{
  "annotation_id": "8832d267-aeee-4a09-96a2-3c5f11517c52",
  "date_created": "2026-03-02T18:02:06.456000Z",
  "date_modified": "2026-03-02T18:02:06.456000Z",
  "file_hash": "61e95e3c129b1a0b51b14fa84dfe2d01cd40b28cf0fc6858cb5ecdb85238d98c",
  "private": false,
  "record": {
    "abstract": "We study the problem of optimal control of dissipative quantum dynamics.\nAlthough under most circumstances dissipation leads to an increase in entropy\n(or a decrease in purity) of the system, there is an important class of\nproblems for which dissipation with external control can decrease the entropy\n(or increase the purity) of the system. An important example is laser cooling.\nIn such systems, there is an interplay of the Hamiltonian part of the dynamics,\nwhich is controllable and the dissipative part of the dynamics, which is\nuncontrollable. The strategy is to control the Hamiltonian portion of the\nevolution in such a way that the dissipation causes the purity of the system to\nincrease rather than decrease. The goal of this paper is to find the strategy\nthat leads to maximal purity at the final time. Under the assumption that\nHamiltonian control is complete and arbitrarily fast, we provide a general\nframework by which to calculate optimal cooling strategies. These assumptions\nlead to a great simplification, in which the control problem can be\nreformulated in terms of the spectrum of eigenvalues of $\\rho$, rather than\n$\\rho$ itself. By combining this formulation with the Hamilton-Jacobi-Bellman\ntheorem we are able to obtain an equation for the globaly optimal cooling\nstrategy in terms of the spectrum of the density matrix. For the three-level\n$\\Lambda$ system, we provide a complete analytic solution for the optimal\ncooling strategy. For this system it is found that the optimal strategy does\nnot exploit system coherences and is a \u0027greedy\u0027 strategy, in which the purity\nis increased maximally at each instant.",
    "arxiv_id": "quant-ph/0402143",
    "authors": [
      "Shlomo E. Sklarz",
      "David J. Tannor",
      "Navin Khaneja"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.69.053408",
    "title": "Optimal Control of Quantum Dissipative Dynamics: Analytic solution for   cooling the three level $\\Lambda$ system",
    "url": "https://arxiv.org/abs/quant-ph/0402143"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d20a9af2-0753-419c-9aac-645c39ec6763",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}