



01431nas a2200169   4500008004100000245007100041210006900112260001400181490000700195520091200202100002001114700001801134700001901152700002301171700002301194856004401217       2005                        eng d00aBragg Spectroscopy of ultracold atoms loaded in an optical lattice0 aBragg Spectroscopy of ultracold atoms loaded in an optical latti  c2005/8/120 v723 a  We study Bragg spectroscopy of ultra-cold atoms in one-dimensional optical
lattices as a method for probing the excitation spectrum in the Mott insulator
phase, in particular the one particle-hole excitation band. Within the
framework of perturbation theory we obtain an analytical expression for the
dynamic structure factor $S(q,\omega)$ and use it to calculate the imparted
energy which has shown to be a relevant observable in recent experiments. We
test the accuracy of our approximations by comparing them with numerically
exact solutions of the Bose-Hubbard model in restricted cases and establish the
limits of validity of our linear response analysis. Finally we show that when
the system is deep in the Mott insulator regime, its response to the Bragg
perturbation is temperature dependent. We suggest that this dependence might be
used as a tool to probe temperatures of order of the Mott gap.
1 aRey, Ana, Maria1 aBlakie, Blair1 aPupillo, Guido1 aWilliams, Carl, J.1 aClark, Charles, W.  uhttp://arxiv.org/abs/cond-mat/0406552v201370nas a2200193   4500008004100000245007200041210006900113260001500182300001400197490000700211520079400218100002001012700001901032700001701051700001801068700002301086700002301109856004401132       2003                        eng d00aBogoliubov approach to superfluidity of atoms in an optical lattice0 aBogoliubov approach to superfluidity of atoms in an optical latt  c2003/03/14  a825 - 8410 v363 a  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.
1 aRey, Ana, Maria1 aBurnett, Keith1 aRoth, Robert1 aEdwards, Mark1 aWilliams, Carl, J.1 aClark, Charles, W.  uhttp://arxiv.org/abs/cond-mat/0210550v2