{
  "annotation_id": "8903210c-683d-4b65-9d8c-a61d409849cb",
  "date_created": "2026-03-02T18:02:41.050000Z",
  "date_modified": "2026-03-02T18:02:41.050000Z",
  "file_hash": "9b24b739f7b8e1c3779e4203c310c963fb75c99223e739a05fe8cde02699dae4",
  "private": false,
  "record": {
    "abstract": "Following the paper by M. Combescure [Ann. Phys. (NY) 204, 113 (1990)], we\napply the quantum singular time dependent oscillator model to describe the\nrelative one dimensional motion of two ions in a trap. We argue that the model\ncan be justified for low energy excited states with the quantum numbers $n\\ll\nn_{max}\\sim 100$, provided that the dimensionless constant characterizing the\nstrength of the repulsive potential is large enough, $g_*\\sim 10^5$. Time\ndependent Gaussian-like wave packets generalizing odd coherent states of the\nharmonic oscillator, and excitation number eigenstates are constructed. We show\nthat the relative motion of the ions, in contradistinction to its center of\nmass counterpart, is extremely sensitive to the time dependence of the binding\nharmonic potential, since the large value of $g_*$ results in a significant\namplification of the transition probabilities between energy eigenstate even\nfor slow time variations of the frequency.",
    "arxiv_id": "quant-ph/9712028",
    "authors": [
      "V. V. Dodonov",
      "V. I. Man\u0027ko",
      "L. Rosa"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.57.2851",
    "journal_ref": "Phys.Rev. A57 (1998) 2851",
    "title": "Quantum singular oscillator as a model of two-ion trap: an amplification   of transition probabilities due to small time variations of the binding   potential",
    "url": "https://arxiv.org/abs/quant-ph/9712028"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "df4649df-5126-4490-a3c1-26dc614089dc",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}