Framework for the Observation of Macroscopic Quantum Effects

While quantum mechanics on microscopic scales is well tested and confirmed, recently comparatively large systems were brought into the quantum regime. The goal is to collect evidence for macroscopic quantum phenomena. It became evermore clear that a theoretical framework is needed that clearly defines the notion of a ``macroscopic quantum effect``. The difficulty is to distinguish this kind of quantum effect from those that are of microscopic origin. A successful demonstration of a macroscopic quantum effect would be an important contribution, on the one hand, to the old question whether quantum mechanics is valid on large scales and, on the other hand, for technological application like quantum computing or quantum metrology. First steps for the establishment of such a framework have been done. Among other contributions, we proposed a framework for finite dimensional Hilbert spaces based on the so-called Quantum Fisher Information (QFI). This attempt unifies the foregoing measures to a large extend and provides a sufficient and experimentally testable condition for the ``macroscopicity`` of quantum states. This proposal for an Erwin-Schrödinger fellowship pursues the following goals: Analysis of current experiments that target to generate macroscopic quantum states and suggestion of novel experiments based on the established framework. Further investigation of the QFI framework and other sufficient criteria for macroscopicity and extension to different physical systems. Comparison of the proposed framework to models that aim to explain the appearance of the classical world with mechanisms like decoherence or weak measurements. The host institution for this project is the group of applied physics at the University of Geneva. It provides the ideal environment, since it offers -besides its international reputation - expertise in this topic and an attractive mixture of theoretical and experimental physicists.

Quantum theory is governed by strange laws this was already clear for its founding fathers and mothers. One of the oddities is the so-called superposition principle. It says that if the theory permits an atom to be in the ground state or in the excited state, it also allows the atom to be in both, ground and excited state at the same time. This completely contradicts our classical logic. On the other side, quantum mechanics was developed to explain nature on the scale of atoms, which are not directly observable. Hence the problem could be pushed far away from our daily experience. In 1935, however, Erwin Schrödinger pointed out that this bizarness can be easily extended to the macroscopic realm, at least in principle, by translating the indetermined state of an atom to that of cat, which is then somehow dead and alive at the same time.For decades, the interpretational questions around Schrödinger's cat were more discussed by philosophy-oriented physicists. Recently, the experimental progress allows to control quantum systems composed of more and more atoms or photons. Even if we are still far away from true cat-like sizes, these developments trigger many practical questions: Which quantum experiments can be seen as "realistic" counterparts to Schrödinger's cat? What are the precise implications from a successful experiment for the interpretation of quantum mechanics on meso- or macroscopic scales? Which are the messurements that have to be implemented in order to find the desired conclusions? Since my PhD thesis I was very much involved in these and similar questions. Before starting this project, I worked out together with my PhD supervisor a framework to successfully treat the above questions in the case of large atomic ensembles. The goal was to distinguish "true" macroscopic quantum effects (like Schrödinger's cat) from just accumulated microscopic quantum effects (i.e., many copies of a small effect). The main results of the present project are: (i) successful expansion of the framework to photonic systems; (ii) proposals for testing our framework in experiments; (iii) proposal to overcome experimental difficulties; (iv) theoretical contributions to the field of quantum parameter estimation, which turned out to be close to our framework.Our contributions are small but important steps to better understand quantum mechanics on large scales. They shed light on questions of how to realize Schrödinger's cat in quantum experiments.