Aspects of the dynamics of a two-level atom dispersively coupled to a damped and driven field mode

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 69, Issue 6, 2004, Pages

  Peixoto De Faria, J G ^a,c   Nemes, M C ^b  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

^c DEPARTAMENTO DE CIÊNCIAS BIOLÓGICAS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; ATOMS; DAMPING; EIGENVALUES AND EIGENFUNCTIONS; ELECTRODYNAMICS; ENTROPY; PHASE SHIFT; STATISTICAL METHODS; SUPERCONDUCTIVITY;

DENSITY OPERATORS; DISSIPATIVE DYNAMICS; QUANTIFICATION; QUANTUM ELECTRODYNAMICS (QED);

QUANTUM THEORY;

EID: 4043118424     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.69.063812     Document Type: Article

References (37)

1. For a review on quantum information and quantum computation, see C. H. Bennet and D. P. DiVincenzo, Nature (London) 404, 247 (2000); A. Ekert and R. Jozsa, Rev. Mod. Phys. 68, 733 (1996); A. Galindo and M. A. Martín-Delgado, ibid. 74, 347 (2002); M. Keyl, Phys. Rep. 369, 431 (2002); See also M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000); J. Preskill, lecture notes, www.theory.caltech.edu/~preskill/ph229.
2. For a review on quantum information and quantum computation, see C. H. Bennet and D. P. DiVincenzo, Nature (London) 404, 247 (2000); A. Ekert and R. Jozsa, Rev. Mod. Phys. 68, 733 (1996); A. Galindo and M. A. Martín-Delgado, ibid. 74, 347 (2002); M. Keyl, Phys. Rep. 369, 431 (2002); See also M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000); J. Preskill, lecture notes, www.theory.caltech.edu/~preskill/ph229.
3. For a review on quantum information and quantum computation, see C. H. Bennet and D. P. DiVincenzo, Nature (London) 404, 247 (2000); A. Ekert and R. Jozsa, Rev. Mod. Phys. 68, 733 (1996); A. Galindo and M. A. Martín-Delgado, ibid. 74, 347 (2002); M. Keyl, Phys. Rep. 369, 431 (2002); See also M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000); J. Preskill, lecture notes, www.theory.caltech.edu/~preskill/ph229.
4. For a review on quantum information and quantum computation, see C. H. Bennet and D. P. DiVincenzo, Nature (London) 404, 247 (2000); A. Ekert and R. Jozsa, Rev. Mod. Phys. 68, 733 (1996); A. Galindo and M. A. Martín-Delgado, ibid. 74, 347 (2002); M. Keyl, Phys. Rep. 369, 431 (2002); See also M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000); J. Preskill, lecture notes, www.theory.caltech.edu/~preskill/ph229.
5. For a review on quantum information and quantum computation, see C. H. Bennet and D. P. DiVincenzo, Nature (London) 404, 247 (2000); A. Ekert and R. Jozsa, Rev. Mod. Phys. 68, 733 (1996); A. Galindo and M. A. Martín-Delgado, ibid. 74, 347 (2002); M. Keyl, Phys. Rep. 369, 431 (2002); See also M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000); J. Preskill, lecture notes, www.theory.caltech.edu/~preskill/ph229.
6. For a review on quantum information and quantum computation, see C. H. Bennet and D. P. DiVincenzo, Nature (London) 404, 247 (2000); A. Ekert and R. Jozsa, Rev. Mod. Phys. 68, 733 (1996); A. Galindo and M. A. Martín-Delgado, ibid. 74, 347 (2002); M. Keyl, Phys. Rep. 369, 431 (2002); See also M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000); J. Preskill, lecture notes, www.theory.caltech.edu/~preskill/ph229.
7. There are several proposals for experimental realizations of quantum computing (see works in [1], and references therein). We emphasize some of them: J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995); C. Monroe et al., ibid. 75, 4714 (1995); S. Lloyd, Science 261, 1569 (1993); J. A. Jones and M. Mosca, J. Chem. Phys. 109, 1648 (1998); T. Calarco et al., Phys. Rev. A 61, 022304 (2000); Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995); X. Maître et al., ibid. 79, 769 (1997); P. Domokos, J. M. Raimond, M. Brune, and S. Haroche, Phys. Rev. A 52, 3554 (1995).
8. There are several proposals for experimental realizations of quantum computing (see works in [1], and references therein). We emphasize some of them: J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995); C. Monroe et al., ibid. 75, 4714 (1995); S. Lloyd, Science 261, 1569 (1993); J. A. Jones and M. Mosca, J. Chem. Phys. 109, 1648 (1998); T. Calarco et al., Phys. Rev. A 61, 022304 (2000); Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995); X. Maître et al., ibid. 79, 769 (1997); P. Domokos, J. M. Raimond, M. Brune, and S. Haroche, Phys. Rev. A 52, 3554 (1995).
