CONFINED ULTRACOLD BOSONS IN ONE DIMENSIONAL OPTICAL LATTICES
CONFINED ULTRACOLD BOSONS IN ONE DIMENSIONAL OPTICAL LATTICES
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Date
2005-08-04
Authors
Pupillo, Guido
Advisor
Williams, Carl J
Hu, Bei-Lok
Hu, Bei-Lok
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Abstract
This dissertation presents my research covering the field of ultracold atoms
loaded in optical lattices. The static and
dynamical properties of atoms in combined periodic and parabolic potentials are studied,
with a focus on the strongly interacting regimes. Because parabolic magnetic and optical
potentials are routinely used to confine atoms, the results
of this research are directly relevant to ongoing experimental
endeavours in atomic physics.
After a review of the basic theory of atoms in homogeneous periodic potentials,
the equilibrium and non-equilibrium
properties of non-interacting and interacting atoms
in periodic plus parabolic potentials are studied.
The problem of the localization of the many-body wavefunction
for systems with arbitrary peak onsite density is presented in Chapters 3 and 4.
The physics pertaining to the experimental realization of Mott insulator states
with one or more atoms per sites in inhomogeneous lattices
is elucidated by introducing an intuitive model
for strongly interacting bosons in one dimension.
This model is then utilized to study the decay
of the dipole oscillations of atomic ensembles
subject to a small displacement of the parabolic potential.
Good agreement is found with results of recent experiments.
Chapters 5 and 6 are dedicated to the characterization
of the Mott insulator state with unit filling, which plays
a central role in proposed schemes for neutral atom quantum computation.
The usefulness of Bragg spectroscopy to probe
the excitation spectrum of the Mott state in homogeneous lattices
is analyzed in Chapter 5, where the limits of validity
of linear response theory in this strongly correlated regime
are delimited. In Chapter 6 the effects of finite temperature on
the confined Mott insulator state are studied, and
a scheme is devised for possibly estimating the system's temperature,
at energies of the order of the inter-particle interaction energy.
Finally, in Chapter 7, a proposal is introduced to utilize the Mott state
as a robust register for neutral atom quantum computation.
Unwanted residual quantum coherences
inherent to the Mott insulator ground state are eliminated
by a judicious choice of the trapping potentials
and a selective measurement on a molecular photo-associative
transition.