Anyon Colliders: A time-dependent quantum Hall particle collider to reveal fractional statistics in the Laughlin sequence
Typ
Examensarbete för masterexamen
Master's Thesis
Master's Thesis
Program
Nanotechnology (MPNAT), MSc
Publicerad
2023
Författare
Varada, Sushanth
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
Elementary particles in nature (3+1 dimensions) are classified into bosons and fermions based on their exchange statistics. However, more general statistics, intermediate be- tween fermionic and bosonic, are possible in 2+1 dimensions. Quasiparticles obeying this intermediary statistics are called anyons. A particularly relevant phase of matter hosting anyons is the fractional quantum Hall effect, where anyonic statistics has recently been demonstrated. Generally, exchange statistics is expected to be accessible in interference experiments, such as in the Hong-Ou-Mandel effect. In this setup, fermions show van- ishing current correlations due to anti-bunching caused by the Pauli exclusion principle. Bosons, instead, bunch together due to Bose-Einstein statistics causing a surge in the current correlations. Can Hong-Ou-Mandel interferometry be extended to probe the frac- tional statistics of anyons?
In this thesis, we investigate this question in a fractional quantum Hall setup in the Laughlin sequence (filling factor ν = 1/(2n + 1), n ∈ Z+), where two anyons collide at a quantum point contact with a tunable time delay. Previous studies investigating sim- ilar systems relate current correlations of quasiparticle collisions with braiding between injected anyons and quasi-particle-hole excitations at the tunneling quantum point con- tact, which emerge due to thermal or quantum fluctuations. However, it remains unclear whether the presently studied Hong-Ou-Mandel effect probes the universal exchange phase (θ) picked up by the quasiparticles or other parameters, such as the non-universal scaling dimension (δ). We show that θ accumulated by the incoming anyons due to interaction with quasi-particle-hole pairs at the quantum point contact cancel out in time-sensitive two-particle interferometry. Instead, the key quantity measured through current correla- tions is the non-universal δ of the quasi-particle-hole excitations.
Beskrivning
Ämne/nyckelord
Anyons , Edge states , Fractional quantum Hall effect , Topological quantum matter , Quantum interference effects