Quantum engineering of topological states in dice Fock-state lattices

Han Cai, Dawei Wang

Ruo Kun Cai, Ling Lin, Chun Wang Wu +2 more

In this paper, Thouless pumping in a one-dimensional semi-infinite Fock-state lattice is investigated. A distinctive feature of such lattices is the intrinsic $\sqrt{n}$-dependent coupling arising from the bosonic mode, which leads to spatially nonuniform hopping amplitudes. In the dimer limit, the topological invariants and the quantized transport dynamics in the Fock-state basis are numerically evaluated and analyzed. By introducing an additional inter-cell coupling and applying a squeezing transformation, the framework is then extended to Thouless pumping in the squeezed Fock-state basis, where a topologically protected scheme for preparing superpositions of squeezed Fock states is proposed. This study establishes Thouless pumping in Fock-state lattices as a useful tool for quantum state engineering, shifting the focus from observing topological transport to harnessing it for the preparation of non-classical states of the bosonic mode.

Jin‐Lei Wu, Tong-Tong Zhang, Pei-Yao Song +3 more

In quantum networks, robust and efficient frequency conversions of photons between microwave (MW) and optical regimes serve as a critical interface bridging superconducting quantum processors and optical communication channels. Recently, a topologically protected paradigm of state transfers, based on the topological nature of quantized light in Fock-state lattices (FSLs), has been demonstrated by a superconducting quantum circuit. However, its extension to quantum networks remains unexplored. Here we develop a topological single-photon MW–optics interface based on FSLs with a single nitrogen-vacancy (NV) center spin embedded in a photonic crystal cavity (PCC). The NV spin mediates the effective strong coupling between the optical PCC mode and a superconducting MW resonator via the adiabatic elimination of an intermediate acoustic mode. This scheme establishes a hybrid MW-NV-optics two-mode Jaynes-Cummings model, yielding a topological FSL. Under the significant constraint of optical mode decay, numerical simulations reveal that the MW-to-optics conversion efficiency can exceed 26% for an input five-photon MW Fock state. This work establishes a topological paradigm for hybrid quantum transduction, offering an efficient solid-state framework for constructing large-scale quantum networks.

Guliuxin Jin

Tomas Andrijauskas, Egidijus Anisimovas, Mantas Račiūnas +4 more

We consider ultracold atoms in a two-dimensional optical lattice of the dice geometry in a tight-binding regime. The atoms experience a laser-assisted tunneling between the nearest neighbor sites of the dice lattice accompanied by the momentum recoil. This allows one to engineer staggered synthetic magnetic fluxes over plaquettes, and thus pave a way towards the realization of topologically nontrivial band structures. In such a lattice the real-valued next-nearest neighbor transitions are not needed to reach a topological regime. Yet, such transitions can increase a variety of the obtained topological phases. The dice lattice represents a triangular Bravais lattice with a three-site basis consisting of a hub site connected to two rim sites. As a consequence, the dice lattice supports three energy bands. From this point of view, our model can be interpreted as a generalization of the paradigmatic Haldane model which is reproduced if one of the two rim sublattices is eliminated. We demonstrate that the proposed upgrade of the Haldane model creates a significant added value, including an easy access to topological semimetal phases relying only on the nearest neighbor coupling, as well as enhanced topological band structures featuring Chern numbers higher than one leading to physics beyond the usual quantum Hall effect. The numerical investigation is supported and complemented by an analytical scheme based on the study of singularities in the Berry connection.

Graham Kells, Diptiman Sen, Johannes K. Slingerland +1 more