Quantum mechanics

Spin (aerodynamics)

Boundary value problem

Center (category theory)

Mathematical optimization

Hamiltonian (control theory)

Band gap

Position and momentum space

Thermodynamics

Physics

Topological order

Periodic boundary conditions

Mathematics

Condensed matter physics

Quantum

Combinatorics

Crystallography

Chemistry

Topology (electrical circuits)

Physical Review Research

We propose an efficient scheme for simulating the topological phases of matter based on silicon-vacancy (SiV) center arrays in phononic crystals. This phononic band gap structure allows for long-range spin-spin interactions with a tunable profile. Under a particular periodic microwave driving, the band-gap mediated spin-spin interaction can be further designed with the form of the Su-Schrieffer-Heeger (SSH) Hamiltonian. In momentum space, we investigate the topological characters of the SSH model, and show that the topological nontrivial phase can be obtained through modulating the periodic driving fields. Furthermore, we explore the zero-energy topological edge states at the boundary of the color center arrays, and study the robust quantum information transfer via the topological edge states. This setup provides a scalable and promising platform for studying topological quantum physics and quantum information processing with color centers and phononic crystals.

Simulation of topological phases with color center arrays in phononic crystals