QUROPE Quantum Information Processing and Communication in Europe

We propose and theoretically investigate a hybrid system composed of a crystal of trapped ions coupled to a cloud of ultracold fermions. The ions form a periodic lattice and induce a band structure in the atoms. This system combines the advantages of high fidelity operations and detection offered by trapped ion systems with ultracold atomic systems.

We propose a method of encoding a topologically-protected qubit using Majorana fermions in a trapped-ion chain. This qubit is protected against major sources of decoherence, while local operations and measurements can be easily realized. Furthermore, we show that an efficient quantum interface and memory for arbitrary multiqubit photonic states can be built, encoding them into a set of entangled Majorana-fermion (MF) qubits inside cavities.

We analyze the Majorana equation in the limit where the particle is at rest. We show that several counterintuitive features, absent in the rest limit of the Dirac equation, do appear, among which are Dirac-like positive energy solutions that turn into negative energy ones by free evolution, or nonstandard oscillations and interference between real and imaginary spinor components for complex solutions. We also study the ultrarelativistic limit, showing that the Majorana and Dirac equations mutually converge. Furthermore, we propose a physical implementation in trapped ions.