Quantized topological phases beyond square lattices in Floquet synthetic dimensions

• URL: http://arxiv.org/abs/2411.02475v1
• Date: Mon, 04 Nov 2024 17:50:48 GMT
• Title: Quantized topological phases beyond square lattices in Floquet synthetic dimensions
• Authors: Samarth Sriram, Sashank Kaushik Sridhar, Avik Dutt,
• Abstract summary: We show that non-square lattice Hamiltonians can be implemented using Floquet synthetic dimensions. Our construction uses dynamically modulated ring resonators and provides the capacity for direct $k$-space engineering of lattice Hamiltonians.
• Score: 0.0
• License:
• Abstract: Topological effects manifest in a variety of lattice geometries. While square lattices, due to their simplicity, have been used for models supporting nontrivial topology, several exotic topological phenomena such as Dirac points, Weyl points and Haldane phases are most commonly supported by non-square lattices. Examples of prototypical non-square lattices include the honeycomb lattice of graphene and the Kagome lattice, both of which break fundamental symmetries and can exhibit quantized transport, especially when long-range hoppings and gauge fields are incorporated. The challenge of controllably realizing long-range hoppings and gauge fields has motivated a large body of research focused on harnessing lattices encoded in "synthetic" dimensions. Photons in particular have many internal degrees of freedom and hence show promise for implementing these synthetic dimensions; however, most photonic synthetic dimensions has hitherto created 1D or 2D square lattices. Here we show that non-square lattice Hamiltonians can be implemented using Floquet synthetic dimensions. Our construction uses dynamically modulated ring resonators and provides the capacity for direct $k$-space engineering of lattice Hamiltonians. Such a construction lifts constraints on the orthogonality of lattice vectors that make square geometries simpler to implement, and instead transfers the complexity to the engineering of complex Floquet drive signals. We simulate topological signatures of the Haldane and the brick-wall Haldane model and observe them to be robust in the presence of external optical drive and photon loss, and discuss unique characteristics of their topological transport when implemented on these Floquet lattices. Our proposal demonstrates the potential of driven-dissipative Floquet synthetic dimensions as a new architecture for $k$-space Hamiltonian simulation of high-dimensional lattice geometries.

Related papers

• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• Real-space detection and manipulation of topological edge modes with ultracold atoms [56.34005280792013]
  We demonstrate an experimental protocol for realizing chiral edge modes in optical lattices. We show how to efficiently prepare particles in these edge modes in three distinct Floquet topological regimes. We study how edge modes emerge at the interface and how the group velocity of the particles is modified as the sharpness of the potential step is varied.
  arXiv  Detail & Related papers  (2023-04-04T17:36:30Z)
• Entanglement blossom in a simplex matryoshka [4.965221313169878]
  This manuscript generalizes the rainbow chain to higher dimensional space on lattices with Hausdorff dimension one and enlarged local Hilbert space. The model interpolates between the SYK model and the free-fermionic XX spin chain, and hence might be potentially useful in understanding black hole physics and holography.
  arXiv  Detail & Related papers  (2023-01-10T19:00:18Z)
• Multi-frequency optical lattice for dynamic lattice-geometry control [0.0]
  We introduce a multi-frequency lattice for fast and flexible lattice-geometry control. We demonstrate it for a three-beam lattice, realizing the full dynamical tunability between honeycomb lattice, boron-nitride lattice and triangular lattice. This scheme will allow further applications such as novel Floquet and quench protocols to create and probe, e.g., topological properties.
  arXiv  Detail & Related papers  (2022-07-08T10:41:08Z)
• Topological multi-mode waveguide QED [49.1574468325115]
  We show how to take advantage of topologically protected propagating modes by interfacing them with quantum emitters. Such capabilities pave the way for generating quantum gates among topologically protected photons as well as generating more complex entangled states of light in topological channels.
  arXiv  Detail & Related papers  (2022-07-05T14:48:50Z)
• Fully solvable finite simplex lattices with open boundaries in arbitrary dimensions [0.0]
  An $n$-simplex represents the simplest possible polytope in $n$ dimensions. We show that $n$-simplex lattices can be constructed from the high-order field-moments space of quadratic bosonic systems.
  arXiv  Detail & Related papers  (2022-06-29T17:24:04Z)
• Design and realization of topological Dirac fermions on a triangular lattice [0.0]
  Large-gap quantum spin Hall insulators are promising materials for room-temperature applications based on Dirac fermions. Key to engineer the topologically non-trivial band ordering and sizable band gaps is strong spin-orbit interaction. Here, we conceive and realize "indenene", a triangular monolayer of indium on SiC exhibiting non-trivial valley physics driven by local spin-orbit coupling.
  arXiv  Detail & Related papers  (2021-06-30T12:46:28Z)
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics [58.720142291102135]
  We propose quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions. We show that our system exhibits topologicalband structures under appropriate conditions.
  arXiv  Detail & Related papers  (2020-08-06T19:58:05Z)
• Radiative topological biphoton states in modulated qubit arrays [105.54048699217668]
  We study topological properties of bound pairs of photons in spatially-modulated qubit arrays coupled to a waveguide. For open boundary condition, we find exotic topological bound-pair edge states with radiative losses. By joining two structures with different spatial modulations, we find long-lived interface states which may have applications in storage and quantum information processing.
  arXiv  Detail & Related papers  (2020-02-24T04:44:12Z)
• Probing chiral edge dynamics and bulk topology of a synthetic Hall system [52.77024349608834]
  Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. Here, we realize a quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension. We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviors.
  arXiv  Detail & Related papers  (2020-01-06T16:59:08Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.