Vortices in two-dimensional condensates: towards a novel platform for quantum technologies

Abstract:

In this thesis, we consider the implementation of a quantum computer in systems of BoseEinstein condensates, quantum vortices and impurities as a roadmap to the investigation of the fundamental physics of these systems. We consider questions of structure, scalability, dynamical stability, robustness against decoherence/perturbations, amenability to external control and availability of quantum resources, which are necessary elements to encode and perform error-tolerant quantum information processing. BECs with vortices are a good platform to explore these questions, since it is well known that vortices in this superfluid are dynamically stable, topologically robust, stationary configurations that can be created in large numbers to form Abrikosov lattices.

Their robustness, structure and scalability suggests the realization of qubits by making impurities occupy the vortex core. Thus, we began by characterizing these bound states to establish a good basis on which to encode a qubit. The next step was to characterize the excitations of the vortex-BEC. Motivated by questions of robustness, we introduced a measure that characterizes these excitations with respect to their interactions with any impurity.

We found that some characteristic excitation modes of this system have an exceptional capacity to interact with impurities, which lead us to suggest a novel mechanism of quantum-level control of impurities. With this work, we have also established that the low-energy excitations of the vortex-BEC have an anomalous dispersion. We then studied the interactions between the two parts of the system, and found that the resulting collective excitations obey a deformed quantum statistics, known as para-Bose statistics.

We characterized geometrically the single-body state of these excitations, known to be non-classical, and found a non-trivial geometric phase. In turn, the many-body states indicate that the excitations are in a condensed state. We attempt to characterize this condensate and discuss its implications towards this system as a quantum platform.