Landau-Zener-St\"uckelberg Interferometry for Majorana Qubit

Stimulated by a very recent experiment observing successfully two superconducting states with even- and odd-number of electrons in a nanowire topological superconductor as expected from the existence of two end Majorana quasiparticles (MQs) [Albrecht \textit{et al.}, Nature \textbf{531}, 206 (2016)], we propose a way to manipulate Majorana qubit exploiting quantum tunneling effects. The prototype setup consists of two one-dimensional (1D) topological superconductors coupled by a tunneling junction which can be controlled by gate voltage. We show that, upon current injection, the time evolution of superconducting phase difference at the junction induces an oscillation in energy levels of the Majorana parity states, whereas the level-crossing is avoided by a small coupling energy of MQs in the individual 1D superconductors. This results in a Landau-Zener-St\"{u}ckelberg (LZS) interference between the Majorana parity states. Adjusting the current pulse and gate voltage, one can build a LZS interferometry which provides an arbitrary manipulation of the Majorana qubit. The LZS rotation of Majorana qubit can be monitored by the microwave radiated from the junction.