Topological quantum matter in synthetic dimensions

Abstract

In the field of quantum simulation of condensed matter phenomena by artificially engineering the Hamiltonian of an atomic, molecular or optical system, the concept of `synthetic dimensions' has recently emerged as a powerful way to emulate phenomena such as topological phases of matter, which are now of great interest across many areas of physics. The main idea of a synthetic dimension is to couple together suitable degrees of freedom, such as a set of internal atomic states, in order to mimic the motion of a particle along an extra spatial dimension. This approach provides a way to engineer lattice Hamiltonians and enables the realisation of higher-dimensional topological models in platforms with lower dimensionality. We give an overview of the recent progress in studying topological matter in synthetic dimensions. After reviewing proposals and realizations in various setups, we discuss future prospects in many-body physics, applications, and topological effects in three or more spatial dimensions.

arXiv comment13 pages, 4 figures; accepted version of the review published on April 1st, 2019

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• Setting Boundaries with Memory: Generation of Topological Boundary States in Floquet-Induced Synthetic Crystals
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• Phases of Attractive Fermi Gases in Synthetic Dimensions
• Vortex-hole duality: a unified picture of weak and strong-coupling regimes of bosonic ladders with flux
• Strings of ultracold molecules in a synthetic dimension
• Realizing the Haldane Phase with Bosons in Optical Lattices
• Devil's staircases in synthetic dimensions and gauge fields
• Measuring Chern numbers in Hofstadter strips
• Topological Superfluid and Majorana Zero Modes in Synthetic Dimension
• Baryon squishing in synthetic dimensions by effective $SU(M)$ gauge fields
• Momentum-space Harper-Hofstadter model
• Momentum-space Landau levels in driven-dissipative cavity arrays
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• Observing dynamical currents in a non-Hermitian momentum lattice
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• Measuring topological invariants in polaritonic graphene
• Spectral Causality and the Scattering of Waves
• Quantized topological energy pumping and Weyl points in Floquet synthetic dimensions with a driven-dissipative photonic molecule
• Topological band structure via twisted photons in a degenerate cavity
• Local Topological Markers in Odd Dimensions
• General corner states in 2D SSH model with intracelluar next-nearest-neighbour hopping
• Creating locally interacting Hamiltonians in the synthetic frequency dimension for photons
• Topologically quantized current in quasiperiodic Thouless pumps
• Synthetic dimensions for topological and quantum phases: Perspective
• Four-dimensional semimetals with tensor monopoles: From surface states to topological responses
• Time reflection and refraction in synthetic frequency dimension
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• Topologically nontrivial Andreev bound states
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• Floquet engineering correlated materials with unpolarized light
• Superfluidity of Light and its Break-Down in Optical Mesh Lattices
• Measurable signatures of bosonic fractional Chern insulator states and their fractional excitations in a quantum-gas microscope
• Topological Microlaser with A non-Hermitian Topological Bulk
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• Observation of flat-band and band transition in the synthetic space
• Isolated Photonic Flatband with the Effective Magnetic Flux in A Synthetic Space including the Frequency Dimension
• Exceptional Cones in 4D Parameter Space
• Extreme defect sensitivity from large synthetic dimensionality
• Electric fields for light: Propagation of microwave photons along a synthetic dimension
• Finite-temperature phases of trapped bosons in a two-dimensional quasiperiodic potential
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• Tunable Topologically-protected Super- and Subradiant Boundary States in One-Dimensional Atomic Arrays
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• Enhanced repulsively bound atom pairs in topological optical lattice ladders
• Synthetic ${\mathbb{Z}}_2$ gauge theories based on parametric excitations of trapped ions
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• Coexistence of stable and unstable population dynamics in a nonlinear non-Hermitian mechanical dimer
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• Large-scale time-multiplexed nanophotonic parametric oscillators
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