- 21 de outubro de 2015
in Optical Lattices
Spinless bosons in optical lattices reveal a
generic quantum phase transition once the depth of the potential
wells is tuned. When the on-site interaction energy is small
compared to the hopping energy, the ground state is superfluid,
as the bosons are delocalized and phase coherent over the whole
lattice. In the opposite limit, where the on-site interaction
energy dominates over the hopping energy, the ground state is a
Mott insulator, as each boson is trapped in one of the
respective potential minima.
In order to describe both thermodynamic and dynamic
properties of this quantum phase transition we developed a
Ginzburg-Landau theory [1,2]. To this end we started from the
microscopic Bose-Hubbard model, applied diagrammatic techniques
within a systematic strong-coupling expansion, and calculated
the underlying effective action. Already the first beyond
mean-field order exhibits for the boundary of the quantum phase
transition in a three-dimensional cubic lattice a relative error
of less than 3% when compared with most recent Quantum Monte
Carlo simulations . Higher orders turn out to be so accurate
that they even allow for the calculation of critical exponents
. Furthermore, the Ginzburg-Landau theory yields excitation
spectra both in the Mott and the superfluid phase, which agree
qualitatively with recent experiments .
Finally, we discuss three intriguing examples how
the quantum phase transition of bosons in optical lattices can
be tuned. In the first example we consider a spinor Bose gas
loaded into a three-dimensional cubic optical lattice, where the
different superfluid phases of spin-1 bosons are tunable due to
the presence of an external magnetic field . Then we deal
with interacting bosons in an optical lattice with a periodic
modulation of the s-wave scattering length, so the location of
the quantum phase boundary turns out to depend quite sensitively
on both driving amplitude and frequency . Afterwards, we
study the Bose-Hubbard model for the optical Kagome
superlattice, where the delicate interplay between onsite
repulsion and artificial symmetry breaking yields an anisotropic
superfluid density, whose directional dependence is tunable by
several system parameters [7,8].
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