6 research outputs found
(3+1) Massive Dirac Fermions with Ultracold Atoms in Optical Lattices
We propose the experimental realization of (3+1) relativistic Dirac fermions
using ultracold atoms in a rotating optical lattice or, alternatively, in a
synthetic magnetic field. This approach has the advantage to give mass to the
Dirac fermions by coupling the ultracold atoms to a Bragg pulse. A dimensional
crossover from (3+1) to (2+1) Dirac fermions can be obtained by varying the
anisotropy of the lattice. We also discuss under which conditions the
interatomic potentials give rise to relativistically invariant interactions
among the Dirac fermions
Optical Flux Lattices for Two-Photon Dressed States
We describe a simple scheme by which "optical flux lattices" can be
implemented in ultracold atomic gases using two-photon dressed states. This
scheme can be applied, for example, to the ground state hyperfine levels of
commonly used atomic species. The resulting flux lattices simulate a magnetic
field with high mean flux density, and have low energy bands analogous to the
lowest Landau level. We show that in practical cases the atomic motion
significantly deviates from the adiabatic following of one dressed state, and
that this can lead to significant interactions even for fermions occupying a
single band. Our scheme allows experiments on cold atomic gases to explore
strong correlation phenomena related to the fractional quantum Hall effect,
both for fermions and bosons.Comment: 6 page
Fractional quantum Hall states of few bosonic atoms in geometric gauge fields
We employ the exact diagonalization method to analyze the possibility of
generating strongly correlated states in two-dimensional clouds of ultracold
bosonic atoms which are subjected to a geometric gauge field created by
coupling two internal atomic states to a laser beam. Tuning the gauge field
strength, the system undergoes stepwise transitions between different ground
states, which we describe by analytical trial wave functions, amongst them the
Pfaffian, the Laughlin, and a Laughlin quasiparticle many-body state. The
adiabatic following of the center of mass movement by the lowest energy dressed
internal state, is lost by the mixing of the second internal state. This
mixture can be controlled by the intensity of the laser field. The
non-adiabaticity is inherent to the considered setup, and is shown to play the
role of circular asymmetry. We study its influence on the properties of the
ground state of the system. Its main effect is to reduce the overlap of the
numerical solutions with the analytical trial expressions by occupying states
with higher angular momentum. Thus, we propose generalized wave functions
arising from the Laughlin and Pfaffian wave function by including components,
where extra Jastrow factors appear, while preserving important features of
these states. We analyze quasihole excitations over the Laughlin and
generalized Laughlin states, and show that they possess effective fractional
charge and obey anyonic statistics. Finally, we study the energy gap over the
Laughlin state as the number of particles is increased keeping the chemical
potential fixed. The gap is found to decrease as the number of particles is
increased, indicating that the observability of the Laughlin state is
restricted to a small number of particles.Comment: 28 pages, 16 figure
Fractional quantum Hall effect in a U(1)xSU(2) gauge field
We consider the bosonic fractional quantum Hall effect in the presence of a
non-Abelian gauge field in addition to the usual Abelian magnetic field. The
non-Abelian field breaks the twofold internal state degeneracy, but preserves
the Landau level degeneracy. Using exact diagonalization, we find that for
moderate non-Abelian field strengths the system's behaviour resembles a single
internal state quantum Hall system, while for stronger fields there is a phase
transition to either two internal state behaviour or the complete absence of
fractional quantum Hall plateaus. Usually the energy gap is reduced by the
presence of a non-Abelian field, but some non-Abelian fields appear to slightly
increase the gap of the and Read-Rezayi states.Comment: 15 pages, 8 figures, submitted to New J. Phy
Particles in non-Abelian gauge potentials - Landau problem and insertion of non-Abelian flux
We study charged spin-1/2 particles in two dimensions, subject to a
perpendicular non-Abelian magnetic field. Specializing to a choice of vector
potential that is spatially constant but non-Abelian, we investigate the Landau
level spectrum in planar and spherical geometry, paying particular attention to
the role of the total angular momentum J = L +S. After this we show that the
adiabatic insertion of non-Abelian flux in a spin-polarized quantum Hall state
leads to the formation of charged spin-textures, which in the simplest cases
can be identified with quantum Hall Skyrmions.Comment: 24 pages, 10 figures (with corrected legends