21 research outputs found
Controlling two-species Mott-insulator phses in an optical lattice to form an array of dipolar molecules
We consider the transfer of a two-species Bose-Einstein condensate into an
optical lattice with a density such that that a Mott-insulator state with one
atom per species per lattice site is obtained in the deep lattice regime.
Depending on collision parameters the result could be either a `mixed' or a
`separated' Mott-insulator phase. Such a `mixed' two-species insulator could
then be photo-associated into an array of dipolar molecules suitable for
quantum computation or the formation of a dipolar molecular condensate. For the
case of a Rb-K two-species BEC, however, the large inter-species
scattering length makes obtaining the desired `mixed' Mott insulator phase
difficult. To overcome this difficulty we investigate the effect of varying the
lattice frequency on the mean-field interaction and find a favorable parameter
regime under which a lattice of dipolar molecules could be generated
Magnetism in a lattice of spinor Bose condensates
We study the ground state magnetic properties of ferromagnetic spinor
Bose-Einstein condensates confined in a deep optical lattices. In the Mott
insulator regime, the ``mini-condensates'' at each lattice site behave as
mesoscopic spin magnets that can interact with neighboring sites through both
the static magnetic dipolar interaction and the light-induced dipolar
interaction. We show that such an array of spin magnets can undergo a
ferromagnetic or anti-ferromagnetic phase transition under the magnetic dipolar
interaction depending on the dimension of the confining optical lattice. The
ground-state spin configurations and related magnetic properties are
investigated in detail
Modulational instability in nonlocal nonlinear Kerr media
We study modulational instability (MI) of plane waves in nonlocal nonlinear
Kerr media. For a focusing nonlinearity we show that, although the nonlocality
tends to suppress MI, it can never remove it completely, irrespectively of the
particular profile of the nonlocal response function. For a defocusing
nonlinearity the stability properties depend sensitively on the response
function profile: for a smooth profile (e.g., a Gaussian) plane waves are
always stable, but MI may occur for a rectangular response. We also find that
the reduced model for a weak nonlocality predicts MI in defocusing media for
arbitrary response profiles, as long as the intensity exceeds a certain
critical value. However, it appears that this regime of MI is beyond the
validity of the reduced model, if it is to represent the weakly nonlocal limit
of a general nonlocal nonlinearity, as in optics and the theory of
Bose-Einstein condensates.Comment: 8 pages, submitted to Phys. Rev.
Theory of orbital state and spin interactions in ferromagnetic titanates
A spin-orbital superexchange Hamiltonian in a Mott insulator with
orbital degeneracy is investigated. More specifically, we focus on a spin
ferromagnetic state of the model and study a collective behavior of orbital
angular momentum. Orbital order in the model occurs in a nontrivial way -- it
is stabilized exclusively by quantum effects through the order-from-disorder
mechanism. Several energetically equivalent orbital orderings are identified.
Some of them are specified by a quadrupole ordering and have no unquenched
angular momentum at low energy. Other states correspond to a noncollinear
ordering of the orbital angular momentum and show the magnetic Bragg peaks at
specific positions. Order parameters are unusually small because of strong
quantum fluctuations. Orbital contribution to the resonant x-ray scattering is
discussed. The dynamical magnetic structure factor in different ordered states
is calculated. Predictions made should help to observe elementary excitations
of orbitals and also to identify the type of the orbital order in ferromagnetic
titanates. Including further a relativistic spin-orbital coupling, we derive an
effective low-energy spin Hamiltonian and calculate a spin-wave spectrum, which
is in good agreement with recent experimental observations in YTiO.Comment: 25 pages, 17 figure
Magnetic Ordering, Orbital Ordering and Resonant X-ray Scattering in Perovskite Titanates
The effective Hamiltonian for perovskite titanates is derived by taking into
account the three-fold degeneracy of orbitals and the strong
electron-electron interactions. The magnetic and orbital ordered phases are
studied in the mean-field approximation applied to the effective Hamiltonian. A
large degeneracy of the orbital states in the ferromagnetic phase is found in
contrast to the case of the doubly degenerate orbitals. Lifting of this
orbital degeneracy due to lattice distortions and spin-orbit coupling is
examined. A general form for the scattering cross section of the resonant x-ray
scattering is derived and is applied to the recent experimental results in
YTiO. The spin wave dispersion relation in the orbital ordered YTiO is
also studied.Comment: 10 pages, 6 figure