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majorana fermions

Majorana fermions are particles that are their own antiparticles, studied in quantum systems.
16 related articles · 1 formulas

Description

Majorana fermions are hypothetical particles that are their own antiparticles, meaning a Majorana particle and its antiparticle are identical. First proposed by Ettore Majorana in 1937, these particles have been sought in particle physics and condensed matter systems. In quantum computing, Majorana fermions are particularly exciting because they can form the basis of topological qubits, which are inherently protected from local noise and decoherence.

History

Ettore Majorana proposed the concept in 1937 as a real solution to the Dirac equation. In the 2000s, theorists like Alexei Kitaev and Liang Fu suggested how to realize them in solid-state systems, leading to intense experimental efforts.

How it works

In condensed matter, Majorana fermions emerge as quasiparticles at the ends of certain one-dimensional wires or in vortices of topological superconductors. They obey non-Abelian statistics, meaning that braiding them around each other changes the quantum state in a way that depends on the order of operations. This braiding can be used to perform quantum computations that are topologically protected: local perturbations cannot easily flip the state, making the qubit robust against errors.

In practice

Majorana fermions are pursued for topological quantum computers, which promise inherently error-resistant qubits. They are also studied for potential applications in quantum sensing and as a probe of fundamental physics.

Fun fact

In 2023, a major experiment claimed to have observed the 'parity anomaly' associated with Majorana modes, but the results remain debated, highlighting how elusive these particles are.

Concept graph →

Formulas

$$H = -it \sum_j \gamma_{2j} \gamma_{2j+1}$$
Hamiltonian for a Kitaev chain with Majorana fermion pairing.
What is in the formula
HvariableHamiltonian operator — hamiltonian joule
tvariablehopping amplitude — energy joule
γ_{2j}variableMajorana operator at site 2j — majorana operator
γ_{2j+1}variableMajorana operator at site 2j+1 — majorana operator
∑operatorsum over lattice sites j — summation
h=-it\sum_{j=1}^{l-1}γ_{2j}γ_{2j+1} · 2606.25653

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