{
  "id": "2505.09654",
  "version": "v1",
  "published": "2025-05-13T19:02:16.000Z",
  "updated": "2025-05-13T19:02:16.000Z",
  "title": "Uniqueness of Squeezed States for One and Two Modes, and a No-Go Beyond",
  "authors": [
    "Arash Azizi"
  ],
  "comment": "14 pages",
  "categories": [
    "quant-ph",
    "hep-th"
  ],
  "abstract": "We investigate the structure and uniqueness of squeezed vacuum states defined by annihilation conditions of the form $(a - \\alpha a^\\dagger)|\\psi\\rangle = 0$ and their multimode generalizations. For $N=1$ and $N=2$, we rigorously show that these conditions uniquely define the standard single- and two-mode squeezed states in the Fock basis. We then analyze a cyclically coupled $N$-mode system governed by $(a_i - \\alpha_i a_{i+1}^\\dagger)|\\psi\\rangle = 0$ with $a_{N+1} \\equiv a_1$. Although the recurrence structure restricts solutions to equal-photon-number states, we prove that for $N>2$ no such state satisfies the full set of conditions. This establishes a sharp no-go result for multipartite squeezed states under cyclic annihilation constraints, underscoring a fundamental structural limitation beyond pairwise squeezing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-13T19:02:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniqueness",
      "recurrence structure restricts solutions",
      "sharp no-go result",
      "cyclic annihilation constraints",
      "fundamental structural limitation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}