{
  "annotation_id": "bc7b1adc-cfb0-4cc9-9bc8-032d5a11a140",
  "date_created": "2026-03-02T18:01:59.813000Z",
  "date_modified": "2026-03-02T18:01:59.813000Z",
  "file_hash": "c6376087a85a82c13ed6879dc7fc87b4d40af5201d65b7f39c953a2b0ade68e2",
  "private": false,
  "record": {
    "abstract": "We introduce a formalism of nonlinear canonical transformations for general\nsystems of multiphoton quantum optics. For single-mode systems the\ntransformations depend on a tunable free parameter, the homodyne local\noscillator angle; for n-mode systems they depend on n heterodyne mixing angles.\nThe canonical formalism realizes nontrivial mixings of pairs of conjugate\nquadratures of the electromagnetic field in terms of homodyne variables for\nsingle-mode systems; and in terms of heterodyne variables for multimode\nsystems. In the first instance the transformations yield nonquadratic model\nHamiltonians of degenerate multiphoton processes and define a class of non\nGaussian, nonclassical multiphoton states that exhibit properties of coherence\nand squeezing. We show that such homodyne multiphoton squeezed states are\ngenerated by unitary operators with a nonlinear time evolution that realizes\nthe homodyne mixing of a pair of conjugate quadratures. Tuning of the local\noscillator angle allows to vary at will the statistical properties of such\nstates. We discuss the relevance of the formalism for the study of degenerate\n(up-)down-conversion processes. In a companion paper, ``Structure of\nmultiphoton quantum optics. II. Bipartite systems, physical processes, and\nheterodyne squeezed states\u0027\u0027, we provide the extension of the nonlinear\ncanonical formalism to multimode systems, we introduce the associated\nheterodyne multiphoton squeezed states, and we discuss their possible\nexperimental realization.",
    "arxiv_id": "quant-ph/0308081",
    "authors": [
      "Fabio Dell\u0027Anno",
      "Silvio De Siena",
      "Fabrizio Illuminati"
    ],
    "categories": [
      "quant-ph",
      "cond-mat",
      "hep-th",
      "math-ph",
      "math.MP",
      "physics.optics"
    ],
    "doi": "10.1103/PhysRevA.69.033812",
    "journal_ref": "Phys.Rev. A69 (2004) 033812",
    "title": "Structure of multiphoton quantum optics. I. Canonical formalism and   homodyne squeezed states",
    "url": "https://arxiv.org/abs/quant-ph/0308081"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a2a516d6-e552-4040-b065-cd806a6de358",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}