Quantum simulation of non-trivial topology

Abstract

We propose several designs to simulate quantum many-body systems in manifolds with a non-trivial topology. The key idea is to create a synthetic lattice combining real-space and internal degrees of freedom via a suitable use of induced hoppings. The simplest example is the conversion of an open spin-ladder into a closed spin-chain with arbitrary boundary conditions. Further exploitation of the idea leads to the conversion of open chains with internal degrees of freedom into artificial tori and Möbius strips of different kinds. We show that in synthetic lattices the Hubbard model on sharp and scalable manifolds with non-Euclidean topologies may be realized. We provide a few examples of the effect that a change of topology can have on quantum systems amenable to simulation, both at the single-particle and at the many-body level.

12 pages, 15 figures

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Cited by in corpus (6)

• Topological quantum matter in synthetic dimensions
• Synthetic dimensions and spin-orbit coupling with an optical clock transition
• Pretopological fractional excitations in the two-leg flux ladder
• Interaction-induced exotic vortex states in an optical lattice clock with spin-orbit coupling
• Local Quantum Thermometry using Unruh-De Witt detectors
• Single atom edge-like states via quantum interference