9. There are several proposals for experimental realizations of quantum computing (see works in [1], and references therein). We emphasize some of them: J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995); C. Monroe et al., ibid. 75, 4714 (1995); S. Lloyd, Science 261, 1569 (1993); J. A. Jones and M. Mosca, J. Chem. Phys. 109, 1648 (1998); T. Calarco et al., Phys. Rev. A 61, 022304 (2000); Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995); X. Maître et al., ibid. 79, 769 (1997); P. Domokos, J. M. Raimond, M. Brune, and S. Haroche, Phys. Rev. A 52, 3554 (1995).
10. There are several proposals for experimental realizations of quantum computing (see works in [1], and references therein). We emphasize some of them: J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995); C. Monroe et al., ibid. 75, 4714 (1995); S. Lloyd, Science 261, 1569 (1993); J. A. Jones and M. Mosca, J. Chem. Phys. 109, 1648 (1998); T. Calarco et al., Phys. Rev. A 61, 022304 (2000); Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995); X. Maître et al., ibid. 79, 769 (1997); P. Domokos, J. M. Raimond, M. Brune, and S. Haroche, Phys. Rev. A 52, 3554 (1995).
11. There are several proposals for experimental realizations of quantum computing (see works in [1], and references therein). We emphasize some of them: J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995); C. Monroe et al., ibid. 75, 4714 (1995); S. Lloyd, Science 261, 1569 (1993); J. A. Jones and M. Mosca, J. Chem. Phys. 109, 1648 (1998); T. Calarco et al., Phys. Rev. A 61, 022304 (2000); Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995); X. Maître et al., ibid. 79, 769 (1997); P. Domokos, J. M. Raimond, M. Brune, and S. Haroche, Phys. Rev. A 52, 3554 (1995).
12. There are several proposals for experimental realizations of quantum computing (see works in [1], and references therein). We emphasize some of them: J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995); C. Monroe et al., ibid. 75, 4714 (1995); S. Lloyd, Science 261, 1569 (1993); J. A. Jones and M. Mosca, J. Chem. Phys. 109, 1648 (1998); T. Calarco et al., Phys. Rev. A 61, 022304 (2000); Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995); X. Maître et al., ibid. 79, 769 (1997); P. Domokos, J. M. Raimond, M. Brune, and S. Haroche, Phys. Rev. A 52, 3554 (1995).
13. There are several proposals for experimental realizations of quantum computing (see works in [1], and references therein). We emphasize some of them: J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995); C. Monroe et al., ibid. 75, 4714 (1995); S. Lloyd, Science 261, 1569 (1993); J. A. Jones and M. Mosca, J. Chem. Phys. 109, 1648 (1998); T. Calarco et al., Phys. Rev. A 61, 022304 (2000); Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995); X. Maître et al., ibid. 79, 769 (1997); P. Domokos, J. M. Raimond, M. Brune, and S. Haroche, Phys. Rev. A 52, 3554 (1995).
14. There are several proposals for experimental realizations of quantum computing (see works in [1], and references therein). We emphasize some of them: J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995); C. Monroe et al., ibid. 75, 4714 (1995); S. Lloyd, Science 261, 1569 (1993); J. A. Jones and M. Mosca, J. Chem. Phys. 109, 1648 (1998); T. Calarco et al., Phys. Rev. A 61, 022304 (2000); Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995); X. Maître et al., ibid. 79, 769 (1997); P. Domokos, J. M. Raimond, M. Brune, and S. Haroche, Phys. Rev. A 52, 3554 (1995).
15. D. Meschede, Phys. Rep. 211, 201 (1992);
16. P. Meystre, ibid. 219, 243 (1992);
17. H. Walther, ibid. 219, 263 (1992).
18. E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963); D. F. Walls and G. J. Milburn, Quantum Optics (Springer, Berlin, 1994); M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997). Studies on JCM with dissipation appear in J. Eiselt and H. Risken, Phys. Rev. A 43, 346 (1991); H.-J. Briegel and B.-G. Englert, ibid. 47, 3311 (1993); A. B. Klimov, S. M. Chumakov, J. C. Retamal, and C. Saavedra, Phys. Lett. A 211, 143 (1996).
