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.

arXiv comment12 pages, 15 figures

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Cited by in corpus (49)

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• Low-dimensional quantum gases in curved geometries
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• Topological spin excitations in Harper-Heisenberg spin chains
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• Pretopological fractional excitations in the two-leg flux ladder
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• Spinor Condensates on a Cylindrical Surface in Synthetic Gauge Fields
• Four-dimensional topological lattices through connectivity
• Measuring Chern numbers in Hofstadter strips
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• Probing the exchange statistics of one-dimensional anyon models
• Dimensional crossovers and Casimir forces for the Bose gas in anisotropic optical lattices
• Different models of gravitating Dirac fermions in optical lattices
• Probing the Hall Voltage in Synthetic Quantum Systems
• Charge density wave and charge pump of interacting fermions in circularly shaken hexagonal optical lattices
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• Local Quantum Thermometry using Unruh-De Witt detectors
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• Single atom edge-like states via quantum interference
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• Time-tronics: from temporal printed circuit board to quantum computer
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• Quantum Entanglement In Inhomogeneous 1D Systems
• Encoding a topological gauge theory on a ring-shaped Raman-coupled Bose gas
• Integrability of Dirac equations in static spherical space-times
• Low-temperature behavior of the $O(N)$ models below two dimensions
• Foundational aspects of spinor structures and exotic spinors