63 research outputs found
Ultracold atoms in artificial gauge fields
The present thesis studies a variety of cold atomic systems in artificial gauge fields. In the first part we focus on fractional quantum Hall effects, asking whether interesting topological states can be realized with cold atoms. We start by making a close connection to solid-state systems and first consider fermionic atoms with dipolar interactions. Assuming the system to be in the Laughlin state, we evaluate the energy gap in the thermodynamic limit as a measure for the robustness of the state. We show that it can be increased by additionally applying a non-Abelian gauge field squeezing the Landau levels. We then switch to bosonic systems with repulsive contact interactions. Artificial magnetic fields for cold bosons have extensively been discussed before in the context of rotating Bose gases. We follow a different approach where the gauge field is due to an atom-laser coupling. Thus, transitions between different dressed states have to be included. They are shown to break the cylindrical symmetry of the system. Modifying the Laughlin state and the Moore-Read state accordingly, we determine the parameter regimes where they are good representations for the ground state of the system obtained via exact diagonalization. One of the most interesting feature of fractional quantum Hall states is the anyonic behavior of their excitations. We therefore also study quasiholes in the Laughlin state and the modified Laughlin state. They are shown to posses anyonic properties, which become manifest even in small systems. Moreover, the dynamics of a single quasihole causes visible traces in the density of the system which allow to clearly distinguish the Laughlin regime from less correlated phases. In the latter, a sequence of collapses and revivals of the quasihole can be observed, which is absent in the Laughlin regime. Extending our study to bosonic systems with a pesudospin-1/2 degree of freedom, we discuss the formation of strongly correlated spin singlets. Strikingly, at filling v=4/3, the system is described by a state with non-Abelian excitations, which is constructed as the zero-energy ground state of repulsive three-body contact interactions. Systems with internal degrees of freedom also allow for implementing artificial spin-orbit coupling. It is shown to give rise to a variety of incompressible states. In the second part of the thesis, we concentrate on condensed system. Bose-Einstein condensates with spin-orbit coupling are shown to have a degeneracy on the mean-field level, which is lifted by quantum and thermal fluctuations. The system becomes experimentally feasible in three dimensions, where the condensate depletion remains finite, and thus allow for an experimental observation of this order-by-disorder mechanism. Finally, we study the influence of Abelian and non-Abelian gauge fields on the quantum phase transitions of bosons in a square optical lattice. Re-entrant superfluid phases and superfluids at finite momenta are interesting properties featured by such systems
Few interacting fermions in one-dimensional harmonic trap
We study spin-1/2 fermions, interacting via a two-body contact potential, in
a one-dimensional harmonic trap. Applying exact diagonalization, we investigate
their behavior at finite interaction strength, and discuss the role of the
ground-state degeneracy which occurs for sufficiently strong repulsive
interaction. Even low temperature or a completely depolarizing channel may then
dramatically influence the system's behavior. We calculate level occupation
numbers as signatures of thermalization, and we discuss the mechanisms to break
the degeneracy
Fermionic Chern insulator from twisted light with linear polarization
A Fermionic Chern insulator serves as a building block for a plethora of
topological phases of matter. Chern insulators have now been realized by
imposing magnetic order on topological insulators, in hexagonal arrays of
helical waveguides, or by driving graphene or graphene-like optical lattices
with circularly polarized light. It is known that light beams, in addition to
spin angular momentum (SAM), can also carry orbital angular momentum (OAM).
Such OAM beams are now being extensively used for new applications in a variety
of fields which include optical communication, quantum information, cosmology,
and attophysics. These beams are characterized by a phase singularity at the
center. The possibility of impinging these beams to create Fermionic
topological phases of matter that can harness the central phase singularity of
an optical vortex beam has not yet been explored. Here, we propose how a
linearly polarized OAM beam can be used to realize a Fermionic Chern insulator.Comment: 7 pages, 4 figure
Chains with loops - synthetic magnetic fluxes and topological order in one-dimensional spin systems
Engineering topological quantum order has become a major field of physics.
Many advances have been made by synthesizing gauge fields in cold atomic
systems. Here, we carry over these developments to other platforms which are
extremely well suited for quantum engineering, namely trapped ions and
nano-trapped atoms. Since these systems are typically one-dimensional, the
action of artificial magnetic fields has so far received little attention.
However, exploiting the long-range nature of interactions, loops with
non-vanishing magnetic fluxes become possible even in one-dimensional settings.
This gives rise to intriguing phenomena, such as fractal energy spectra, flat
bands with localized edge states, and topological many-body states. We
elaborate on a simple scheme for generating the required artificial fluxes by
periodically driving an XY spin chain. Concrete estimates demonstrating the
experimental feasibility for trapped ions and atoms in waveguides are given.Comment: 9 pages, 6 figure
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