Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 2 (2006), 069, 9 pages      nlin.SI/0610031      https://doi.org/10.3842/SIGMA.2006.069
Contribution to the Vadim Kuznetsov Memorial Issue

Integrable Models of Interaction of Matter with Radiation

Vladimir I. Inozemtsev a and Natalia G. Inozemtseva b
a) Laboratory of Theoretical Physics, JINR, Dubna, Russia
b) Moscow Technical University, Dubna Branch, Russia

Received July 18, 2006, in final form September 19, 2006; Published online October 13, 2006

Abstract
The simplified models of interaction of charged matter with resonance modes of radiation generalizing the well-known Jaynes-Cummings and Dicke models are considered. It is found that these new models are integrable for arbitrary numbers of dipole sources and resonance modes of the radiation field. The problem of explicit diagonalisation of corresponding Hamiltonians is discussed.

Key words: integrability; radiation; Gaudin models.

pdf (201 kb)   ps (158 kb)   tex (11 kb)

References

  1. Dicke R., Coherence in spontaneous radiation processes, Phys. Rev., 1953, V.93, 99-108.
  2. Cummings F.W., Stimulated emission of radiation in a single mode, Phys. Rev. A, 1965, V.140, 1051-1062.
  3. Heitler W., The quantum theory of radiation, New York, Oxford, 1954.
  4. Allen L., Eberly J., Optical resonance and two-level atoms, New York, Wiley-Interscience Publication, 1975.
  5. Li X., Bei N., A generalized three-level Jaynes-Cummings model, Phys. Lett. A, 1984, V.101, 169-175.
  6. Abdel-Hafez A., Obada A., Ahmad M., N-level atom and N-1 modes: statistical aspects and interaction with squeezed light, Phys. Rev. A, 1987, V.35, 1634-1647.
  7. Gaudin M., Diagonalisation d'une classe d'hamiltoniens de spin, J. de Physique, 1976, V.37, 1087-1098.
  8. Gaudin M., La fonction d'onde de Bethe, Paris, Masson, 1983.
  9. Jurco B., On quantum integrable models related to nonlinear quantum optics. An algebraic Bethe ansatz approach, J. Math. Phys., 1989, V.30, 1739-1744.
  10. Dukelsky J., Dussel G.G., Esebbag C., Pittel S., Exactly solvable models for atom-molecule Hamiltonians, Phys. Rev. Lett., 2004, V.93, 050403, 4 pages, cond-mat/0406190.
  11. Kundu A., Integrable multi-atom matter-radiation models without rotating-wave approximation, Phys. Lett. A, 2006, V.350, 210-213, cond-mat/0411166.
  12. Kuznetsov V.B., Separation of variables for the Dn-type periodic Toda lattice, J. Phys. A: Math. Gen., 1997, V.30, 2127-2138, solv-int/9701009.

Previous article   Next article   Contents of Volume 2 (2006)