19. E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963); D. F. Walls and G. J. Milburn, Quantum Optics (Springer, Berlin, 1994); M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997). Studies on JCM with dissipation appear in J. Eiselt and H. Risken, Phys. Rev. A 43, 346 (1991); H.-J. Briegel and B.-G. Englert, ibid. 47, 3311 (1993); A. B. Klimov, S. M. Chumakov, J. C. Retamal, and C. Saavedra, Phys. Lett. A 211, 143 (1996).
20. E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963); D. F. Walls and G. J. Milburn, Quantum Optics (Springer, Berlin, 1994); M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997). Studies on JCM with dissipation appear in J. Eiselt and H. Risken, Phys. Rev. A 43, 346 (1991); H.-J. Briegel and B.-G. Englert, ibid. 47, 3311 (1993); A. B. Klimov, S. M. Chumakov, J. C. Retamal, and C. Saavedra, Phys. Lett. A 211, 143 (1996).
21. E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963); D. F. Walls and G. J. Milburn, Quantum Optics (Springer, Berlin, 1994); M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997). Studies on JCM with dissipation appear in J. Eiselt and H. Risken, Phys. Rev. A 43, 346 (1991); H.-J. Briegel and B.-G. Englert, ibid. 47, 3311 (1993); A. B. Klimov, S. M. Chumakov, J. C. Retamal, and C. Saavedra, Phys. Lett. A 211, 143 (1996).
22. E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963); D. F. Walls and G. J. Milburn, Quantum Optics (Springer, Berlin, 1994); M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997). Studies on JCM with dissipation appear in J. Eiselt and H. Risken, Phys. Rev. A 43, 346 (1991); H.-J. Briegel and B.-G. Englert, ibid. 47, 3311 (1993); A. B. Klimov, S. M. Chumakov, J. C. Retamal, and C. Saavedra, Phys. Lett. A 211, 143 (1996).
23. E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963); D. F. Walls and G. J. Milburn, Quantum Optics (Springer, Berlin, 1994); M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997). Studies on JCM with dissipation appear in J. Eiselt and H. Risken, Phys. Rev. A 43, 346 (1991); H.-J. Briegel and B.-G. Englert, ibid. 47, 3311 (1993); A. B. Klimov, S. M. Chumakov, J. C. Retamal, and C. Saavedra, Phys. Lett. A 211, 143 (1996).
24. M. C. de Oliveira, M. H. Y. Moussa, and S. S. Mizrahi, Phys. Rev. A 61, 063809 (2000).
25. M. Brune, S. Haroche, J. M. Raimond, L. Davidovich, and N. Zagury, Phys. Rev. A 45, 5193 (1992); L. Davidovich, M. Brune, J. M. Raimond, and S. Haroche, ibid. 53, 1295 (1996).
26. M. Brune, S. Haroche, J. M. Raimond, L. Davidovich, and N. Zagury, Phys. Rev. A 45, 5193 (1992); L. Davidovich, M. Brune, J. M. Raimond, and S. Haroche, ibid. 53, 1295 (1996).
27. C. C. Gerry, Phys. Rev. A 65, 063801 (2002).
28. S. Hill and W. K. Wootters, Phys. Rev. Lett. 78, 5022 (1997); W. Wootters, ibid. 80, 2245 (1998).
29. S. Hill and W. K. Wootters, Phys. Rev. Lett. 78, 5022 (1997); W. Wootters, ibid. 80, 2245 (1998).
30. Note added: Recently it has come to our attention that the concurrence was employed to measure the degree of entanglement of a particular bipartite system undergoing nonunitary evolution in M. Jakob, Y. Abranyos, and J. A. Bergou, Phys. Rev. A 66, 022113 (2002).
31. A. Perelomov, Generalized Coherent States and their Applications (Springer, Berlin, 1986).
32. J. G. Peixoto de Faria and M. C. Nemes, Phys. Rev. A 59, 3918 (1999).
33. W. H. Zurek, S. Habib, and J. P. Paz, Phys. Rev. Lett. 70, 1187 (1993);
34. J. I. Kim, M. C. Nemes, A. F. R. de Toledo Piza, and H. E. Borges, ibid. 77, 207 (1996).
35. T. Yu and J. H. Eberly, Phys. Rev. B 66, 193306 (2002); T. Yu and J. H. Eberly, ibid. 68, 165322 (2003). In these works, the time scales of coherence loss and disentanglement are compared. The authors concluded that, for a system composed by two qubits coupled to an environment, the characteristic time of disentanglement is generally shorter than the corresponding decoherence time of the global system.
36. T. Yu and J. H. Eberly, Phys. Rev. B 66, 193306 (2002); T. Yu and J. H. Eberly, ibid. 68, 165322 (2003). In these works, the time scales of coherence loss and disentanglement are compared. The authors concluded that, for a system composed by two qubits coupled to an environment, the characteristic time of disentanglement is generally shorter than the corresponding decoherence time of the global system.
37. R. F. Werner, Phys. Rev. A 40, 4277 (1989).