretchen K. Campbell
%A Mark Edwards
%A Eite Tiesinga
%X 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.
%B Physical Review A
%V 92
%P 033602
%8 2015/09/03
%G eng
%U http://arxiv.org/abs/1506.09149v2
%N 3
%! Phys. Rev. A
%R 10.1103/PhysRevA.92.033602
%0 Journal Article
%J Physical Review A
%D 2008
%T Tunneling phase gate for neutral atoms in a double-well lattice
%A Frederick W. Strauch
%A Mark Edwards
%A Eite Tiesinga
%A Carl J. Williams
%A Charles W. Clark
%X We propose a new two--qubit phase gate for ultra--cold atoms confined in an experimentally realized tilted double--well optical lattice [Sebby--Strabley et al., Phys. Rev. A {\bf 73} 033605 (2006)]. Such a lattice is capable of confining pairs of atoms in a two--dimensional array of double--well potentials where control can be exercised over the barrier height and the energy difference of the minima of the two wells (known as the ``tilt''). The four lowest single--particle motional states consist of two pairs of motional states in which each pair is localized on one side of the central barrier, allowing for two atoms confined in such a lattice to be spatially separated qubits. We present a time--dependent scheme to manipulate the tilt to induce tunneling oscillations which produce a collisional phase gate. Numerical simulations demonstrate that this gate can be performed with high fidelity.
%B Physical Review A
%V 77
%8 2008/5/12
%G eng
%U http://arxiv.org/abs/0712.1856v1
%N 5
%! Phys. Rev. A
%R 10.1103/PhysRevA.77.050304
%0 Journal Article
%J Journal of Physics B: Atomic, Molecular and Optical Physics
%D 2003
%T Bogoliubov approach to superfluidity of atoms in an optical lattice
%A Ana Maria Rey
%A Keith Burnett
%A Robert Roth
%A Mark Edwards
%A Carl J. Williams
%A Charles W. Clark
%X We use the Bogoliubov theory of atoms in an optical lattice to study the approach to the Mott-insulator transition. We derive an explicit expression for the superfluid density based on the rigidity of the system under phase variations. This enables us to explore the connection between the quantum depletion of the condensate and the quasi-momentum distribution on the one hand and the superfluid fraction on the other. The approach to the insulator phase may be characterized through the filling of the band by quantum depletion, which should be directly observable via the matter wave interference patterns. We complement these findings by self-consistent Hartree-Fock-Bogoliubov-Popov calculations for one-dimensional lattices including the effects of a parabolic trapping potential.
%B Journal of Physics B: Atomic, Molecular and Optical Physics
%V 36
%P 825 - 841
%8 2003/03/14
%G eng
%U http://arxiv.org/abs/cond-mat/0210550v2
%N 5
%! J. Phys. B: At. Mol. Opt. Phys.
%R 10.1088/0953-4075/36/5/304