Quantum violation of classical physics in macroscopic systems

While quantum theory has been tested to an incredible degree on
microscopic scales, quantum effects are seldom observed in our
everyday macroscopic world. The curious results of applying quantum
mechanics to macroscopic objects are perhaps best illustrated by
Erwin Schrödinger's famous thought experiment, where a cat can be
put into a superposition state of being both dead and alive.
Obviously, these quantum predictions are in stark contradiction to
our common experience. Even with plenty of theoretical explanations
put forward to explain this discrepancy, a large number of
questions about the frontier between the quantum and the classical
world remain unanswered. To distinguish between classical and
quantum behavior, two fundamental concepts inherent to classical
physics have been established over the years: The world view of
local realism limits the power of classical experiments to
establish correlations over space, while the world view of
macroscopic realism (or macrorealism) restricts temporal
correlations. Necessary conditions for both world views have been
formulated in the form of Bell and Leggett-Garg inequalities, and
Bell inequalities have been shown to be violated by quantum
mechanics through increasingly conclusive experiments. Furthermore,
many challenging steps towards convincing violations of
macrorealism have been taken in a number of recent experiments. In
the first part of this thesis, conditions for macrorealism are
analyzed in detail. Two necessary conditions for macrorealism, the
original Leggett-Garg inequality and the recently proposed
no-signaling in time condition, are presented. It is then shown
that a combination of no-signaling in time conditions is not only
necessary but also sufficient for the existence of a macrorealistic
description. Finally, an operational formulation of no-signaling in
time, in terms of positive-operator valued measurements and
Hamiltonians, is derived. In the next part, we argue that these
results lead to a suitable definition of classical behavior. In
particular, we provide a formalism to judge the classicality of
measurements and time evolutions. We then proceed to apply it to a
number of exemplary measurement operators and Hamiltonians.
Finally, we argue for the importance of spontaneously realized
Hamiltonians in our intuition of classical behavior. Next,
differences between local realism and macrorealism are analyzed.
For this purpose, the probability polytopes for spatially and
temporally separated experiments are compared, and a fundamental
difference in the power of quantum mechanics to build both types of
correlations is discovered. This result shows that Fine's theorem,
which states that a set of Bell inequalities is necessary and
sufficient for local realism, is not transferable to macrorealism.
Thus, (Leggett-Garg) inequalities are in principle not well-suited
for tests of macrorealism, as they can never form a necessary and
sufficient condition, and unnecessarily restrict the violating
parameter space. No-signaling in time is both better suited and
more strongly motivated from the underlying physical theory. In the
final part of this thesis, a concrete experimental setup for
implementing quantum experiments with macroscopic objects is
proposed. It consists of a superconducting micro-sphere in the
Meißner state, which is levitated by magnetic fields. Through its
expelled magnetic field, the sphere's center-of-mass motion couples
to a superconducting quantum circuit. Properly tuned, ground state
cooling can be realized, since the sphere's motion is extremely
well isolated from the surrounding environment. This setup
therefore is a promising candidate for the observation of quantum
effects in macroscopic systems.