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

TL;DR

This paper proposes a method to manipulate Majorana qubits using Landau-Zener-Stückelberg interferometry in a topological superconductor setup, enabling quantum control via current pulses and gate voltages.

Contribution

It introduces a novel approach to control Majorana qubits through LZS interferometry, exploiting quantum tunneling and phase dynamics in coupled topological superconductors.

Findings

Demonstrates energy level oscillations induced by current injection.

Shows how to achieve arbitrary qubit manipulation via gate voltage and current pulses.

Proposes monitoring qubit rotation through microwave radiation.

Abstract

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.