Interacting Fibonacci anyons in a Rydberg gas

By Igor Lesanovsky, Hosho Katsura. 2012

145 citations recorded by the source corpus.

A defining property of particles is their behavior under exchange. In two dimensions anyons can exist which, opposed to fermions and bosons, gain arbitrary relative phase factors or even undergo a change of their type. In the latter case one speaks of non-Abelian anyons - a particularly simple and aesthetic example of which are Fibonacci anyons. They have been studied in the context of fractional quantum Hall physics where they occur as quasiparticles in the $k=3$ Read-Rezayi state, which is conjectured to describe a fractional quantum Hall state at filling fraction $\nu=12/5$. Here we show that the physics of interacting Fibonacci anyons can be studied with strongly interacting Rydberg atoms in a lattice, when due to the dipole blockade the simultaneous laser excitation of adjacent atoms is forbidden. The Hilbert space maps then directly on the fusion space of Fibonacci anyons and a proper tuning of the laser parameters renders the system into an interacting topological liquid of non-Abelian anyons. We discuss the low-energy properties of this system and show how to experimentally measure anyonic observables.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/b9bd3bf064970ab34515e069382d9574d75d70d9

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum simulation and computing with Rydberg-interacting qubits (2020, background): “…have been theoretically studied in 1D 225,230–232 and more recently 2D on diﬀerent lattices 233,234 and found to exhibit liquid like ground states 230 , interacting Fi-bonacci anyons 231 and quantum scars (particular states that do not thermalize) 225,229,232 and synchronization eﬀects 233,234 .”
Quantum many-body scars and weak breaking of ergodicity (2020, background): “The experimental findings have been corroborated by theoretical studies of the idealized model of atoms in the Rydberg blockade – the so-called “PXP” model [13],”
Observation of many-body scarring in a Bose-Hubbard quantum simulator (2022, methodology): “Finally, the effective Hamiltonian is equivalent to the PXP Hamiltonian ĤPXP = N∑ j=1 (P̂j−1σ̂+j P̂j+1 + P̂j−1σ̂−j P̂j+1) = N∑ j=1 P̂j−1X̂ j P̂j+1, (A4) when we set = −√2J and N = L − 1, with X̂ j ≡ |◦ j〉〈• j | + |• j〉〈◦ j | denoting the usual Pauli x matrix.”
Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians (2019, background): “D shows an explicit construction, relating the minimal Hamiltonian we consider to the PXP model [41, 72] that appears in the context of quantum many-body scars [73].”
Probing many-body dynamics on a 51-atom quantum simulator (2017, background): “dynamics due to Rydberg blockade and large separations of timescales (Vi,i+1 Ω Vi,i+2 [39]) that result in an effective Hilbert-space dimension that is determined by the golden ratio (1 + √ 5)/2 [40, 41].”
A quantum processor based on coherent transport of entangled atom arrays (2021, unknown): “Underpinned by special, non-thermal eigenstates called quantum many-body scars [13, 14, 42], these states”