Splitting of a Cooper pair by a pair of Majorana bound states

TL;DR

This paper proposes a method to test the nonlocality of Majorana bound states via crossed Andreev reflection, showing that at low energies, current fluctuations into two bound states are maximally correlated, indicating Cooper pair splitting.

Contribution

It introduces a novel experimental approach using crossed Andreev reflection to demonstrate nonlocality in Majorana bound states, advancing topological quantum computing research.

Findings

Crossed Andreev reflection dominates over local processes at low energies.

Current fluctuations into two Majorana bound states are maximally correlated.

The method provides a way to experimentally test Majorana nonlocality.

Abstract

Majorana bound states are spatially localized superpositions of electron and hole excitations in the middle of a superconducting energy gap. A single qubit can be encoded nonlocally in a pair of spatially separated Majorana bound states. Such Majorana qubits are in demand as building blocks of a topological quantum computer, but direct experimental tests of the nonlocality remain elusive. Here we propose a method to probe the nonlocality by means of crossed Andreev reflection, which is the injection of an electron into one bound state followed by the emission of a hole by the other bound state (equivalent to the splitting of a Cooper pair over the two states). We have found that, at sufficiently low excitation energies, this nonlocal scattering process dominates over local Andreev reflection involving a single bound state. As a consequence, the low-temperature and low-frequency fluctuations $\delta I_{i}$ of currents into the two bound states $i=1,2$ are maximally correlated: $\overline{\delta I_{1}\delta I_{2}}=\overline{\delta I_{i}^{2}}$.