Doctor of Philosophy, The Ohio State University, 2016, Physics
A large portion of cold atom researches have been devoted to finding novel systems
by taking advantage of the high manipulability of cold atom experiments. From the
original Bose-Einstein condensates, to the recent realization of Harper-Hofstadter models,
cold atoms have kept feeding the world with surprises of realizing systems that were
once thought to be purely theoretical constructions. Such trend of research have propelled
this thesis to seek for possible new physics based on current cold atom technologies, and
to discuss its unique properties.
In the first part, we will discuss the local spin ordering for systems made of large spin
fermions. This is a generalization of the usual magnetic ordering for spin-1/2 systems, and
we shall see that the large spin characters have made qualitative difference. Here we provide
a general tensorial classification for fermionic systems of arbitrary spin, and discussed
their general character and associated topological defects in the Majorana representation.
We have also identified a series of highly symmetric “Platonic solid states” that are stable
against perturbations, and have good chance of being observed in experiments.
The second part focuses on another topic, which is the eects of background manifold
on the quantum systems residing on it. We will first examine the vortex physics for Bose
condensates confined on non-trivial 2D surfaces with synthetic gauge fields. In particular,
we discuss in detail the cylindrical surface as an example where two types of vortices and a
peculiar “necklace” pattern show up as a result of the confining geometry. Then we discuss the topic of Hall viscosity, a unique dissipationless viscosity coeffcient that is related to
the adiabatic change of space geometry. We relate it to the density response of a system,
and therefore provide an alternative way to compute and measure such a quantity.
Committee: Tin-Lun Ho (Advisor); Eric Braaten (Committee Member); Richard Furnstahl (Committee Member); Jay Gupta (Committee Member)
Subjects: Physics