Topological phases in Fock-state lattices

Jiale Yuan, Jinfeng Deng, Da-Wei Wang

Tom D. Imbo

Xing Yao Mi, Yong‐Chun Liu, Zhi Jiao Deng +2 more

Fock-state lattice (FSL) offers a powerful quantum simulator for topological phenomena due to the unbounded scalability and ease of implementation. Nevertheless, the unique topological properties induced by its site-dependent coupling have remained elusive, mainly due to the challenge of handling an infinite state space without translational symmetry. Here, we rigorously analyze the topological features of a semi-infinite FSL-based Su-Schrieffer-Heeger (SSH) model, in both Hermitian and non-Hermitian realms, by mapping it to the solvable Jaynes-Cummings model via a unitary displacement transformation. We find a topological zero mode persisting across all parameter regimes, which is more stable than the conventional SSH model. It originates from the bound state at the inherent domain wall under anisotropic conditions. With gain and loss introduced, we predict a non-Hermitian bound effect, i.e., any state overlapping with the bound state will quickly stabilize to the domain wall, with the minimal stabilization time occurring in the vicinity of exceptional point. The parity-time phase transition can be observed by the oscillating-to-steady crossover of dynamics in the subspace orthogonal to the bound state. Furthermore, a concrete experimental proposal based on the trapped-ion setup is provided.

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.

Piergiorgio Ferraro, Caio B. Naves, Jonas Larson

We analyze Fock-state lattices (FSLs) from an algebraic viewpoint. Starting from a Lie algebra, we associate a FSL constructed from the action of its generators: diagonal (Cartan) generators define the lattice sites, while off-diagonal (root) generators determine the lattice bonds. This construction reveals that identifying an underlying algebraic structure provides direct physical insight into FSLs, including their dimensionality, connectivity, symmetry constraints, and possible transport and revival phenomena. By examining several common Lie algebras, we identify not only their associated FSLs but also the corresponding Lie phase spaces, thereby establishing a systematic connection between FSL dynamics and phase-space geometry. In many cases, both the phase space and the FSL exhibit nontrivial curvature, opening possibilities for exploring quantum dynamics in curved synthetic spaces. We further address whether every integrable Hamiltonian admits an underlying Lie algebra that reproduces the same FSL structure. We show that this is not generally the case, particularly for Hamiltonians that are nonlinear in the generators, and that for systems combining different types of degrees of freedom the appropriate underlying structure may instead be a Lie superalgebra.

Emmanuel V. C. Lopes