dorsal/arxiv
View SchemaCreating quanta with "annihilation" operator
| Authors | S. S. Mizrahi, V. V. Dodonov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0207035 |
| URL | https://arxiv.org/abs/quant-ph/0207035 |
| DOI | 10.1088/0305-4470/35/41/315 |
| Journal | J. Phys. A, v.35, no.41, p.8847-8857 (2002) |
Abstract
An asymmetric nature of the boson `destruction' operator $\hat{a}$ and its `creation' partner $\hat{a}^{\dagger}$ is made apparent by applying them to a quantum state $|\psi>$ different from the Fock state $|n>$. We show that it is possible to {\em increase} (by many times or by any quantity) the mean number of quanta in the new `photon-subtracted' state $\hat{a}|\psi >$. Moreover, for certain `hyper-Poissonian' states $|\psi>$ the mean number of quanta in the (normalized) state $\hat{a}|\psi>$ can be much greater than in the `photon-added' state $\hat{a}^{\dagger}|\psi > $. The explanation of this `paradox' is given and some examples elucidating the meaning of Mandel's $q$-parameter and the exponential phase operators are considered.
{
"annotation_id": "fbfeed1a-3b09-4a3d-99c2-f05c5d6a4df8",
"date_created": "2026-03-02T18:01:52.305000Z",
"date_modified": "2026-03-02T18:01:52.305000Z",
"file_hash": "73de9935dea0a2c0706dcc3fb8e56f99d58392f611e5f7a13d858e7fe8a9c34c",
"private": false,
"record": {
"abstract": "An asymmetric nature of the boson `destruction\u0027 operator $\\hat{a}$ and its\n`creation\u0027 partner $\\hat{a}^{\\dagger}$ is made apparent by applying them to a\nquantum state $|\\psi\u003e$ different from the Fock state $|n\u003e$. We show that it is\npossible to {\\em increase} (by many times or by any quantity) the mean number\nof quanta in the new `photon-subtracted\u0027 state $\\hat{a}|\\psi \u003e$. Moreover, for\ncertain `hyper-Poissonian\u0027 states $|\\psi\u003e$ the mean number of quanta in the\n(normalized) state $\\hat{a}|\\psi\u003e$ can be much greater than in the\n`photon-added\u0027 state $\\hat{a}^{\\dagger}|\\psi \u003e $. The explanation of this\n`paradox\u0027 is given and some examples elucidating the meaning of Mandel\u0027s\n$q$-parameter and the exponential phase operators are considered.",
"arxiv_id": "quant-ph/0207035",
"authors": [
"S. S. Mizrahi",
"V. V. Dodonov"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/35/41/315",
"journal_ref": "J. Phys. A, v.35, no.41, p.8847-8857 (2002)",
"title": "Creating quanta with \"annihilation\" operator",
"url": "https://arxiv.org/abs/quant-ph/0207035"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "13805118-224c-42d4-9215-843c21943678",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}