Integrable spin-boson interaction in the Tavis-Cummings model from a generic boundary twist

  • L. AmicoEmail author
  • K. Hikami
Mathematical Physics


We construct models describing interaction between a spin s and a single bosonic mode using a quantum inverse scattering procedure. The boundary conditions are generically twisted by generic matrices with both diagonal and off-diagonal entries. The exact solution is obtained by mapping the transfer matrix of the spin-boson system to an auxiliary problem of a spin-j coupled to the spin-s with general twist of the boundary condition. The corresponding auxiliary transfer matrix is diagonalized by a variation of the method of Q-matrices of Baxter. The exact solution of our problem is obtained applying certain large-j limit to su(2)j, transforming it into the bosonic algebra.


Spectroscopy Boundary Condition Neural Network Exact Solution Complex System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom-photon interactions (Wiley, New York, 1992) Google Scholar
  2. D. Kleppner, Phys. Rev. Lett. 47, 233 (1981) ADSGoogle Scholar
  3. G. Rempe, F. Schmidt-Kaler, H. Walther, Phys. Rev. Lett. 64, 2783 (1990) ADSGoogle Scholar
  4. E.T. Jaynes, F.W. Cummings, Proc. IEEE 51, 89 (1963) CrossRefGoogle Scholar
  5. J.I. Cirac et al., Phys. Rev. A 46, 2668 (1992) ADSGoogle Scholar
  6. R.J. Hughes et al., Fortsch. Phys. 46, 329 (1998) ADSGoogle Scholar
  7. S. Datta, B. Das, Appl. Phys. Lett. 56, 665 (1990); L.W. Molenkamp, G. Schmidt, G.E.W. Bauer, Phys. Rev. B 64, 121202 (2001) ADSGoogle Scholar
  8. M. Tavis, F.W. Cummings, Phys. Rev. 170, 379 (1969); M. Tavis, F.W. Cummings, Phys. Rev. 188, 692 (1969)ADSGoogle Scholar
  9. K. Hepp, E. Lieb, Ann. Phys. 76, 360 (1973) ADSMathSciNetGoogle Scholar
  10. T. Brandes, N. Lambert, Phys. Rev. B 67, 125323 (2003) ADSMathSciNetGoogle Scholar
  11. M. Paternostro et al., Phys. Rev. B 69, 214502 (2004); F. Plastina, G. Falci, Phys. Rev. B 67, 224514 (2003) ADSGoogle Scholar
  12. C. Emary, T. Brandes, Phys. Rev. E 67, 066203 (2003) ADSMathSciNetGoogle Scholar
  13. N. Lambert, C. Emary, T. Brandes, Phys. Rev. Lett. 92, 073602 (2004) ADSGoogle Scholar
  14. V.E. Korepin, N.M. Bogoliubov, A.G. Izergin, Quantum Inverse Scattering Method and Correlation Functions (Cambridge Univ. Press, Cambridge, 1993) Google Scholar
  15. E. Sklyanin, J. Phys. A 21, 2375 (1988) ADSMathSciNetGoogle Scholar
  16. B. Jurco, J. Math. Phys. 30, 1739 (1989) zbMATHADSMathSciNetGoogle Scholar
  17. N.M. Bogoliubov, R.K. Bullough, J. Timonen, J. Phys. A 29, 6305 (1996) zbMATHADSMathSciNetGoogle Scholar
  18. A. Rybin et al., J. Phys. A 31, 4705 (1998)ADSMathSciNetGoogle Scholar
  19. A. Kundu, Phys. Rev. Lett. 82, 3936 (1999); A. Kundu, quant-ph/0307102 zbMATHADSMathSciNetGoogle Scholar
  20. A. Di Lorenzo et al., Nucl. Phys. B 644, 409 (2002)Google Scholar
  21. R.J. Baxter, Exactly solved models in statistical mechanics (Academic Press, London, 1982) Google Scholar
  22. E.I. Rashba, Sov. Phys. Solid State 2, 1109 (1960) Google Scholar
  23. C. Emary, T. Brandes, Phys. Rev. A 69, 053804 (2004) ADSMathSciNetGoogle Scholar
  24. R. Gilmore, Lie groups, Lie algebras, and some of their applications (Wiley, New York, 1974) Google Scholar
  25. C.M. Yung, M.T. Batchelor, Nucl. Phys. B 446, 461 (1995) zbMATHADSMathSciNetGoogle Scholar
  26. D.M. Meekhof et al., Phys. Rev. Lett. 76, 1796 (1996) ADSGoogle Scholar
  27. C. D’Helon, G.J. Milburn, quant-ph/9705014 Google Scholar
  28. G.A.P. Ribeiro, M.J. Martins, W. Galleas, Nucl. Phys. B 675, 567 (2003) zbMATHADSMathSciNetGoogle Scholar
  29. Ultimately, this results to preserve the integrability of the Hamiltonian. It can be proved that off-diagonal are equivalent to diagonal twists for SU(N) models, ancestors of the spin-boson models (see also W. Galleas, M.J. Martins, nlin.SI/0407027) Google Scholar
  30. J. Schliemann, J.C. Egues, D. Loss, Phys. Rev. B 67, 085302 (2003) ADSGoogle Scholar
  31. M. Tinkham, Introduction to superconductivity (Mc Graw-Hill, New York, 1996) Google Scholar
  32. I. Chiorescu et al., Nature 431, 159 (2004); P. Orlando et al., Science 285, 1036 (1999) Google Scholar
  33. K.V.R.M. Murali et al., cond-mat/0311471 Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Authors and Affiliations

  1. 1.Dipartimento di Metodologie Fisiche e Chimiche (DMFCI)Universitá di CataniaUnitá di CataniaItaly
  2. 2.Department of PhysicsGraduate School of Science, University of TokyoTokyoJapan

Personalised recommendations