{
  "id": "cond-mat/0310425",
  "version": "v3",
  "published": "2003-10-17T19:18:50.000Z",
  "updated": "2003-12-12T04:40:53.000Z",
  "title": "Hamiltonian for coupled flux qubits",
  "authors": [
    "Alec Maassen van den Brink"
  ],
  "comment": "REVTeX4, 16pp., one figure. N.B.: \"Alec\" is my first, and \"Maassen van den Brink\" my family name. Informal note. v2: completely rewritten; correction of final result and major expansion. v3: added numerical verification plus a discussion of Ref. [2]",
  "journal": "Phys. Rev. B_71_, 064503 (2005)",
  "doi": "10.1103/PhysRevB.71.064503",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.supr-con"
  ],
  "abstract": "An effective Hamiltonian is derived for two coupled three-Josephson-junction (3JJ) qubits. This is not quite trivial, for the customary \"free\" 3JJ Hamiltonian is written in the limit of zero inductance L. Neglecting the self-flux is already dubious for one qubit when it comes to readout, and becomes untenable when discussing inductive coupling. First, inductance effects are analyzed for a single qubit. For small L, the self-flux is a \"fast variable\" which can be eliminated adiabatically. However, the commonly used junction phases are_not_ appropriate \"slow variables\", and instead one introduces degrees of freedom which are decoupled from the loop current to leading order. In the quantum case, the zero-point fluctuations (LC oscillations) in the loop current diverge as L->0. Fortunately, they merely renormalize the Josephson couplings of the effective (two-phase) theory. In the coupled case, the strong zero-point fluctuations render the full (six-phase) wave function significantly entangled in leading order. However, in going to the four-phase theory, this uncontrollable entanglement is integrated out completely, leaving a computationally usable mutual-inductance term of the expected form as the effective interaction.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-12-12T04:40:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coupled flux qubits",
      "strong zero-point fluctuations render",
      "loop current diverge",
      "leading order",
      "3jj hamiltonian"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. B"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}