{
  "id": "2305.08700",
  "version": "v1",
  "published": "2023-05-15T15:01:09.000Z",
  "updated": "2023-05-15T15:01:09.000Z",
  "title": "Synthetic $\\mathbb{Z}_2$ gauge theories based on parametric excitations of trapped ions",
  "authors": [
    "O. Băzăvan",
    "S. Saner",
    "E. Tirrito",
    "G. Araneda",
    "R. Srinivas",
    "A. Bermudez"
  ],
  "categories": [
    "quant-ph",
    "cond-mat.quant-gas",
    "hep-lat"
  ],
  "abstract": "We present a detailed scheme for the implementation of $\\mathbb{Z}_2$ gauge theories with dynamical bosonic matter using analog quantum simulators based on crystals of trapped ions. We introduce a versatile toolbox based on a state-dependent parametric excitation, which can be implemented using different interactions that couple the ions' internal qubit states to their motion, and induces a tunneling of the vibrational excitations of the crystal mediated by the trapped-ion qubits. To evaluate the feasibility of this toolbox, we perform numerical simulations of the considered schemes using realistic experimental parameters. This building block, when implemented with a single trapped ion, corresponds to a minimal $\\mathbb{Z}_2$ gauge theory on a synthetic link where the qubit resides, playing the role of the gauge field. The vibrational excitations of the ion along different trap axes mimic the dynamical matter fields carrying a $\\mathbb{Z}_2$ charge. We discuss how to generalise this minimal case to more complex settings by increasing the number of ions. We describe various possibilities which allow us to move from a single $\\mathbb{Z}_2$ plaquette to full $\\mathbb{Z}_2$ gauge chains. We present analytical expressions for the gauge-invariant dynamics and confinement, which are benchmarked using matrix product state simulations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-15T15:01:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gauge theory",
      "trapped ion",
      "vibrational excitations",
      "matrix product state simulations",
      "state-dependent parametric excitation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}