Viewing Majorana Bound States by Rabi Oscillations.

Zhi Wang,Dao-Xin Yao,Qi-Feng Liang,Xiao Hu

doi:10.1038/srep11686

Abstract

We propose to use Rabi oscillation as a probe to view the fractional Josepshon relation (FJR) associated with Majorana bound states (MBSs) expected in one-dimensional topological superconductors. The system consists of a quantum dot (QD) and an rf-SQUID with MBSs at the Josephson junction. Rabi oscillations between energy levels formed by MBSs are induced by ac gate voltage controlling the coupling between QD and MBS when the photon energy proportional to the ac frequency matches gap between quantum levels formed by MBSs and QD. As a manifestation of the Rabi oscillation in the whole system involving MBSs, the electron occupation on QD oscillates with time, which can be measured by charge sensing techniques. With Floquet theorem and numerical analysis we reveal that from the resonant driving frequency for coherent Rabi oscillation one can directly map out the FJR cos(πΦ/Φ0) as a signature of MBSs, with Φ the magnetic flux through SQUID and Φ0 = hc/2e the flux quantum. The present scheme is expected to provide a clear evidence for MBSs under intensive searching.

Highlights

We propose to use Rabi oscillation as a probe to view the fractional Josepshon relation (FJR) associated with Majorana bound states (MBSs) expected in one-dimensional topological superconductors
Rabi oscillations between energy levels formed by MBSs are induced by ac gate voltage controlling the coupling between quantum dot (QD) and MBS when the photon energy proportional to the ac frequency matches gap between quantum levels formed by MBSs and QD
With Floquet theorem and numerical analysis we reveal that from the resonant driving frequency for coherent Rabi oscillation one can directly map out the FJR cos(πΦ/Φ0) as a signature of MBSs, with Φ the magnetic flux through SQUID and Φ0 = hc/2e the flux quantum

Summary

OPEN Viewing Majorana Bound States by Rabi Oscillations

Zhi Wang[1,2], Qi-Feng Liang[2,3], Dao-Xin Yao1 & Xiao Hu2 received: 05 January 2015 accepted: 26 May 2015 Published: 08 July 2015. As a major distinct property, MBSs transport supercurrent through a junction between two topological superconductors in terms of the fractional Josephson relation (FJR) I ~ ± E sin(φ/2), where ± E are energies of the two Andreev bound states formed by MBSs and φ is the gauge invariant phase difference between the two superconductors[2,28] This looks to indicate a critical Josephson current with 4π period. We propose to directly view the FJR using Rabi oscillations between energy levels formed by MBSs. As schematically shown, our setup is constructed by a Majorana rf-SQUID and a nearby quantum dot (QD), where an ac gate voltage is applied to tune the coupling between QD and MBS periodically in time; the magnetic flux through SQUID modulates the phase difference between the two MBSs at junction. The present scheme is expected to be able to provide an unambiguous evidence for MBSs in one-dimensional topological superconductors

Results

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Methods

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