Four-body ring-exchange interactions and anyonic statistics within a minimal toric-code Hamiltonian

Abstract

Ring exchange is an elementary interaction for modeling unconventional topological matters which hold promise for efficient quantum information processing. We report the observation of fourbody ring-exchange interactions and the topological properties of anyonic excitations within an ultracold atom system. A minimum toric code Hamiltonian in which the ring exchange is the dominant term, was implemented by engineering a Hubbard Hamiltonian that describes atomic spins in disconnected plaquette arrays formed by two orthogonal superlattices. The ring-exchange interactions were resolved from the dynamical evolutions in the spin orders, matching well with the predicted energy gaps between two anyonic excitations of the spin system. A braiding operation was applied to the spins in the plaquettes and an induced phase 1.00(3)π in the four-spin state was observed, confirming 1 2 -anynoic statistics. This work represents an essential step towards studying topological matters with many-body systems and the applications in quantum computation and simulation.Exploiting the laws of quantum mechanics, quantum information processing can be exponentially faster than the classical counterpart [1]. To make this technology a reality, scientists have to solve the crucial problem of decoherence and systematic errors in real quantum systems, which is very difficult due to the request of an extremely small error threshold to enable error corrections [2,3]. A very encouraging solution to this problem is the Kitaev model [4] of fault-tolerant quantum computation by anyons, a sort of topological quasiparticles being neither bosons nor fermions [5]. In this model, anyons are exploited to encode and manipulate information in a manner which is resistant to errors, the so-called topological protection. Unfortunately, except that signatures of anyonic statistics emerged in the fractional quantum Hall systems [6,7], there has been no conclusive observation of anyons in any existing matters. A proposal suggests to solely mimic anyonic statistics with non-interacting qubits [8] and experimental demonstrations were achieved with entangled photons [9, 10] and ions [11]. However, because the background interacting Hamiltonian does not exist in such systems, it is not possible to define anyonic excitations [12]. Therefore, the observation of anyons remains challenging.To construct the appropriate Hamiltonian for studying anyons, a practical scheme [13] was proposed to create artificial topological matters by manipulating ringexchange interactions [14] among ultracold atoms in optical lattices [15,16]. Although a large category of manybody models [17][18][19][20][21] have been realized with optical lattices, implementing the ring-exchange Hamiltonian is notoriously difficult due to its nature of the fourth-order spin interaction, which is greatly suppressed compared to the lower order processes, such as superexchange interactions [19,20]. So, generation and observation of the ring-exchange interactions and the correlated anyonic excitations become the ...

Nagaoka ferromagnetism observed in a quantum dot plaquette

“…Modelling and simulating such systems can in some instances only be achieved through the use of engineered, controllable systems that operate in the quantum regime [1]. Efforts to build quantum simulators have already demonstrated great promise at this early stage [10], mainly led by the ultracold atom community [11][12][13][14][15][16][17]. More broadly, quantum simulations of many-body fermionic systems have been carried out in a range of experimental systems such as quantum dot lattices [18], dopant atoms [19], superconducting circuits [20] and trapped ions [21].…”

Coupling ultracold matter to dynamical gauge fields in optical lattices: From flux attachment to ℤ 2 lattice gauge theories

“…Here we propose a realistic scheme to implement a genuine Z 2 LGT with minimal coupling of the matter to the gauge-field on all links of a square lattice. On the one hand, this realizes one of the main ingredients of Kitaev's toric code [23,55,56] -a specific version of a LGT coupled to matter, which displays local Z 2 gauge symmetry and hosts excitations with non-Abelian anyonic statistics. On the other hand, the systems that can be implemented with our technique are reminiscent of models studied in the context of nematic magnets [21,29,57] and strongly correlated electron systems [22,31,32].…”

Non-Hermitian dynamic strings and anomalous topological degeneracy on a non-Hermitian toric-code model with parity-time symmetry

“…It is still of challenge both to experimentally investigate PT symmetric Hamiltonian related physics in quantum systems and to realize the toric-code model. A possible approach is cold-atom experiments: On the one hand, non-Hermitian Hamiltonians arise in cold-atom experiments due to spontaneous decay [29][30][31]; On the other hand, a small system for toric-code model has also been realized in cold atoms [32].…”